[693]*693GIBBONS, J., delivered the opinion of the court, in which SILER, J., joined, and WHITE, J., joined in part. WHITE, J. (pp. 701-05), delivered a separate opinion dissenting from sections IV and V of the majority opinion.
OPINION
JULIA SMITH GIBBONS, Circuit Judge.
David Miller appeals the district court’s dismissal of his petition for a writ of habeas corpus under 28 U.S.C. § 2254. Miller was convicted of first-degree murder in 1982 and sentenced to death, a sentence that was upheld by the Tennessee Supreme Court. He now claims that the state improperly denied him assistance from an independent medical expert, in violation of his clearly established constitutional right under Ake v. Oklahoma, 470 U.S. 68, 105 S.Ct. 1087, 84 L.Ed.2d 53 (1985). Miller also claims that the district court erred in finding that improper jury instructions given by the state court amounted to harmless error. For the reasons that follow, we affirm the decision of the district court.
I.
On May 20, 1981, Lee Standifer, a twenty-three-year-old woman diagnosed with diffused brain damage and mild retardation, was murdered in Knoxville, Tennessee. State v. Miller (Miller I), 674 S.W.2d 279, 280 (Tenn.1984). A medical examiner testified that Standifer had been stabbed repeatedly all over her body with both a large knife and a fireplace poker; some stab wounds were so deep (including two that pierced the ribcage) that the examiner speculated a hammer-like object had been used to drive in the knife. Id. at 281. The evidence suggested that a large rope was used to bind the victim’s body after the murder and drag it into a wooded area. An examination also showed that Standifer had engaged in sexual intercourse shortly before her death.
The evidence at trial established the following course of events. Miller and Standifer had arranged to go on a date the night of May 20, and the two of them eventually took a cab to the house of Benjamin Thomas, where Miller was staying. Id. at 280. Later that evening, Thomas returned to his home and found Miller hosing the basement floor; he also found streaks of blood inside the house. Id. The next day, Thomas discovered Standifer’s body in his backyard, as well as a blue t-shirt belonging to Miller stained with blood of the same type as Standifer’s. Miller, who had left Knoxville, was apprehended in Columbus, Ohio, and transported back to Knoxville. Id. After waiving his Miranda rights, he admitted to hitting Standifer with his fist and then dragging her outside Thomas’s house after she was non-responsive and not breathing. Id. at 281-82.
Miller was indicted for Standifer’s murder on August 3, 1981. On October 19, 1981, Miller’s counsel requested a psychiatric examination in order to investigate Miller’s competency to stand trial. The trial court granted the motion and ordered that Miller be examined by qualified staff members at the Helen Ross McNabb Mental Health Center. The order explicitly provided the staff with two inquiries:
The medical authorities ... shall furnish the Court with a report of their findings and will advise the Court of their opinion as to whether the defendant is mentally ill to the extent that he cannot sufficiently understand the nature and object of the proceedings going on against him, and cannot advise with counsel in a rational manner.... Additionally, the medical authorities will make a determination as to whether the defendant was [694]*694mentally competent and understood the nature and consequences of his act on or about May 21, 1981, and will report said findings to the Court.
Dr. George Gee, a psychiatrist at Helen Ross McNabb, prepared a letter in November 1981, which was presented to the court and shared with the government and defense counsel. The letter stated that Miller’s affect and thought processes were normal, and Gee concluded that he did not believe Miller was insane at the time of the offense. Miller v. Bell, 655 F.Supp.2d 838, 847 (E.D.Tenn.2009).1
On December 11, 1981, Miller filed a “motion for appointment of psychiatric expert,” requesting that the trial court appoint a psychiatrist at the State’s expense to assist in the preparation of Miller’s defense. The district court denied the motion, concluding that Miller was not entitled to a second medical expert in addition to the assistance that Dr. Gee could offer him. Miller’s trial was subsequently scheduled for March 1982.
