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OPINION CALLAHAN, Circuit Judge: In December 1988, Michael Apelt (“Apelt”) and his brother, Rudi, murdered Apelt’s wife of less than two months in order to collect on her life insurance policy. The brothers were tried separately, convicted of first degree murder, and given death sentences. Having obtained no relief in the Arizona courts, Apelt filed a habeas petition in the United States District Court for the District of Arizona. After a stay of proceedings to allow Apelt to advance a claim in the state courts based on the Supreme Court’s decision in Atkins v. Virginia, 536 U.S. 304, 122 S.Ct. 2242, 153 L.Ed.2d 335 (2002), the district court granted the writ on one issue, ineffective assistance of counsel (“LAC”) at sentencing, and denied relief on all of Apelt’s other claims. In No. 15-99013, the state of Arizona appeals, challenging the district court’s jurisdiction to reach the merits of Apelt’s IAC claim, as well as its grant of the writ. In No. 15-99015, Apelt appeals two claims certified by the district court: the denial in state court of funding to investigate mitigating evidence, and the determination that Apelt had failed to show that he was intellectually disabled under Atkins. In addition, Apelt raises two issues that were not certified by the district court: whether the Arizona Supreme Court applied an unconstitutional causal nexus requirement in reviewing Apelt’s sentence; and whether trial counsel was ineffective in failing to challenge Apelt’s competency to be tried and sentenced. Apelt’s habeas petition is subject to review under the Antiterrorism and Effective Death Penalty Act of 1996 (“AED-PA”), 28 U.S.C. § 2254(d). See Mann v. Ryan, 828 F.3d 1143, 1151 (9th Cir. 2016) (en banc). We first determine that federal court review was not procedurally barred. We then vacate the district court’s grant of relief because we cannot find the Arizona Supreme Court’s determination that Apelt’s counsel’s deficient performance at sentencing was not prejudicial to be clearly unreasonable. See Davis v. Ayala, — U.S. —, 135 S.Ct. 2187, 2199, 192 L.Ed.2d 323 (2015); Cullen v. Pinholster, 563 U.S. 170, 189, 131 S.Ct. 1388, 179 L.Ed.2d 557 (2011). We affirm the district court’s denial of relief on Apelt’s claims of inadequate funding to investigate mitigating evidence, and mental disability pursuant to Atkins, 536 U.S. 304, 122 S.Ct. 2242. We grant the certificate of appealability for Apelt’s claims of an application of an unconstitutional causal nexus standard by the Arizona Supreme Court and for ineffective assistance of counsel in failing to challenge Apelt’s competency to stand trial, and we deny those claims on the merits. I. A. The Facts Michael .Apelt, the youngest of seven siblings, was born in August 1963 in Germany. He came to the United States in the late summer of 1988. The underlying facts leading to Apelt’s conviction were fairly and fully set forth in the Arizona Supreme Court’s opinion, State v. Apelt, 176 Ariz. 349, 861 P.2d 634 (Ariz. 1993), as follows: In August 1988, the defendant, his brother Rudi Apelt, Rudi’s wife Susanne, and Michael’s ex-girlfriend Anke Dorn, all German citizens, traveled to San Diego, California. The defendant and his brother met two women in a nightclub. Cheryl Rubenstein and Trudy Waters lived in Phoenix and were in San Diego to cater a party for Cheryl’s brother. They spent the evening chatting with the Apelts. Because Michael’s English was not very good and Rudi’s was worse, communication was difficult until they found an interpreter among the other patrons of the bar. The Apelts first claimed to be wind surfing board manufacturers, then Mercedes importers. Rudi denied being married. Before leaving, the women gave the Apelts their addresses and phone numbers. Approximately two weeks later the Apelts flew to Phoenix. Cheryl picked them up at the airport and took them to a hotel in Mesa. They soon moved to a nearby Motel 6, but pretended to be staying at the Holiday Inn, a more expensive hotel nearby. After a couple of weeks, they flew back to San Diego, picked up Anke Dorn and returned to Phoenix. Susanne, Rudi’s wife, returned to Germany. Over the next month the brothers met and “conned” a series of women, spinning tales of wealth and intrigue. The immediate goal of at least some of their ruses was to get money and other assistance. They were looking for a woman to marry Michael. On October 6, the Apelts met Annette Clay at Bobby McGee’s, a bar and restaurant. Rudi claimed to be an international banker. Annette gave him her phone number, and Rudi called her on Saturday. She met the Apelts at Bobby McGee’s that evening, and introduced them to her friends, Cindy and Kathy Monkman. Michael immediately focused on Cindy and spent the evening dancing and talking with her. He said several times “you’re the woman I want to marry” and “me you marry.” He and Rudi claimed to be computer and banking experts. During the next week Annette and Cindy saw the Apelts several times. When Cindy noticed that after the Apelts visited her apartment she was missing over $100 in cash, she and Annette began to get suspicious. They questioned whether the Apelts were actually staying at the Holiday Inn and, by calling several hotels in the area, discovered that the Apelts were registered at the Motel 6. When confronted with this information, the Apelts insisted that there was some mistake. That evening, after dropping the Apelts at the Holiday Inn, the women located their room at the Motel 6 and discovered Anke Dorn. The next day, the Apelts were furious and claimed that the women’s snooping destroyed their “high security clearance” and cost them their jobs and their work visas. They explained that Anke was a family friend whose husband was in the hospital. The women were apologetic and suggested various ways they could help the Apelts get their jobs back or find new jobs, but the Apelts refused these suggestions. Finally, in frustration, Annette exclaimed “what do you want us to do, marry you?” The Apelts replied, “yes.” Rudi moved into Annette’s apartment and Michael moved into Cindy’s. Annette discussed with Rudi the possibility of a sham marriage so that he could work in the United States, but Rudi insisted that he loved her and that if they married it would be forever. He also insisted that they keep the marriage secret. Rudi had been staying with Annette less -than a week when Annette discovered that the story regarding Anke was a lie. Annette asked Rudi to leave and did not see him again. Rudi and Anke moved into a motel. Thereafter, Michael told Annette several times that Rudi had returned to Germany. Cindy also believed that Rudi and Anke had left the country. On October 28, 1988, Cindy and Michael were married in Las Vegas. They did not tell anyone about the marriage. On November 7, at Michael’s suggestion, they consulted Doug Ramsey about a million dollar life insurance policy. Cindy believed Michael was wealthy and that purchasing large insurance policies was a customary investment practice for couples ,in Germany. Ramsey informed them that they could not get such a large policy but that they might qualify for a, $400,000 policy, They filled out an application, and Cindy wrote a check for the first month’s premium. Around this time, and continuing up to the time of the murder, the Apelts and Anke began a series of shopping sprees. They looked at expensive Piaget and Rolex watches, at one