BYBEE, Circuit Judge.

We must decide whether a state court's failure to hold an evidentiary hearing sua sponte when presented with evidence of juror bias is contrary to, or an unreasonable application of, clearly established federal law as determined by the United States Supreme Court. 28 U.S.C. § 2254(d)(1) (2000). We hold that it is not. Accordingly, we affirm the decision of the district court denying the appellant's petition for a writ of habeas corpus.

I

The appellant, Michael Sims, was charged in California Superior Court with, inter alia, one count of first degree robbery and two counts of second degree robbery with enhancements for infliction of great bodily injury. See CAL. PENAL CODE §§ 211, 12022.7. Several hours after his case was submitted to the jury for deliberation, the court received a note from the jury foreman reading as follows:

We the jury in this case request the following: Discussion about the forms we filled out before jury selection. There's considerable alarm among jurors about Mr. Simms [sic] being allowed to review our forms. We thought we were under the protection of anonymity. The jurors viewed he was talking [sic] notes while reviewing the forms.

With both the prosecutor and defense counsel's written approval, the trial judge responded with the following note:

In response to your most recent request, please be advised that none of the parties ever had your addresses or telephone numbers or other identifying information. . . . You will also recall that at the commencement of the jury selection process I informed you that the court reporter's transcript relating to that portion of the trial is ordered to be sealed and not made available to any party or person, unless good cause is shown. . . . Likewise, the copies of the juror's questionnaire that the district attorney and the defense attorney had during the jury selection process, was ordered by the court to be returned to the clerk and those copies have been shredded and destroyed. I hope that this is a satisfactory answer to your inquiry. If it is not, please send me a further communication.

Subsequently, the jury sent a second note, this time requesting "a copy of the questionnaire that the defense attorney/defendant did get to see — even a blank form." The note further inquired as to whether the juror's "names, [and/or] places of employment [were] blocked out," expressing lingering concern "about whether [their] names and employers were on the form." Again with the approval of both parties, the judge responded by providing the jurors a blank questionnaire. The record does not indicate that the judge held a hearing, formal or informal, prior to either response, or that defense counsel requested such a hearing.

Approximately one hour after the judge's second response, the jury reached a verdict, finding Sims guilty of two counts of second degree robbery and one count of first degree robbery. Sims was sentenced to an aggregate term of sixty-three years to life.

Shortly thereafter, Sims sought review by the California Court of Appeal, arguing that his conviction violated his Fourteenth Amendment due process rights. The court rejected this claim, concluding that Sims had not established that his verdict was negatively influenced by the jurors' fear of recourse. See People v. Sims, No. A079107, at *9 (Cal.Ct.App. Dec. 17, 1999). On the contrary, the court reasoned that a "much stronger hypothesis is that, if fear influenced the jurors at all, it was in the direction of acquittal." Id. at *11 (emphasis in original). Accordingly, the court denied Sims's due process claim, holding that "any error in not conducting a formal inquiry into whether jurors were improperly influenced by fear of Sims is not shown to be prejudicial." Id. The California Supreme Court denied review.

Sims next petitioned the United States District Court for the Northern District of California for a writ of habeas corpus, reasserting his due process claim. Relying on our decision in Tracey v. Palmateer, 341 F.3d 1037, 1045 (9th Cir. 2003), the district court denied the petition, reasoning that due process does not require the trial court to question the jurors any time evidence of juror bias comes to light. See Sims v. Rowland, No. C-01-2355 MMC, 2003 WL 22384777 (N.D.Cal. Oct.14, 2003) (Order Denying Petition for Writ of Habeas Corpus). In addition, the court observed that, even assuming that the trial judge erred by not questioning the jurors as to whether fear of Sims affected their deliberations, Sims had not demonstrated that the error prejudiced him. Id. at *8 (citing Brecht v. Abrahamson, 507 U.S. 619, 638, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993)). Accordingly, the court held that the state court's decision denying post-conviction relief was not objectively unreasonable.