At trial, Miller’s counsel argued that the circumstances of the crime were so irrational that one could infer that Miller was insane; counsel, however, introduced no expert to support the defense and instead tried to demonstrate insanity through lay testimony. The prosecution, aiming to prove Miller’s sanity, called Gee to the stand and questioned him about the conclusions he drew based on his examinations. On direct examination, Gee testified that he believed Miller was sane at the time of the offense and did not suffer from a mental disease or defect. During the defense’s cross-examination, Gee acknowledged that Miller disclosed during the June interview that he had previously “heard some voices, someone call[ing] his name.” Gee, however, testified that Miller told him in June that these voices had stopped three months before (and therefore prior to the murder); Gee also explained that he did not consider these voices evidence of a “psychotic hallucination.” 2
The jury convicted Miller of first-degree murder and sentenced him to death. Miller appealed his conviction on multiple grounds, including the district court’s refusal to provide him with an independent psychiatrist for trial. In May 1984, the Tennessee Supreme Court remanded Miller’s case for resentencing on the grounds that the State had impermissibly introduced evidence of two prior arrests for rape during the sentencing phase, since Miller had never been convicted of either allegation. Miller I, 674 S.W.2d at 284. The court, however, affirmed Miller’s conviction. Id.
Upon remand, Miller renewed his motion for a new trial, claiming that he was entitled to the psychiatric assistance previously requested under the United States Supreme Court’s recent decision in Ake v. Oklahoma, 470 U.S. 68, 105 S.Ct. 1087, 84 [695]*695L.Ed.2d 53 (1985). Ake, according to Miller, “addressed the exact issue on psychiatric assistance which Mr. Miller had presented” to the trial court and on his first direct appeal. As a result, Miller claimed his conviction was predicated on a denial of his due process rights. Miller also filed a state habeas corpus petition making the same argument about Ake. The trial court denied both motions without explanation. A second jury sentenced Miller to death.
On a second direct appeal, Miller asked the courts “to reconsider two issues involved in the guilt-innocent phase of the first trial, to wit, the trial judge’s instruction allegedly shifting the burden of proof in violation of Sandstrom v. Montana, 442 U.S. 510 [99 S.Ct. 2450, 61 L.Ed.2d 39] (1979)[,] and denial of appointment of a psychiatrist to aid defendant, allegedly in violation of Afce[.]” State v. Miller (Miller II), 771 S.W.2d 401, 402-03 (Tenn.1989) (internal citations omitted). The Tennessee Supreme Court rejected Miller’s appeals, concluding that “[a]ll of the issues relevant to the guilt or innocence of defendant ... were dealt with in this Court’s opinion released in 1984.” Id. at 403. The Tennessee Supreme Court concluded that “the guilt-innocent issues were foreclosed when the 1984 opinion sustaining defendant’s conviction of first degree murder became final, except such issues as are permissible in a post-conviction proceeding.” Id. The court then affirmed the second death sentence. Id. at 405.
In May 2002, Miller filed a petition for a writ of habeas corpus under 28 U.S.C. § 2254. The district court rejected all of Miller’s claims and denied the petition. Miller now appeals that denial.
II.
We review de novo a district court’s denial of a petition for a writ of habeas corpus. Tolliver v. Sheets, 594 F.3d 900, 915 (6th Cir.2010). Because Miller filed his petition after April 24, 1996, it is subject to the requirements of the Anti-terrorism and Effective Death Penalty Act of 1996 (“AEDPA”). Carter v. Mitchell, 443 F.3d 517, 524 (6th Cir.2006). Under AEDPA, a writ may not be granted unless the state court’s adjudication of the claim: (1) resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established federal law, as determined by the Supreme Court; or (2) resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented in the state court proceedings. 28 U.S.C. § 2254(d)(1)-(2). “A state court renders an adjudication ‘contrary to’ federal law when it ‘arrives at a conclusion opposite to that reached by [the Supreme] Court on a question of law’ or ‘decides a case differently than [the Supreme] Court has on a set of materially indistinguishable facts.’ ” Biros v. Bagley, 422 F.3d 379, 386 (6th Cir.2005) (quoting Williams v. Taylor, 529 U.S. 362, 412-13, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000)). “A state court unreasonably applies Supreme Court precedent ‘if the state court identifies the correct governing legal rule ... but unreasonably applies it to the facts of the particular [defendant’s] case.’” Barnes v. Elo, 339 F.3d 496, 501 (6th Cir.2003) (quoting Williams, 529 U.S. at 407, 120 S.Ct. 1495). Factual determinations made by state courts during the underlying proceedings are presumed to be correct unless rebutted by clear and convincing evidence. 28 U.S.C. § 2254(e)(1).