time contracting to buy three for a total price of approximately $130,000. They looked at expensive boats and cars, arranging to buy two Jaguars for $144,000 and two Toyota Supras for about $66,000. Their pattern was to fill out a purchase contract, make a nominal down-payment with assurances that they would pay cash upon receiving money from sources in Germany, and then never return. They drove to the stores and car dealers in Cindy’s Volkswagen. During one of the first shopping trips, Michael told Anke that if Cindy died an unnatural death, he would be rich. By this time they were without funds. Michael paid most of Rudi’s and Anke’s expenses with Cindy’s money, even though Cindy’s, income from her two part-time jobs- was very modest. She withdrew over $4,000 from an account from October through December 1988. On November 25, Ramsey informed Michael and Cindy that they could only get a $100,000 life insurance policy. They executed a change form and, on November 30, applied for a $300,000 policy from another company. Early in December, Rudi and Anke reserved a rental car for December 9, specifically requesting one with a large trunk. Around this time, Ramsey informed Cindy that the second insurance company would not approve their application for a $300,000 policy until it had more background and financial information. Cindy provided the needed information, and Ramsey resubmitted the application. In,the interim, Rudi cancelled the car reservation., On December 22, 1988, Ramsey informed Cindy and Michael that the $300,000 policy was approved and would be effective after Cindy gave him a check- for the premium. He also delivered the $100,000 policy. On the morning of December 23, Cindy and Michael took the Volkswagen in for some repairs and rented a Subaru. Cindy was busy getting ready to leave the next day for Illinois with her sister Kathy. She made plans to meet her'friend Annette for dinner at 8:00 p.m. to exchange gifts. She also planned to bring along Maria, a young woman she had been counseling. The Apelts also were busy. Michael took Rudi and Anke to a rental agency where they rented the car .with the large trunk that they had originally- reserved for December 9. Late in the afternoon, Michael returned to Rudi’s and Anke’s motel room. Michael told them that they could have a “lot of money” if he killed Cindy. They agreed to kill Cindy that evening. They made plans to meet in front of a German restaurant and proceed from there to the desert, where Cindy would be killed. Michael stated that he would bring Cindy and make sure she could not see where they were going. Cindy spoke with her father on the phone and then had a telephone conversation with Maria from 6:50 p.m. to 7:00 p.m. confirming that she and Michael would pick her up at 7:45 p.m. Maria heard Michael arriving in the background. Anke and Rudi drove their rented car to the German restaurant at around 7:00 p.m. and waited. Michael drove by in the Subaru approximately 15 minutes later, but Anke did not see Cindy in the car. Anke and Rudi followed Michael on Main street toward a desert area where they had earlier practiced shooting a crossbow. Rudi turned off the road when he reached this location, but Michael continued on. Rudi drove around in the desert for a while before spotting Michael’s car. He drove toward it, stopped some distance away, and got out of the car after ordering Anke to remain. He returned to the car after about five minutes and both he and Michael drove to the motel where Anke and Rudi were staying. The brothers showered and changed clothes. The Apelts and Anke met at Bobby McGee’s at 10:30 p.m. and asked for a table for four. After waiting a while, ostensibly for Michael’s wife, they ordered dinner. Michael and Rudi discussed their alibi. They had several drinks after dinner in the lounge area and then went to another nightclub. Michael arrived home at around 2:00 a.m. on December 24th after leaving Rudi and Anke at their motel. There were many calls on the answering machine from Annette, Kathy, and Maria, all of whom were worried because Cindy failed to show up for dinner or call Kathy as planned. Annette called again and spoke with Michael, who told her that Cindy left the house at around 7:00 p.m. after receiving a phone call from an angry man. He claimed that she said she had to meet someone and would meet Michael at Bobby McGee’s at 10:00 p.m. Annette came over to the apartment and called the police. She noticed that Cindy’s purse was still in the apartment. A police officer came and spoke with Michael and Annette. Michael told his story to the officer. Cindy’s body was found in the early afternoon of December 24th. She had been stabbed once in the lower chest and four times in the back. Her throat had been slashed so deeply that her head was nearly severed from her body. There were a tremendous number of bruises on her face and body. Police found a length of nylon cord and a blood soaked beach towel near her. There were many tire tracks in the area, although only two were clear enough to be of use. These were consistent with the tires on the car driven by Anke and Rudi. There was also a fairly good shoe impression near the body and a partial shoe print on the victim’s face as though the murderer had kicked or stepped on her head. These were later found to be consistent with a particular style of Reebok tennis shoes. Anke and Rudi were interviewed later that day and corroborated Michael’s story. They claimed they saw Cindy leaving the apartment at 7:00 p.m, as they were arriving, at which time she promised to meet them later at Bobby McGee’s. When questioned, Michael denied owning tennis shoes. Late on the evening of December 25, Rudi and Anke accompanied Michael as he drove the rented Subaru around the Salt River bottom. He drove erratically, making hard turns and slamming on the brakes in an effort to change the tread of the tires so they could not be linked to the murder scene. Two of the tires had to be replaced after the car was returned to the rental agency because they had flat spots caused by his driving. Michael borrowed some money, using the insurance policy as collateral, and the threesome flew to Illinois for Cindy’s funeral on December 31st. Although Michael cried at the funeral, Kathy saw him laughing and being jovial as he drove away after the service. That evening, Michael told Anke that Cindy had signed her own death warrant when she signed the insurance papers, but he regretted killing her. The Apelts and Anke returned to Phoenix on January 2nd. The next morning they flew to Los Angeles and paid a homeless man $20 to record the following message over the phone and onto Cindy’s answering machine: Hear what I have to talk. I have cut through the throat of your wife and I stabbed and more frequently in the stomach in the back with a knife. If I don’t get my stuff, your girlfriend is next and then your brother and last it is you. Do it now, if not, you see what happens. My eyes are everywhere. They then returned to Phoenix. Michael contacted Detective Davis, a police officer who spoke fluent German, and asked him to translate the message. Detective Davis listened to the message over the phone and instructed the Apelts to bring the tape to the police station the next day. The police had discovered the insurance policy and identified Michael as a possible suspect in Cindy’s murder. The bogus taped threat confirmed their suspicions and, fearing that Anke or the Apelts