Sims timely appealed to this court.

II

This court reviews de novo a district court's denial of a petition for a writ of habeas corpus. See Alvarado v. Hill, 252 F.3d 1066, 1068 (9th Cir. 2001). It is undisputed that the Antiterrorism and Effective Death Penalty Act of 1996, Pub.L. No. 104-132, 110 Stat. 1214 (1996) ("AEDPA"), governs our review of the California state court's decision denying post-conviction relief on the merits.

Under AEDPA, Sims is entitled to habeas relief "with respect to any claim that was adjudicated on the merits in State court proceedings" only if one of two conditions of deferential review are met: "the 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 of the United States; 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 proceeding." 28 U.S.C. § 2254(d)(1)-(2). See also Lambert v. Blodgett, 393 F.3d 943, 973-74 (9th Cir. 2004). In this appeal, Sims argues that the California Court of Appeal's decision was both contrary to, as well as an unreasonable application of, clearly established federal law.

The phrase "clearly established Federal law" refers to the holdings, as opposed to the dicta, of Supreme Court decisions. See Lockyer v. Andrade, 538 U.S. 63, 71, 123 S.Ct. 1166, 155 L.Ed.2d 144 (2003) (citing Williams v. Taylor, 529 U.S. 362, 412, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000)); Lambert, 393 F.3d at 974. A state court decision is contrary to clearly established federal law if the state court either applies a rule that contradicts the governing law set forth by the Supreme Court or arrives at a different result when confronted by a set of facts that are materially indistinguishable from a decision of the Supreme Court. See Williams, 529 U.S. at 405-06, 120 S.Ct. 1495.

Although the statutory formulation restricts federal law to Supreme Court precedent, we have previously observed that "Ninth Circuit precedent may be persuasive authority for purposes of determining whether a particular state court decision is an unreasonable application of Supreme Court law, and may also help us determine what law is clearly established." Robinson v. Ignacio, 360 F.3d 1044, 1057 (9th Cir. 2004) (citing Duhaime v. Ducharme, 200 F.3d 597, 600 (9th Cir. 1999)) (internal quotations omitted). However, the Court has emphasized that "[a] federal court may not overrule a state court for simply holding a view different from its own, when the precedent from [the Supreme] Court is, at best, ambiguous." Mitchell v. Esparza, 540 U.S. 12, 17, 124 S.Ct. 7, 157 L.Ed.2d 263 (2003) (per curiam). Thus, "[a]lthough lower federal court and state court precedent may be relevant when that precedent illuminates the application of clearly established federal law as determined by the United States Supreme Court, if it does not do so, it is of no moment." Casey v. Moore, 386 F.3d 896, 907 (9th Cir. 2004). See also Hernandez v. Small, 282 F.3d 1132, 1140 (9th Cir. 2002) ("[D]ecisions of [the Supreme] Court are the only ones that can form the basis justifying habeas relief; `lower federal courts cannot themselves establish such a principle with clarity sufficient to satisfy the AEDPA bar.'") (citing Williams, 529 U.S. at 381, 120 S.Ct. 1495). In short, our reference to Ninth Circuit precedent cannot be used to circumvent the requirement that, in order to grant the writ, we must be persuaded that the state court's decision is contrary to clearly established Supreme Court precedent.

AEDPA also permits relief where the state court's adjudication "resulted in a decision that . . . 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). Importantly, "an unreasonable application of federal law is different from an incorrect application of federal law." Williams, 529 U.S. at 410, 120 S.Ct. 1495. See also id. at 411, 120 S.Ct. 1495 ("a federal habeas court may not issue the writ simply because that court concludes in its independent judgment that the relevant state-court decision applied clearly established federal law erroneously or incorrectly.") A state court decision is an unreasonable application of Supreme Court precedent when the court applies those precedents to the facts in an objectively unreasonable manner. See Brown v. Payton, 544 U.S. ___, ___, 125 S.Ct. 1432, 161 L.Ed.2d 334 (2005) (citing Williams, 529 U.S. at 405, 120 S.Ct. 1495). This phrase also encompasses an unreasonable failure to extend the holding or legal principle of a Supreme Court decision to a situation in which it "should have controlled." Ramdass v. Angelone, 530 U.S. 156, 166, 120 S.Ct. 2113, 147 L.Ed.2d 125 (2000) (plurality opinion).