III.
Miller first argues that he is entitled to habeas relief because he was denied state funds to obtain assistance with his defense from an “independent mental health expert,” in violation of Ake v. Okla[696]*696homa. The warden asserts two defenses to Miller’s Ake claim. First, he alleges that Ake is not “clearly established Federal law” for purposes of this case. Second, the warden argues that even if Ake is the controlling authority in this case, the constitutional right to psychiatric assistance, as established by Ake, did not entitle Miller to state funds for a second psychiatrist, when he had already been evaluated by a competent psychiatrist appointed by the trial court.3
A.
The first issue before us is whether the Supreme Court’s Ake decision is relevant at all. The Supreme Court has clarified that under § 2254(d)(1), the relevant decision for purposes of determining “clearly established Federal law” is the last state court decision that adjudicated the claim on the merits. Greene v. Fisher, — U.S. -, 132 S.Ct. 38, 44-45, 181 L.Ed.2d 336 (2011). This is because § 2254(d)(1) “requires federal courts to Tocu[s] on what a state court knew and did,’ and to measure state court decisions ‘against this Court’s precedents as of the time the state court renders its decision.’ ” Id. at 44 (quoting Cullen v. Pinholster, — U.S. ——, 131 S.Ct. 1388, 1399, 179 L.Ed.2d 557 (2011)). The state supreme court adjudicated the merits of Miller’s claim about psychiatric assistance in 1984, when it affirmed Miller’s conviction. Miller I, 674 S.W.2d at 284. Although Miller raised his claim predicated on Ake, which was issued in February 1985, in his second set of direct appeals following his resenfencing, the state supreme court very clearly declined to address the merits of his claim. Miller II, 771 S.W.2d at 403. The court explained that “[a]ll of the guilt-innocent issues were foreclosed when the 1984 opinion sustaining defendant’s conviction of first degree murder became final, except such issues as are permissible in a post-conviction proceeding____ [and] such issues are never relevant at a sentence hearing or a resentence hearing.” Id. Although a post-conviction petition would have been timely, Miller did not seek post-conviction review of his Ake claim. The relevant state court decision, therefore, was issued before the Supreme Court’s decision in Ake and Miller may not rely on Ake as clearly established federal law.4
B.
Even if we were to look past the restrictions imposed by Greene and address the underlying merits of Miller’s claim — that is, whether Ake established a due process right to independent, non-neutral psychiatric assistance — Miller would still not be entitled to relief on this ground.
Miller claims that under Ake he was entitled to the assistance of an “independent mental health expert.” In psychiatric assistance claims, “independent” has become a term of art referring to a psychiatrist assigned exclusively to assist the accused in his defense. See, e.g., Carter v. Mitchell, 443 F.3d 517, 526 (6th Cir.2006). In contrast, a “neutral” psychiatrist is “one whose report is available to both the defense and the prosecution.” Powell v. Col[697]*697lins, 332 F.3d 376, 392 (6th Cir.2003). In this case, the trial court provided Miller with neutral psychiatric assistance — that of Dr. Gee — but denied Miller his own hired psychiatric assistance.
1.
Because Miller appeals under AEDPA, to obtain relief he must show that the decision of the state court was “contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States.” 28 U.S.C. § 2254(d)(1). We therefore consider whether the Supreme Court has spoken to the issue of independent psychiatric assistance.
The Supreme Court’s opinion in Ake does not speak to psychiatric assistance retained by a defendant. Ake was arrested for murder; before trial, he was diagnosed by a neutral psychiatrist as a paranoid schizophrenic and deemed temporarily incompetent to stand trial. Ake, 470 U.S. at 71, 105 S.Ct. 1087. After six weeks of hospitalization and medication, the trial court concluded that Ake had become competent to stand trial. Id. at 71-72, 105 S.Ct. 1087. At that time, his counsel informed the court that he would pursue an insanity defense and “asked the court either to arrange to have a psychiatrist perform the examination, or to provide funds to allow the defense to arrange one.” Id. at 72, 105 S.Ct. 1087. The trial court denied the request, finding the Constitution did not require that an “indigent defendant receive the assistance of a psychiatrist when that assistance is necessary to the defense.” Id.