might leave the country, the police arranged to have a surveillance team watch them on the night of January 5. Eleven officers were deployed around the apartment complex at 5:30 p.m. Shortly after 8:30 p.m. one of the officers knocked on the Apelt’s [sic] door to make sure they were home. When Michael answered the door, the officer asked for a fictitious person and was told he had the wrong apartment. Immediately after this, Rudi and Michael called the police and reported that three tall black men had just appeared at their door and threatened them. The surveillance team was contacted, and they confirmed that this had not occurred. Detective Davis told the Apelts and Anke to come to the police station the next day to make composite sketches of their assailants. Accordingly, on January 6th, Anke and the Apelts went to the police station. The police spoke with Michael and Rudi individually and played along with them by preparing artist’s sketches. After leaving Anke in the lobby for a couple of hours, the police began interrogating her. They urged her to tell the truth. They threatened her with prosecution, promised her immunity in exchange for her confession, and showed her photographs of Cindy’s body in an appeal to her conscience. Anke confessed and the Apelts were arrested. On January 9th, the police searched Cindy’s apartment pursuant to a warrant. They seized a number of items, including the Apelts’ shoes, the crossbow, and business cards that led the police to some of the jewelry stores and car dealerships that the Apelts visited on their shopping sprees. They also seized two rolls of film that contained pictures of Michael wearing tennis shoes with tread matching the footprint and impression left at the murder scene. While the brothers were in jail, Anke wrote to Rudi several times. These letters, which contained various incriminating statements reflecting Anke’s version of the events surrounding the murder, were seized pursuant to two search warrants. Michael sent Rudi a note in German that, translated, stated in part: I have a guy who is getting out in two-four days and then we’ll be free in one to two weeks. It won’t matter if the police have anything or not. We’re in jail and won’t be able to have done that, so don’t do anything, okay! Because when a woman is dead, the same thing will have happened, we’ll be free and I’ll have the money because the police won’t be able to do anything. The note was intercepted by a fellow inmate and turned over to the police. After the police interviewed this inmate, they obtained and executed a search warrant of Michael’s, Rudi’s, and adjoining cells. Police seized other communications between the brothers, several of which were introduced at trial. Michael and Rudi were tried separately. Anke was granted immunity from prosecution in exchange for her testimony at both trials. 861 P.2d at 638-42. B. The Trial and Sentencing Apelt was charged with first ■ degree murder and conspiracy to commit first degree murder, and attorney Michael Villarreal was appointed to represent Apelt. Apelt was tried in April 1990, testified in his own defense, and was convicted of both murder and conspiracy to commit murder. Apelt, 861 P.2d 634. A presentence hearing was set for August 7, 1990. On June 8, Villarreal filed a motion for travel funds for him to go to Germany to investigate possible mitigating evidence. He told the court: Basically, Your Honor, what I need to do—and I think the Court is aware my partner went to Germany at our expense last year, as far as travel, not the hours worked, and the reason for that trip was to contact—basically, we are building up a character defense, and I was looking into some areas of my client having been in some type of psychological institution early in his life. We gathered—we learned other information. We did not get any information we used at trial as far as good character witnesses or any rule—we didn’t file any Rule 11 hearing nor anything of that sort based on what we learned over there at that time. However, Your Honor, I think it’s important and necessary that we travel at this time, that I travel this time to Germany to locate and contact witnesses there. Mr. Apelt has had his entire life in Germany except for the year and a half now that we know he was here in the United States, and there is also the issue of that psychological hospitalization that he under went, and I want to explore that area. Also, Your Honor, there are some other matters that came to light in his past regarding a difficult child birth, things of this sort that I need to check into, and I would ask permission to travel to Germany. I believe the airfare right now, going only on what I see in the newspaper, Your Hon- or, is somewhere around $800.00 round trip to Dusseldorf. I think that’s out of Los Angeles, I’m not sure. I also filed a companion motion for an interpreter. My partner, who went on that trip, found herself at a great disadvantage traveling in Germany. She, like myself, does not understand a word of German, and we thought family members would be able to interpret for us. It just didn’t work out. Their English wasn’t good enough. Other people who they thought might be able to help, friends and whatnot who would be able to help with interpreting weren’t available. I understand they have their own lives to lead, have their own jobs and whatnot. So if I do go, Your Honor, I am going to need an interpreter. I need someone so there is no problem, no delay and I can understand and I can make myself understood to the people I am talking to. I am going on that $50.00 based on what our interpreter believes she believes is the going rate over there. I don’t know what it is, Your Honor. The prosecutor interjected that perhaps it would be more efficient and economical to hire an investigator in Germany. Villarreal responded: I do have leads on what I’m looking for, Your Honor. I’m .not just, going over there on a fishing expedition. I have also gone through the consulate here. I have learned through the consulate iñ Los Angeles that they are not going to be much help in this case. The German government’s position in these matters, and as I understand from the consulate and a Mr; Fisher I have spoken to in Los Angeles, they let the German citizen go through the entire process, all the way through to the ending of appeals, actually serving of the sentence or in this case if my client were to receive the death penalty, the possibility of the impending death penalty. At that point the German government would take a position. They do have apparently a very strong anti-death penalty position in their country, because they don’t have the death penalty in their country and they don’t like it when other, countries impose the- death penalty on their citizens, but my understanding is they keep their hands off and they let the other country take, care of the crime and punishment, and then only at that point they take the position whether or not .they will assist in anyway or whatever help the German government feels it needs to make. So. I’ve gotten no help from the German government. I was hoping at the beginning of this case that they would be more cooperative. I believe Ms. Hughes mentioned a year or so ago when she went to Germany she didn’t get a whole lot of cooperation other than the police department was a little cooperative to some degree, but that was ’about it. The trial judge commented that “this has been a very expensive case