We apply these principles and standards of review to address Sims's argument that the decision of the California Court of Appeals was both contrary to, and an unreasonable application of, clearly established federal law.

A

Sims first argues that the decision of the California Court of Appeal is contrary to clearly established federal law because the court's reason for denying his due process claim — namely, because he failed to demonstrate prejudice — was erroneous. Specifically, he argues that the state trial court's failure to investigate potential juror bias presents structural error which requires a new trial even where there is no showing of actual prejudice.

Sims's assertion is supported to some extent by our decision in Dyer v. Calderon, wherein we noted the similarities to a biased judge and stated that "[t]he presence of a biased juror cannot be harmless; the error requires a new trial without a showing of actual prejudice." 151 F.3d 970, 973 n. 2 (9th Cir. 1998) (en banc) (citing United States v. Allsup, 566 F.2d 68, 71 (9th Cir. 1977)). Indeed, trial before a biased judge is an archetypal example of a constitutional error that necessarily renders a trial fundamentally unfair and, for that reason, is not amenable to harmless error analysis. See Neder v. United States, 527 U.S. 1, 8, 119 S.Ct. 1827, 144 L.Ed.2d 35 (1999) (noting that the Supreme Court has found "an error to be `structural', and thus subject to automatic reversal, only in a `very limited class of cases'," and citing Tumey v. Ohio, 273 U.S. 510, 47 S.Ct. 437, 71 L.Ed. 749 (1927), for the proposition that trial before a biased judge presents such a case). Yet, we have never held that the failure to investigate potential juror bias presents structural error. Cf. United States v. Dutkel, 192 F.3d 893, 899 n. 4 (9th Cir. 1999) (acknowledging that jury tampering presents trial error); Thompson v. Borg, 74 F.3d 1571, 1574 (9th Cir. 1996) (concluding that a venireman's prejudicial remark during jury selection presents trial error).

More importantly, no Supreme Court precedent holds that a failure to investigate potential juror bias presents structural error, and even if we were to read Dyer to address potential juror bias, it would be insufficient authority under AEDPA. See Hernandez, 282 F.3d at 1140. Although the Supreme Court recognized in Tumey v. Ohio that a trial before a biased judge presents structural error, it has not applied this principle to trials by biased jurors, much less in cases where there is only potential bias. 273 U.S. 510, 47 S.Ct. 437, 71 L.Ed. 749 (1927).

Accordingly, it remains for us to decide whether the state court's failure to hold an evidentiary hearing sua sponte when presented with evidence of juror bias is contrary to, or an unreasonable application of, clearly established federal law as determined by the United States Supreme Court. 28 U.S.C. § 2254(d)(1). We hold that it is not. The reason is simple: the Supreme Court has not yet decided whether due process requires a trial court to hold a hearing sua sponte whenever evidence of juror bias comes to light.

B

The Supreme Court has twice addressed the propriety of holding a hearing to investigate evidence of juror bias. See Remmer v. United States, 347 U.S. 227, 74 S.Ct. 450, 98 L.Ed. 654 (1954); Smith v. Phillips, 455 U.S. 209, 102 S.Ct. 940, 71 L.Ed.2d 78 (1982). Neither case mandates a hearing whenever evidence of juror bias is raised; nor does either case address the situation presented here, where no party has requested a hearing to investigate evidence of juror bias.