In setting aside the conviction, the Ake Court held that “the Constitution requires that a State provide access to a psychiatrist’s assistance on this issue if the defendant cannot otherwise afford one.” Id. at 74, 105 S.Ct. 1087. The Ake Court, however, never addressed what would constitute “access” and whether provision of a neutral psychiatrist would be sufficient.5 Because Ake’s counsel had asked for either an independent or neutral psychiatrist, the Court did not need to address whether assistance had to be independent. The question therefore remained an open one subsequent to the Ake decision.
After Ake, the Supreme Court passed on a chance to clarify whether due process required independent psychiatric assistance. In Granviel v. Lynaugh, the Fifth Circuit concluded that Ake was satisfied when the government provided a defendant with neutral psychiatric assistance. 881 F.2d 185, 191 (5th Cir.1989); see also White v. Johnson, 153 F.3d 197, 200 n. 2 (5th Cir.1998) (treating Granviel as good law). In doing so, the Fifth Circuit deviated from the decisions of other Courts of Appeals, which had held that a defendant was entitled to independent, non-neutral psychiatric assistance. See United States v. Sloan, 776 F.2d 926, 929 (10th Cir.1985); United States v. Byers, 740 F.2d 1104, 1114 (D.C.Cir.1984) (en banc).6 The Supreme Court, however, declined to hear the case and resolve the circuit split, despite the urging of two justices to do so. Granviel v. Texas, 495 U.S. 963, 963, 110 [698]*698S.Ct. 2577, 109 L.Ed.2d 758 (1990) (Marshall, J., dissenting from denial of certiorari).
Because the Supreme Court elected not to hear Granviel, the circuit split over the scope of the right to psychiatric assistance remained unresolved when Miller’s conviction became final in 1990. As we have previously noted, a disagreement among the circuit courts is evidence that a certain matter of federal law is not clearly established. Baranksi v. Fifteen Unknoum Agents of Bureau of ATF, 452 F.3d 433, 449 (6th Cir.2006) (“[T]his disagreement among the circuits ... shows that the [government] did not violate clearly established law.”); see also Narlock v. Hofbauer, 118 Fed.Appx. 34, 35 (6th Cir. 2004) (“At the time of the petitioner’s trial ... using a defendant’s pre-Miranda silence as substantive evidence had not been addressed by the Supreme Court and was the subject of disagreement among the circuits. Hence ... there was no rule ‘clearly established’ by holdings of the Supreme Court that would have applied .... ”); Tunstall v. Hopkins, 306 F.3d 601, 611 (8th Cir.2002) (“When the federal circuits disagree on the application of [a Supreme Court precedent], it is difficult to say the [state] court’s decision is contrary to, or involved an unreasonable application of, clearly established federal law, as determined by the Supreme Court.”).
2.
Our reading of Ake and the case law that subsequently interpreted it is supported by an examination of our precedent involving the issue of independent psychiatric assistance. This case law is relevant in that it reiterates the unsettled nature of a defendant’s right to psychiatric assistance during the decades following Ake. While we cannot “rel[y] upon [our] own decision[s]” to resolve a habeas case before us under § 2254, Renico v. Lett, — U.S. -, 130 S.Ct. 1855, 1865-66, 176 L.Ed.2d 678 (2010), in this case we merely look to our precedent as “evidence” of whether “Supreme Court precedents ha[ve] clearly established a rule as of a particular time.” 2 Randy Hertz & James S. Liebman, Federal Habeas Corpus Practice and Procedure § 32.3, at 1585 n. 10 (5th ed.2005); see also Hill v. Hofbauer, 337 F.3d 706, 716 (6th Cir.2003) (“Although only Supreme Court case law is relevant under the AEDPA in examining what Federal law is ‘clearly established,’ the decisions of the United States Courts of Appeals may be informative to the extent we have already reviewed and interpreted the relevant Supreme Court case law....”). In this case, we feel that our own internal conflict about the scope of Ake evidences the reasonableness of the state court decision.