to this point in time, and I am concerned about when it is the defendant has the right to have all these things furnished to him at no cost.” The judge noted that the costs had already exceeded $200,000.00. The court gave Villarreal a week to submit a statement, “a verification as to those items that you feel that your trip to Germany is a necessity for.” Villarreal did not submit such a statement. Instead, at the August 7, 1990 .hearing, he sought a continuance- and again argued that he needed to undertake an investigation in Germany. Arizona objected to a further continuance, arguing that the court had “indulged every whim of this defendant and his counsel in allowing him to present an adequate defense and fully investigate this case.” The prosecutor further noted that Villarreal had provided some documents that he acquired through a German lawyer and through Amnesty International. Villarreal denied that either the attorney or Amnesty International had been of any help. The trial court denied Villarreal’s motion to continue, and proceeded with the pre-sentencing hearing. The prosecutor indicated that she would rely on the testimony presented during the course of the trial and asserted three aggravating circumstances: (1) Apelt committed the crime for pecuniary gain; (2) the crime was heinous, cruel and depraved; and (3) Apelt procured the assistance of another by promise of payment. The court then asked Villarreal for whatever evidence he would proffer in mitigation. He offered eight exhibits that he had received the day before through fax and overnight mail. After receiving the exhibits, which had just been translated into English the night before, the court took a recess to allow the prosecutor to review the documents. After the recess, the prosecution called Detective Ronald Davis as a rebuttal witness. Davis spoke German, had been involved in the investigation of Cindy’s murder, and had traveled to Germany to investigate Apelt. He testified that he spent an entire day with the Dusseldorf police who did not show him Apelt’s criminal record, but read the record to Davis. Villarreal objected to Davis’ testimony as unsubstantiated hearsay. The prosecutor responded that the letters submitted by Villarreal were in the nature of character references and Arizona was entitled to rebut them. The judge initially was dubious of Arizona’s position, but was persuaded by Arizona’s argument that the testimony was relevant to whether the life sentence for conspiracy should run consecutively or concurrently with the death penalty. Davis then testified that Apelt had a felony conviction and that Apelt’s former wife told him that Apelt had “been involved in some sort of attack involving a knife with a homosexual partner.” Davis reported that the former wife also stated that Apelt was quite capable of committing murder for money, and had asked her to donate one of her kidneys in order for him to get money. In her summation, the prosecutor, after noting the three aggravating factors, argued that there were no mitigating factors. She argued: There are none of the factors that are so frequently offered to avoid the death penalty, such as poor childhood. This defendant himself told the probation officer that he had a normal childhood. There is no evidence of any mental disease or defect such that might mitigate his crime and call for leniency. In fact, the medical records that were submitted to the Court, albeit they are probable records by people not qualified to give it, but his family doctor seems to indicate that there was no sign of any mental disease or defect. In response, Villarreal first questioned whether there was really evidence of intent for financial gain or that the crime was particularly cruel, heinous, and depraved. He then offered the following arguments in mitigation: (1) Apelt was only 25 years old at the time of the crime; (2) there is remorse; (3) he cooperated in the pre-sentence report; (4) Apelt has recently found Christ; (5) there is a lack of a prior record of any serious crime; (6) Apelt has an honorable military discharge; (7) Apelt displayed good behavior at trial; (8) Germany has a strong position against the death penalty; and (9) some of the victims favored a life sentence. Villarreal also mentioned some of the areas of mitigation that he had not been able to pursue, such as Apelt’s capacity to appreciate wrongfulness of conduct, reports of “hospitalization in a clinic, some type of psychiatric clinic, emotional disturbance clinic of some sort in Germany,” and possible low intelligence and lack of education. But, because he could not travel to Germany, he was not able to obtain such information. On April 13, 1990, the trial judge imposed the death sentence. Villarreal continued to represent Apelt on his direct appeal. C. Initial Post-Conviction Proceedings Rudi was tried the week after Apelt and was sentenced and convicted of first degree murder. On May 28, 1991, Villarreal filed a post-conviction petition on behalf of Apelt. The petition was based on the testimony of a Dr. DiMaio in Rudi’s trial. The petition asserted: The Testimony of Dr. DiMaio was clearly that the murderer of Cynthia Apelt was right handed. Michael Apelt is left handed. The testimony of Dr. DiMaio would have added credibility to Michael Apelt’s testimony that he did not kill his wife. It would also have impeached the testimony of Anke Dorn that Michael Apelt killed his wife. The Superior Court of Pinal County denied the petition oh May 28, 1991. The Arizona Supreme Court then consolidated the denial of the first post-conviction petition with’ Apelt’s direct appeal. The Arizona Supreme Court affirmed Apelt’s conviction and sentence, rejecting a host of arguments advanced by Villarreal. Apelt, 861 P.2d 634. Of greatest concern in this federal habeas proceeding is the court’s treatment of Apelt’s challenges to his sentence. The court characterized the first-challenge as whether “the trial court err[ed] by refusing to fund a trip to Germany so defense counsel could look for mitigating evidence.” Id. at 642. The court determined that there was no error because a defendant must demonstrate how the requested assistance would be beneficial and why it is necessary for a fair trial, and Apelt had failed to make such a showing. Id. at 661. The court noted that Villarreal failed to file a statement showing why the proposed trip to Germany was necessary, and that the adequacy of a showing is left-to the discretion of the trial judge. Id. The court commented that counsel did not explain why psychological hospitalization might be mitigating, or “why a difficult childhood and lack of education would be mitigating.” Id. It concluded that because Apelt “failed to show that helpful evidence was available in Germany,” he had no right to funding under the statute or the due process clause of the Fourteenth Amendment. Id. at 662. The Arizona Supreme Court addressed two questions concerning the appropriateness of the death sentence: (1) did the court err in finding three aggravating factors; and (2) did the court err in “finding that there were no mitigating factors sufficient to outweigh the aggravating factors.” Id. at 642. The court found that there was more than sufficient evidence to support each of the three aggravating elements. Id. at 662-63. It also found that the trial court had considered the “mitigating” factors proffered by counsel and had not imposed an impermissibly high burden or failed to