In Remmer, 347 U.S. at 228, 74 S.Ct. 450, a juror in a federal criminal trial reported to the trial judge that he had been contacted by a third party and told that he (the juror) could profit from bringing in a verdict favorable to the petitioner. The judge alerted the prosecution, but not the defense, to this evidence.

After the FBI investigated the incident, both the judge and the prosecution reviewed the FBI report, without notice to or participation by the defense, and "apparently concluded that the statement to the juror was made in jest." Id. at 228, 74 S.Ct. 450. Nothing further was done or said about the matter. After the verdict was returned, the petitioner became aware of the investigation and requested a hearing on the issue of possible bias. He also moved for a new trial. The district court denied the motion without holding the requested hearing. Under these circumstances, the Court stated that the trial court should not have decided "and take[n] final action ex parte on information such as was received in this case, but should determine the circumstances, the impact thereof upon the juror, and whether or not it was prejudicial, in a hearing with all interested parties permitted to participate." Id. at 229-30, 74 S.Ct. 450. Accordingly, the Court remanded to the district court with instructions to hold a hearing, in which all parties could participate, on the issue of possible juror bias.

Remmer provides little prospective guidance as to when a hearing is required or even appropriate. One might argue that Remmer stands for the proposition that when confronted with evidence of jury tampering and an explicit request for a hearing on the issue of juror bias, the trial court must hold the requested hearing. See Tracey v. Palmateer, 341 F.3d 1037, 1044 (9th Cir. 2003) (" Remmer's command that hearings are warranted in every case is unique to the tampering context, where the potential effect on the jury is severe.") (emphasis in original). A similarly plausible reading posits that the Remmer Court merely condemned the ex parte manner in which the trial judge and the prosecutor handled the situation without the knowledge of the defendant or his counsel. In either case, such a rule would have little application in a context such as this, where there are no allegations of jury tampering and the defendant not only fails to request a hearing but, through counsel, ostensibly approves of the manner in which the trial judge responds to evidence of juror bias.

Nearly thirty years later, the Supreme Court revisited the issue of juror bias, this time in the habeas context. See Smith, 455 U.S. at 214-16, 102 S.Ct. 940. Smith involved a juror who, during the pendency of a state court trial, applied to the state District Attorney's office for employment as an investigator. Id. at 212, 102 S.Ct. 940. With full knowledge of the juror's application, the prosecution opted not to inform the court or defense counsel until after the verdict was returned. Id. at 212-13, 102 S.Ct. 940. Once informed of the application, the defendant moved to set aside the verdict. Id. at 213, 102 S.Ct. 940. The trial court held a hearing on the motion, at which both the prosecution and the juror testified. Id. Afterwards, the court determined that the juror was not, in fact, biased as a result of his application and no evidence suggesting a "sinister or dishonest motive" on the part of the prosecuting attorneys existed. Id. at 214, 102 S.Ct. 940. Finding the trial court's hearing insufficient, the federal district court subsequently granted habeas relief, ordering a new trial, and the Second Circuit Court of Appeals affirmed. Id.

The Supreme Court reversed, finding the trial court's hearing sufficient to comply with due process. The bulk of the Court's opinion was devoted to justifying the adequacy, as a matter of due process, of the hearing conducted in the state trial court. See id. at 215, 102 S.Ct. 940 ("This Court has long held that the remedy for allegations of juror partiality is a hearing in which the defendant has the opportunity to prove actual bias."). The Court emphasized that, rather than ordering a new trial whenever allegations of juror bias are raised, "determinations [of juror bias] may properly be made at a hearing like that ordered in Remmer and held in this case." Id. at 217, 102 S.Ct. 940. Observing that "in the federal system a post-trial hearing such as that conducted here is sufficient to decide allegations of juror partiality," the Court declined to require a state to do more in order to comply with the Due Process Clause of the Fourteenth Amendment. Id. at 218, 102 S.Ct. 940 (emphasis added). By focusing on the sufficiency of the procedures employed by the state trial court at the defendant's request, Smith did not answer or even comment on the constitutional question presented in this case: whether a hearing is required whenever evidence of juror bias is brought to light despite the absence of a request from defense counsel.