We first considered whether Ake demanded the appointment of an independent psychiatric expert, in the en banc case Kordenbrock v. Scroggy, 919 F.2d 1091 (6th Cir.1990). A number of judges in Kordenbrock opined that access to a neutral psychiatrist did not satisfy the Ake right to psychiatric assistance. Id. at 1107-08 (plurality). Other judges, however, concluded that provision of a neutral psychiatrist did satisfy Ake. Id. at 1117-18 (Kennedy, J., dissenting) {“Ake merely requires that a competent psychiatrist be provided to assist indigent defendants, not the psychiatrist of their choice.”). Both positions, however, failed to garner a majority of votes. Id. at 1135 (Nelson, J., concurring) (finding that “[b]ecause it appears that a[n independent] psychiatric expert will be provided on retrial, I do not think it is necessary for us to decide the issue” of whether the provision of a neutral psychiatrist satisfies Ake). Because the Supreme Court had also declined to hear [699]*699Granviel the year before, the issue remained unresolved in this circuit.
Our decisions subsequent to KordenbrocJc reached different conclusions about the constitutional right to independent psychiatric assistance. In 2003, a panel of our court concluded “that an indigent criminal defendant’s constitutional right to psychiatric assistance in preparing an insanity defense is not satisfied by court appointment of a ‘neutral’ psychiatrist.” Powell, 332 F.3d at 392. The same year, however, a different panel of our court deemed this language to be dicta and concluded Ake was satisfied by the appointment of a neutral psychiatrist. Smith v. Mitchell, 348 F.3d 177, 208 n. 10 (6th Cir.2003). In 2006, a third panel revived the Powell rule, noting that “this court has extended Ake to require an ‘independent’ psychiatrist rather than a neutral, court-appointed psychiatrist when a defendant’s mental health is in issue.” Carter, 443 F.3d at 526.
This examination of our own precedent indicates that, while a defendant is today entitled in this circuit to independent psychiatric assistance, this is a right that has developed in the wake of Ake and was not established by Ake itself. Even in the eases that acknowledge the right to independent psychiatric assistance, this court’s decisions have framed this right as an extension of Ake, not as a rule established by the Supreme Court’s own precedent. See Carter, 443 F.3d at 526 (noting Powell “extended Ake”)-, Powell, 332 F.3d at 392 (“Today, we join those circuits that have held that an indigent criminal defendant’s constitutional right to psychiatric assistance in preparing an insanity defense is not satisfied by court appointment of a ‘neutral’ psychiatrist....” (emphasis added)); see also Smith, 348 F.3d at 208 n. 10 (“Ake did not hold that due process requires the State to provide an independent psychiatrist, merely a competent one. The [Powell ] panel’s holding is an extension of Ake.” (internal quotation marks omitted)). And our failure to resolve the issue in Kordenbrock shows that the scope of Ake was murky even years after the Supreme Court issued its decision in that case.
The limited inquiry by the Ake Court, the subsequent circuit split that developed in the wake of Ake, the Supreme Court’s decision not to resolve the circuit split, and our own conflicted jurisprudence about the constitutional right to independent psychiatric assistance all guide us to one inevitable conclusion: even if Ake were relevant, Ake did not represent “clearly established federal law” requiring the provision of independent, non-neutral psychiatric assistance. The Tennessee court did not act unreasonably in limiting Miller’s psychiatric assistance to Dr. Gee. We affirm the district court’s decision denying Miller’s petition for habeas relief on this ground.
IV.
Miller’s second claim is that the jury instruction on the subject of malice was unconstitutional and did not amount to harmless error.7 This issue was addressed by the Tennessee Criminal Court of Appeals during Miller’s petition for post-conviction relief. The state court found that the instructions given by the trial court [700]*700impermissibly shifted the burden of proof to Miller, in violation of Sandstrom v. Montana, 442 U.S. 510, 99 S.Ct. 2450, 61 L.Ed.2d 39 (1979). Miller v. State, No. 03C01-9805-CR-00188, 1999 WL 1046415, at *4-5 (Tenn.Ct.Crim.App. Nov. 19, 1999). However, applying harmless error analysis, the court concluded that the Sandstrom error did not compel setting the conviction aside. Id. at *5. The Tennessee Supreme Court affirmed the appellate court’s decision without further comment on the Sandstrom issue. Miller v. State, 54 S.W.3d 743, 748 (Tenn.2001). These decisions are entitled to AEDPA deference.