weigh the factors properly. Id. at 663. It independently reviewed the record and found three aggravating and no mitigating factors. Id. at 664. As to the post-conviction petition, the court rejected Apelt’s request for an evi-dentiary hearing, finding that Dr. DiMaio’s testimony would not have changed the outcome of the trial because it made no difference whether Apelt or Rudi wielded the murder weapon. Id. D. Apelt’s Second Post-Conviction Proceedings ■ On December 4, 1995, Apelt, now represented by new counsel, filed an “amended petition for post-conviction relief1' in the Superior Court for the County of Pina (the amended petition is generally referred to as the “PCR”). The PCR raised ten issues, including assertions that Apelt was denied effective assistance of counsel during the penalty phase of his case, on direct appeal, and on his first postconviction petition. Many of the assertions were based on newly discovered materials. The federal district court described the materials- as follows: In support of these claims - regarding Villareal’s performance, PCR counsel pointed out Villareal had been aware Apelt had been hospitalized in Germany but Villareal “failed to gather the records and background information necessary for a thorough and complete mental health evaluation.” Villareal had also “failed to investigate, develop, and present substantial mental health evidence”; failed “to identify, locate and investigate potential mitigation witnesses”; and “failed to properly develop- or present adequately expert testimony.” PCR counsel further claimed Villareal had failed to present evidence that Apelt “came from a family background of gross poverty, alcoholism and violence which included emotional, physical and sexual abuse”; that Apelt “has a history of mental illness and has received psychiatric/psychotherapeutic treatment in Germany”; that Apelt “was in special education as a child,” “suffered from a nervous disorder,” and had attempted suicide “and that Apelt was mentally, physically, and sexually abused by older men throughout his childhood and mentally disturbed while in school.” These claims by PCR counsel were supported by “a plethora of documents from Germany obtained by ... counsel through correspondence.” The documents submitted by PCR counsel included “a report on the situation of the Apelt family,” prepared by'the Dusseldorf Industrial Welfare Organization. The report-was-based on information provided by Apelt’s mother and social worker who had worked with the family when Apelt was a child. The documents also included an affidavit from Apelt’s mother.- The report and: affidavit recounted what follows. Apelt’s father was- an abusive alcoholic who beat his wife and children, including Apelt, with an iron rod. Apelt’s father sexually abused his wife and attempted to engage in sexual misconduct against his daughters. As a child, Apelt was sexually molested by older men on two occasions. The first time was when Apelt was seven. He was taken from his yard and driven to a house where he was forced to have intercourse. The second time was when Apelt was thirteen.- Apelt had been walking home from school when he and a friend were tricked into going into, a cellar where a man holding a knife forced Apelt to have intercourse. The incidents left Apelt “mentally disturbed.” ... Apelt’s family was very poor while he was growing up. The family of nine lived in a five-bedroom apartment and his father did not work on a regular basis. The family survived on government support and his mother’s earnings as a cleaning lady. The children were forced to go to work at age fourteen. All of the Apelt children “immediately after reaching emancipation, left home in order' to escape the abusive, sexually abusive and violent situations.” Beyond the report from governmental agency and affidavit from Apelt’s mother, PCR counsel also submitted a medical report from the- Psychosomatic Clinic in Dusseldorf where Apelt received inpatient treatment. That medical report was from 1986 and it described Apelt as suffering from “shortness of breath, vertigo, and pain in the left arm.” The report indicated that Apelt may have suffered medical complications during his birth. The report recounted that Apelt had attended special education because he spoke with a lisp. Attached to the PCR was an affidavit from attorney Villarreal. He stated that: (a) he “did not hire an investigator in Germany to investigate any mitigation”; (b) he “did not file a supplementary statement at the court’s request following the denial of funds by the court for the trip to Germany”; (c) “[a]ny lack of investigation or preparation during the penalty phase of this case was not a tactical or strategic decision”; (d) “Mr. Apelt did not take an active role in the development of mitigation”; and (e) he “did not withhold any objections, claims or defenses in order to gain a tactical or strategic advantage.” On January 23, 1996, Apelt filed a supplement to the PCR asserting that he was entitled to an evidentiary hearing (a) pursuant to Ake v. Oklahoma, 470 U.S. 68, 105 S.Ct. 1087, 84 L.Ed.2d 53 (1985), concerning his constitutional right to state-funded expert assistance, and (b) on whether his trial counsel was ineffective in failing to thoroughly investigate material aspects of his case. Arizona filed a comprehensive response to the PCR, setting forth a detailed account of Apelt’s actions leading up to the murder. It then argued that most of Apelt’s claims, including his IAC claims, are precluded under Arizona Rule of Criminal Procedure 32,2, which, in essence, provides that a defendant may not raise an issue that was not raised but could have been raised “at trial, on appeal, or in any previous collateral proceeding. The response also asserted that although Apelt’s claim of IAC by appellate counsel was not precluded, Apelt had not alleged any specific misdeeds that would overcome the deference due to counsel. The response also denied that Apelt had alleged any colorable claim of newly discovered material evidence. The evidence concerning Apelt’s background could not be newly discovered because it was within Apelt’s personal knowledge and was not diligently presented. Arizona further argued that Apelt cannot tie the evidence “to his coldblooded commission of the murder, and none is ‘positive’ character mitigation—at most it seeks some sort of pity or sympathy, which [Apelt] is not entitled to have considered in mitigation.” The response also argued that there is no possibility that the alleged newly discovered evidence would have changed Apelt’s sentence because Apelt exaggerates what is actually in the documents. Arizona also argued in the alternative that Apelt’s claims of IAC were meritless. Arizona asserted that, under Strickland, there is a strong presumption that counsel exercised reasonable professional judgment. Focusing on counsel’s performance at sentencing, Arizona first noted that Villarreal asked for funds to go to Germany but did not file a verified statement as requested by the trial court. The State argued that Villarreal did all he could, given the lack of any mitigation in Apelt’s background. It argued that Apelt and his attorneys “have had more than 5 years to cherry-pick through [Apelt’s] past and dredge up mitigation, yet have failed to present anything that would arguably warrant a sentence less than death.” On September 4, 1996, the Arizona Superior Court for Pinal County denied Apelt’s PCR. It held that