Nonetheless, Sims points to Remmer and Smith in support of his argument that the decision of the California Appeals Court is contrary to, or an unreasonable application of, clearly established Supreme Court precedent. We find no support for this proposition in either case.

C

We have previously addressed the question of whether a hearing is required whenever evidence of juror bias is brought to light. In Tracey, 341 F.3d at 1044, we concluded that " Remmer and Smith do not stand for the proposition that any time evidence of juror bias comes to light, due process requires the trial court to question the jurors alleged to have bias." Rather, we concluded that when read in combination, these cases provide "a flexible rule." Id. The elasticity of this rule is reflected in our own cases interpreting the Fifth Amendment's Due Process Clause, which uniformly hold that a federal court is not required to hold a hearing in order to comply with due process, but should "consider the content of the allegations, the seriousness of the alleged misconduct or bias, and the credibility of the source" when determining whether a hearing is required. Id. (citing United States v. Angulo, 4 F.3d 843, 847 (9th Cir. 1993)). See also United States v. Hanley, 190 F.3d 1017, 1031 (9th Cir. 1999) (concluding that the district court complied with due process despite its refusal to hold an evidentiary hearing where "[i]t considered the content and the seriousness of the alleged statements [of juror bias] and properly determined that such vague statements did not expose Defendants to unfair prejudice"); United States v. Langford, 802 F.2d 1176, 1180 (9th Cir. 1986) ("While we recognize that where a trial court learns of a possible incident of jury misconduct, it is preferable to hold an evidentiary hearing . . . not every allegation [of misconduct] requires a full-dress hearing"); United States v. Halbert, 712 F.2d 388, 389 (9th Cir. 1983) (affirming the district court's refusal to hold a hearing regarding extraneous information considered by a juror when the district court knew the exact scope and nature of the information). It would be anomalous to require more of a state trial judge in order to comply with the Fourteenth Amendment's Due Process Clause. See Smith, 455 U.S. at 218, 102 S.Ct. 940 ("[I]f in the federal system a post-trial hearing such as that conducted here is sufficient to decide allegations of juror partiality, the Due Process Clause of the Fourteenth Amendment cannot possibly require more of a state court system.").

In sum, contrary to Sims's argument, Remmer does not speak to the issue presented here, and " Smith leaves open the door as to whether a hearing is always required and what else may be `sufficient' to alleviate any due process concerns." Tracey, 341 F.3d at 1044. Thus, we are persuaded that Smith and Remmer do not stand for the proposition that a hearing is required in every case of potential juror bias.

Our ruling in Dyer, 151 F.3d at 973, is not to the contrary. In Dyer we held that

[a] court confronted with a colorable claim of juror bias must undertake an investigation of the relevant facts and circumstances. An informal in camera hearing may be adequate for this purpose; due process requires only that all parties be represented, and that the investigation be reasonably calculated to resolve the doubts raised about the juror's impartiality. So long as the fact-finding process is objective and reasonably explores the issues presented, the state trial judge's findings based on that investigation are entitled to a presumption of correctness.

Id. at 974-75 (citations omitted). Rather than establishing a "hard-and-fast rule requiring [an] automatic, full-fledged hearing," Tracey, 341 F.3d at 1044 n. 4, our decision in Dyer merely observed that the Fourteenth Amendment Due Process Clause forbids a trial judge from remaining idle in the face of evidence indicating probable juror bias. The extent of "investigation" required to comply with due process was not addressed. Thus, even if AEDPA permitted us to grant habeas relief where the state court decision is contrary to clearly established Ninth Circuit precedent, we could not do so in this case. Although "Ninth Circuit precedent may be persuasive authority for purposes of determining whether a particular state court decision is an unreasonable application of Supreme Court law," Robinson, 360 F.3d at 1057 (internal quotations omitted), in this case it only persuades us that federal law on this issue is not clearly established as required by AEDPA. See 28 U.S.C. § 2254(d)(1).