We have previously found, and the warden concedes, that the presumption-of-malice instruction given in this case violated Sandstrom. Caldwell v. Bell, 288 F.3d 838, 841 (6th Cir.2002); Houston v. Dutton, 50 F.3d 381, 385 (6th Cir.1995). After a jury instruction is found to be unconstitutional, the court must then conduct a harmless-error analysis. Caldwell, 288 F.3d at 842. “[A]n error is not to be deemed harmless if it had a ‘substantial or injurious effect or influence in determining the jury’s verdict.’ ” Id. (quoting Brecht v. Abrahamson, 507 U.S. 619, 623, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993)). This court, however, “may not grant [Miller]’s habeas petition ... if the state court simply erred in concluding that the State’s errors were harmless; rather, habeas relief is appropriate only if the [state court] applied harmless-error review in an ‘objectively unreasonable’ manner.” Mitchell v. Esparza, 540 U.S. 12, 18, 124 S.Ct. 7, 157 L.Ed.2d 263 (2003).
Under Tennessee state law, malice is defined as an “intent to do harm or cause injury to another, but not necessarily to cause death.” Welch v. State, 836 S.W.2d 586, 591 (Tenn.Crim.App.1992). The state court concluded that the evidence presented at Miller’s trial overwhelmingly showed a finding of “ill will” indicating malice:
[t]he proof shows that [Miller] killed the victim by striking her twice with great force with a fire poker and indicates those blows were so hard they bent the poker. Prior to this, [he] had handled the victim with sufficient roughness to bruise her arms and legs. Further, [Miller] inflicted multiple lacerations of great force on the victim. The evidence clearly supports a finding of “ill will.”
Miller, 1999 WL 1046415, at *5. This assessment seems entirely reasonable. The physical evidence presented of the killing — indicating that Standifer was killed with immense force and that some of the blows were given by using a hammer-like object to drive the knife into the victim-— leads to the conclusion that the murder was committed with an intent to do harm. The government also presented Miller’s post-arrest statement in which he admitted hitting Standifer. This statement indicates that at least some of the blows were maliciously inflicted.
Miller argues that harmless error cannot be proven because the evidence as to his “mental state” was in question; essentially, he tries to argue that he lacked the ability to form the requisite intent. In support, Miller points to evidence suggesting that he was under the influence of LSD and alcohol at the time of the crime. The state court. dismissed this argument by noting that the jury had explicitly rejected intoxication as an affirmative defense and that the physical evidence overwhelmingly indicated evidence of malice. Id. Again, this assessment seems entirely reasonable. While there was testimony that Miller had taken alcohol and narcotics on the day in question, there was also testimony at trial that he appeared cogent, indicating his ability to form the requisite intent. Moreover, the physical evidence in[701]*701dicated that Miller had used a piece of rope to drag the body from the house in order to hide it, had hidden his bloodied shirt in the backyard, had tried to clean up the murder scene, and had lied to Thomas, the homeowner, about the source of the blood in the house (Miller claimed he received a bloody nose in a fight). This evidence strongly indicates that Miller was in control of his senses at the time of the crime and was aware of what was occurring; it seems exceedingly improbable that he could have “los[t] contact with reality,” as Miller claims he had, and yet have acted so deliberately to hide evidence of the crime.
Based on these facts, it was reasonable for the state court to conclude that the evidence of Miller’s intoxication was insufficient for a jury to conclude that he lacked the intent to kill or seriously injure. It was therefore also reasonable for the state court to conclude that the court’s errant jury instruction regarding malice was harmless. As a result, the district court was correct to reject Miller’s petition for habeas corpus on this ground.
V.
For the reasons stated above, we affirm the decision of the district court, and Miller’s petition for the writ of habeas corpus is denied.