most of the claims were precluded under Arizona’s Rules of Criminal Procedure either because they had been adjudicated on direct appeal or because they were not raised at trial, on appeal, or in Apelt’s first post-conviction petition. This included most of Apelt’s IAC contentions, except his claim of IAC in his first post-conviction petition, which the court held was not cognizable in the proceeding. Two of the court’s final three paragraphs are particularly relevant. The court held: The following claim is meritless because Petitioner fails to make a showing that counsel acted below objective standards of reasonableness in deciding what claims to raise on appeal and Petitioner fails to make a showing that the Arizona Supreme Court’s decision would have been any different: Claim 10 (ineffective assistance of counsel on direct appeal). Alternatively, the Court finds that Petitioner’s claim of ineffective assistance of counsel at trial and sentencing fails to allege colorable claims because Petitioner fails to make a sufficient preliminary showing that counsel’s performance fell below objective standards of reasonableness, and fails to make a preliminary showing that, in light of the allegations, there exists a reasonable probability that the result of the trial or sentencing hearing would have been different. Apelt filed a petition for review to the Arizona Supreme Court, which summarily, denied review on April 23,1998. E. Initial Proceedings in the District Court for Arizona Apelt filed his federal habeas petition in the United States District Court for the District of Arizona in May 1998. However, before the district court could resolve the petition, the Supreme Court decided Atkins, 536 U.S.-304, 122 S.Ct. 2242, holding that the Eighth Amendment prohibits the execution of intellectually disabled persons. Based on the possibility that Atkins applied to Apelt, the district court stayed Apelt’s sentencing-related claims to permit him to return to state court and exhaust his Atkins claim. In the meantime, the district court considered and denied Apelt’s conviction-related claims. F. The Atkins Proceedings in State Court The superior court conducted an eviden-tiary hearing regarding the Atkins claims by both Apelt and his brother, Rudi, in April and May 2007. The superior court applied A.R.S. § 13-753(K)(3), which, at that time, defined intellectual disability as “a condition based on a mental deficit that involves significant subaverage general intellectual functioning, existing concurrently with significant impairment in adaptive behavior, where onset of the foregoing conditions occurred before the defendant reached the age of eighteen.” The superior court found that Apelt met none of the criteria: based ón thé three IQ scores and the accepted “margin of error for the tests administered,” the Court is confronted with the following ranges: 88 (German school), 56 to 66 (Ruff), 32 to 62 (or 50 to 80) (Kury). Based upon the lack of evidence to support the marked decrease in IQ score, and the experts’ opinions that the defendant was malingering, the Court finds that the defendant has failed to establish by even a preponderance of the evidence that he suffers from significant subaverage intellectual functioning. As to the second criterion, adaptive behavior, the court rejected the assessment of Apelt’s expert, Dr. Ruff, as focused more on Apelt’s, maladaptive behavior rather than his ability to perform daily tasks. Reviewing Apelt’s adulthood, the court .noted that Apelt “has consistently, displayed the ability to engage in independent and self-directed thinking, planning and conduct.” The court commented that Apelt had “worked at various jobs, at least one for an extended time, served in the military and was honorably discharged, married, and lived independently.” It further observed that Apelt had traveled to the United States and Mexico,- and had learned English “sufficiently to communicate and interact appropriately with others, negotiated purchases of vehicles and apartment leases, understood foreign currency exchange rates, and obtained employment.” The court concluded that Apelt “ha[d] not proved by even a preponderance of the evidence that throughout his childhood and adult life he has suffered' from significant impairment in adaptive behavior in meeting the standards of personal independence and social responsibility expected of a person of his age and cultural group.” Finally, the superior court concluded that Apelt had failed to prove by even a preponderance of the evidence the onset of subaverage intelligence prior to reaching the age of eighteen. In contrast, the superior court found that Rudi was intellectually disabled and vacated his death sentence. Rudi’s IQ was lower than Apelt’s IQ with test results ranging from 49 to 61. The court also found that Rudi exhibited developmental disabilities from an early age, had been' “unable to attain gainful employment or function on his own,” had been dismissed from military service after serving for less than a year, had never lived alone, and depended on Apelt to take care of him. G. The District Court’s September 1, 2015 Order Following the superior court’s denial of Apelt’s petition for post-conviction relief based oh Atkins, Apelt was allowed to amend his federal habeas petition to raise, an Atkins claim. On September 1, 2015, the district court issued its order granting Apelt relief on one issue and otherwise rejecting his claims. The district court addressed the issues relevant to this appeal in the following order. 1. Procedural Status of Claims The district court recognized that a state prisoner must exhaust his remedies in state court before filing a federal habeas petition, and that, when a claim is procedurally defaulted under state law, a federal court usually cannot reach the merits of the claim. It reasoned that before 2012, a procedural default would be excused only if the petitioner demonstrated both cause and prejudice, but that Martinez v. Ryan, 566 U.S. 1, 132 S.Ct. 1309, 182 L.Ed.2d 272 (2012), set forth a new standard. Citing our opinion in Cook v. Ryan, 688 F.3d 598, 607 (9th Cir. 2012), the district court held that now a petitioner may overcome a procedural default “by demonstrating two things: (1) ‘counsel in the initial-review collateral proceeding, where the claim should have been raised, was ineffective under the standards of Strickland ... ’ and (2) ‘the underlying ineffective-assistance-of-trial-counsel claim is a substantial one, which is to say that the prisoner must demonstrate that the claim has some merit.’ ” Apelt asserted that his claims for IAC at sentencing (Claim 12), for failure to challenge' his competency to stand trial (Claim 1-B), and for failure to challenge his competency at sentencing (Claim 1-D), are excused under Martinez by Villarreal’s ineffective performance on his first postconviction petition. Arizona made a two-fold response. It argued that these claims were procedurally defaulted, but it also argued that if the court were to find Martinez applicable, the court would have to consider that the state court also denied the claims on their merits. Accordingly, if the court reached the merits, it should give deference to the state court’s ruling and not review the IAC claims de novo. The district court agreed that it had to “accept that the two claims were resolved by the state court on their merits -and review their rejection under the deferential standard applicable to Apelt’s other claims.” 