Furthermore, the state court's decision cannot be deemed contrary to Smith and Remmer under the second basis provided for in Williams, as neither case controls the outcome of this appeal. See Williams, 529 U.S. at 405-06, 120 S.Ct. 1495 (reasoning that a state court's decision is contrary to clearly established federal law if the state court is confronted by a set of facts that are materially indistinguishable from a decision of the Supreme Court but arrives at a different result). Rather, both cases are easily distinguished.

First, in both Smith and Remmer the defendant explicitly requested that the trial court conduct a hearing on the issue of juror bias. No such request was made in this case. Indeed, in Sims's case, unlike in Smith and Remmer, defense counsel approved, in writing, the form and content of the trial judge's response to the evidence of juror bias. The Supreme Court has not yet ruled on a trial judge's duty in the face of such approval. Finally, Remmer — the only case in which the Supreme Court actually ordered a hearing — is categorically different from the case at bar, as it concerned allegations of outright jury tampering sufficient to prompt an FBI investigation. Sims has alleged, at most, incidental and unintentional juror influence.

Because the California Court of Appeal did not either apply a rule that contradicts the governing law set forth by the Supreme Court or arrive at a different result when confronted by a set of facts that are materially indistinguishable from a decision of the Supreme Court, we hold that the state court's decision, denying petitioner's due process claim on the merits, is not contrary to clearly established federal law as determined by the Supreme Court. See 28 U.S.C. § 2254(d)(1).

D

For similar reasons, the state court's decision cannot be deemed an "unreasonable application" of Smith and Remmer to the facts of Sims's case. See Williams, 529 U.S. at 409, 120 S.Ct. 1495 (observing that a state court decision is an unreasonable application of Supreme Court precedent when the court applies those precedents to the facts in an objectively unreasonable manner). Sims argues that despite his counsel's approval of the judge's response to the evidence of juror bias, the trial judge had an affirmative and independent duty to conduct an investigation into the potential bias and he failed to do so. Specifically, Sims argues that the judge should have, at least, held an informal hearing to inquire into the bias and admonish the jurors.

We have not been directed to, nor can we identify, any decision of the Supreme Court that can rationally be understood to stand for the proposition that a trial judge has a duty, sua sponte, to conduct a hearing when presented with facts such as those alleged by Sims. Instead of referring us to a clear statement by the Supreme Court establishing a trial judge's sua sponte duty to hold some type of hearing — or, indeed, a hearing at all — Sims relies on two patently equivocal words in Smith: due process requires "a trial judge ever watchful to prevent prejudicial occurrences and to determine the effect of such occurrences when they happen." Smith, 455 U.S. at 217, 102 S.Ct. 940 (emphasis added). From these words Sims would have us find an affirmative and independent duty, on the part of a trial judge, to hold a hearing to investigate any evidence suggesting the possibility of juror bias, as a matter of Supreme Court law. We decline to infer such a rule from two words written in a different context.

It is simply untenable for us to conclude that the state court was "objectively unreasonable" in refusing to find that the trial judge was required to hold a hearing in this case when we ourselves have clearly stated that a hearing is "not mandated every time there is an allegation of juror bias." Tracey, 341 F.3d at 1044. In short, AEDPA does not permit us to conclude that the state court's denial of Sims's due process claim on the merits was an unreasonable application of clearly established federal law as determined by the Supreme Court. See 28 U.S.C. § 2254(d)(1).

Accordingly, we hold that it was not an objectively unreasonable application of federal law for the California Court of Appeal to refrain from imposing a sua sponte duty to conduct a hearing as a matter of Fourteenth Amendment due process.

III

We hold that the decision of the California Court of Appeal is not contrary to, nor 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 affirm the district court's decision denying Appellant's petition for a writ of habeas corpus.

AFFIRMED.