2. Claim 12—IAC at Sentencing The district court recognized that Apelt’s IAC claim was governed by AED-PA and thus relief was only available if the state court’s decision was an unreasonable application of clearly established Federal law or an unreasonable determination of the facts. See 28 U.S.C. § 2254(d). The court acknowledged that relief was precluded as long as ‘“fairminded 'jurists could disagree’ on the correctness of the state court’s decision,” Harrington v. Richter, 562 U.S. 86, 101, 131 S.Ct. 770, 178 L.Ed.2d 624 (2011), and that review was “limited to the record that was before the state court that adjudicated the claim on its merits.” Cullen v. Pinholster, 563 U.S. 170, 181, 131 S.Ct. 1388, 179 L.Ed.2d 557 (2011). Accordingly, the record could be expanded only once a petitioner showed that there was no reasonable basis for the state court denial of relief. As Apelt alleged that Villarreal was ineffective because he failed to present classic mitigating evidence about his background and mental health, the district court stated that it had tc determine “whether there is any reasonable - argument that. Villareal's performance at sentencing met the well-established constitutional minimum for effective assistance of counsel.” The district court recognized that, under AEDPA, the Strickland standard was “doubly deferential.” Knowles v. Mirzayance, 556 U.S. 111, 123, 129 S.Ct. 1411, 173 L.Ed.2d 251 (2009), Quoting Richter, 562 U.S. at 105, 131 S.Ct; 770, the district court stated that “the question is not whether [Villarreal’s] actions- were reasonable. The question is whether there is any reasonable argument that [Villarreal] satisfied Strickland’s deferential standard.” The court further held:that only the evidence presented to the state court would be considered. Turning to the substantive law, the district court stated that, in a capital case, counsel has an obligation to conduct a thorough investigation of the defendant’s background. Williams v. Taylor, 529 U.S. 362, 396, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). The court commented that although the exact contours of the obligation will vary, counsel “should obtain readily available documentary evidence such as school, employment, and medical records, and obtain information about the defendant’s character and background” (Robinson v. Schriro, 595 F.3d 1086, 1108-09 (9th Cir. 2010)); should make “inquiries into social background and evidence of family abuse” (Summerlin v. Schriro, 427 F.3d 623, 630 (9th Cir. 2005)); and should review such evidence of mental impairment as might be found in mental health records (Lambright v. Schriro, 490 F.3d 1103, 1117 (9th Cir. 2007) (per curiam)). The court further noted that while an investigation typically begins with the defendant’s interview, it cannot end there unless the “defendant has given counsel reason to believe that pursuing certain investigations would be fruitless or even harmful.” Robinson, 595 F.3d at 1109 (quoting Strickland, 466 U.S. at 691, 104 S.Ct. 2052). The district court concluded: Villareal clearly did not meet these responsibilities. Based on the state court record, Villareal did not collect records from social service agencies, welfare agencies, doctors, hospitals, or employers. Villareal did not interview potential mitigation witnesses, including Apelt’s family members, or consult with any mental health experts. Villareal did not obtain Apelt’s readily-available mental health records from the Pinal County jail which described Apelt receiving various medications as well as Apelt’s placement on suicide watch. And Villareal did not present a single witness at the sentencing hearing. This was deficient performance. The district court explained that, in reaching its conclusion, it had taken into consideration Villarreal’s statement that Apelt did not actively participate in the sentencing phase of trial. It found, however, that Apelt’s lack of cooperation did not eliminate Villarreal’s duty to investigate. See Hamilton v. Ayers, 583 F.3d 1100, 1118 (9th Cir. 2009); and Landrigan v. Schriro, 441 F.3d 638 (9th Cir. 2006) (en banc), rev’d, 550 U.S. 465, 127 S.Ct. 1933, 167 L.Ed.2d 836 (2007). The court acknowledged that Villarreal’s investigation was hampered by the need to obtain funding to travel to Germany, but concluded that his performance was nevertheless legally deficient. He failed to provide additional information to the trial court, as invited by the court, and offered no explanation for his failure. The court further noted that “[i]t is telling that PCR counsel obtained voluminous material regarding mitigation without traveling to Germany.” The district court also rejected Arizona’s suggestion that Villarreal’s conduct may have been strategic. It cited Wiggins v. Smith, 539 U.S. 510, 527, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003), and noted that, because Villarreal “intended to seek information about Apelt’s mental health, including his hospitalization in Germany, ... he knew it was material evidence and, inexplicably, failed to pursue it.” The court added that Villarreal “failed to present evidence of Apelt’s childhood poverty and abuse— humanizing information that would have been within the parameters of good character evidence,” and that Villarreal admitted that there was “no strategic basis for his failure to investigate or present more relevant mitigating evidence.” The district court concluded that “[n]o fairminded jurist could conclude Villareal’s performance was sufficient.” The court also found that the deficient performance was prejudicial: there was a reasonable probability that the result of the proceeding would have been different absent Villarreal’s deficient performance. See Strickland, 466 U.S. at 694, 104 S.Ct. 2052. Villarreal’s “case in mitigation contained no evidence of Apelt’s alleged poverty, no evidence of childhood physical abuse, no evidence of repeated childhood sexual abuse, and no meaningful evidence of mental health problems.” Indeed, the prosecutor stressed that Apelt had a normal childhood, and Villarreal submitted a statement from Apelt’s mother that he had had a normal childhood. The court concluded that “the sentencing court was presented with a picture of Apelt’s background that bore ‘no relation’ to the picture presented by PCR counsel with apparently reliable evidence,” and the “magnitude of the difference between the mitigating evidence that was presented at sentencing and the evidence that could have been presented through competent investigation is sufficient to undermine confidence in the outcome.” Arizona filed a motion for reconsideration, arguing that (1) the court committed manifest error by applying Martinez to excuse the procedural default of Claim 12, and (2) the court “erred in its assessment of Strickland’s prejudice prong by failing to reweigh the totality of the mitigating evidence against the aggravating factors.” The district court rejected the second argument, holding that it had taken “into account the aggravating factors as well as the totality of the mitigating evidence.” The court explained its rejection of the first argument as follows: the Court did not apply Martinez to excuse the default but instead reviewed the state court’s alternative merits ruling. The Court noted Martinez, but only in the context of reassessing its earlier determination that Claim 12 was procedurally defaulted and barred from federal review. The Court concluded, citing Clabourne v. Ryan, 745 F.3d 362, 382 (9th Cir. 2014), that the state court’s alternative merits ruling was subject to review under § 2254(d). In a footnote, the district court further noted that in Martinez, “the Arizona Attorney General’s Office argued on remand that the presence of an alternative merits ruling meant that alternative ruling had to be reviewed under a deferential standard.” 3. Claims 1-B & 1-D (Mental Competence at Trial and Sentencing) Apelt asserted that he was “severely mentally ill and grossly overmedicated” when he was tried and that Villarreal was ineffective in failing to challenge his competence. The district court rejected this contention, noting that “co-counsel traveled to Germany, in part to investigate Apelt’s placement in a psychological institution” and did not find any evidence to support a motion to determine competency. Moreover, “the record does not support a finding that Apelt lacked a rational and factual understanding of the proceedings or the ability to consult with counsel.” Apelt was actively involved in his defense and the trial proceedings. In addition, his trial testimony revealed no traces of incompetence. Furthermore, the district court determined that the fact that Apelt was on medication did not mean that he was unable to consult with his lawyer and understand the proceedings. See United States v. Shan Wei Yu, 484 F.3d 979, 985 (8th Cir. 2007). Also, the facts that he had been placed on suicide watch and had a history of mental health problems did not show that he was incompetent to stand trial. The court stated: “Apelt has failed to identify an instance in which he behaved irrationally, appeared not to understand the proceedings, or did not communicate effectively with Villarreal.” The district court concluded that Apelt had not met his burden of showing IAC in Villarreal’s failure to doubt his competency. 4. Claim, 11 (Denial of Funds to Travel to Germany) The district .court reviewed the proceedings in the state courts and concluded that the denial of Villarreal’s request for funds to travel to Germany was not unreasonable. Despite being given an opportunity to supplement his request, Villarreal never offered any specific information to support his request. Thus, he did not make a “threshold showing” that the additional funds would be helpful. Williams v. Stewart, 441 F.3d 1030, 1054,(9th Cir. 2006) (per curiam). The court held that “because Villareal offered only ‘undeveloped assertions’ in support of his request for funds to travel to Germany,” the Arizona Supreme Court did not unreasonably apply Caldwell v. Mississippi, 472 U.S. 320, 323 n.1, 105 S.Ct. 2633, 86 L.Ed.2d,231 (1985), in denying this claim. 5. Claim 17 (failure to consider certain mitigating evidence) Apelt argued that the Arizona Supreme Court erred by excluding from its consideration certain mitigating evidence in violation of Tennard v. Dretke, 542 U.S. 274, 124 S.Ct. 2562, 159 L.Ed.2d 384 (2004). The district court rejected this claim, finding that both the Arizona trial court and the Arizona Supreme Court considered all of Apelt’s proffered mitigating factors. 6.Claim 26 (intellectually disabled . under Atkins) • The district court first noted that under Arizona law Apelt bore the burden of proving intellectual disability by clear and convincing evidence (A.R.S. § 13-753(G)), and that under AEDPA, Apelt had to show that the state court’s' decision was an unreasonable application of Atkins or was based on an unreasonable determination of the facts.'Apelt focused on the state court’s analysis of the evidence presented in the Atkins proceedings, objécting to the determinations that he had failed to show he had a subaverage intellect'and had not shown significant deficits in adaptive behavior. Although Apelt’s experts, Dr. Kury and Dr. Ruff, concluded that Apelt suffered from “Mild Mental Retardation,” and was intellectually disabled, the district court noted that Apelt had been tested as a child and found to have an overall IQ of 88. While the experts were skeptical about this test result, the district court noted that “the only specific challenge they offered was that Apelt would not have been placed in a special education school if his IQ had been that high.” The court found this “unpersuasive as a criticism of the test because no one contests that Apelt’s IQ was measured at 88 and, notwithstanding that result, he was in fact placed in a special education school.” Perhaps more important to the district court was the evidence of malingering: that Apelt sought to appear on the tests to be less intelligent than- he is. Kury and Ruff administered eight separate IQ tests of Apelt and averaged them to arrive at a full-scale IQ score of 65, but the district court shared the state court’s concern that these scores were the result of Apelt’s malingering. The district court noted that Kury had detected “slight malingering” and that Ruff acknowledged it was possible Apelt malingered on some tests. Although Kury.and Ruff doubted that the indications of malingering were strong enough to change their overall evaluations, they could not exclude the possibility that Apelt malingered or that all the testing data was reliable. The district court concluded that the state court had not clearly erred “by taking into account evidence of malingering in considering whether Apelt met his burden of establishing subaverage intelligence.” Although Apelt’s experts opined that he suffered from significant deficits in adaptive behavior, particularly social/interpersonal skills, financial responsibility, functional academics, and work, Dr. Moran, Arizona’s expert, thought “Apelt’s conduct was actually indicative of anti-social personality disorder.” The district court found that the state court was entitled to assess the relative credibility of the experts and that , its decision to credit one qualified expert over the others was not enough to merit relief. The district court concluded that the state court did not clearly err when it found Apelt had- failed to prove he met the adaptive behavior prong of intellectual disability and that the state court’s ruling on the Atkins issue was not based on an unreasonable determination of facts. 7. Claim 27 (standard for proving intellectual disability) Finally, the district court rejected Apelt’s argument that Arizona had violáted his right to due process and freedom from cruel and unusual punishment set forth in Cooper v. Oklahoma, 517 U.S. 348, 116 S.Ct. 1373, 134 L.Ed.2d 498 (1996), by requiring that he prove his intellectual disability. It noted that the Supreme Court in Atkins expressly permitted states to establish their own procedures for determining intellectual disability, and, thus, “there is no clearly established federal law setting a burden of proof in Atkins cases or extending Cooper to claims of intellectual disability.” The September 1, 2015 order concluded with the issuance of a certificate of appeal-ability on two issues: denial of funds to travel to Germany, and the Atkins claim. The court also asked the parties to file supplemental briefs on whether an eviden-tiary hearing was • necessary ' on IAC at sentencing. ■ H. The District Court’s December 1, 2015 Order No party thought that an evidentiary hearing was necessary, but Arizona .filed a motion for reconsideration, which the . district court denied. In doing so, the court expanded on its reasons for granting relief. The court noted that Villarreal’s initial