Effect of strong disorder in a three-dimensional topological insulator: Phase diagram and maps of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>invariant

Leung, Bryan; Prodan, Emil

doi:10.1103/physrevb.85.205136

Cited by 36 publications

(38 citation statements)

References 58 publications

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“…Support for this picture can be drawn from Ref. 52, in which careful numerical simulations on a disordered lattice model showed a finite-width region of metallic phase as the system was driven from the TI to the NI phase with increasing disorder strength while other parameters were held fixed. In our case the disorder strength remains approximately constant, but the ratio of disorder strength to energy gap varies with x, so that a metallic plateau may still be expected.…”

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confidence: 88%

Topological phase transitions in (Bi1−xInx)2Se
Liu
¹
,
Vanderbilt
²

2013
Phys. Rev. B

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We study the phase transition from a topological to a normal insulator with concentration x in (Bi1−xInx)2Se3 and (Bi1−xSbx)2Se3 in the Bi2Se3 crystal structure. We carry out first-principles calculations on small supercells, using this information to build Wannierized effective Hamiltonians for a more realistic treatment of disorder. Despite the fact that the spin-orbit coupling (SOC) strength is similar in In and Sb, we find that the critical concentration xc is much smaller in (Bi1−xInx)2Se3 than in (Bi1−xSbx)2Se3. For example, the direct supercell calculations suggest that xc is below 12.5% and above 87.5% for the two alloys respectively. More accurate results are obtained from realistic disordered calculations, where the topological properties of the disordered systems are understood from a statistical point of view. Based on these calculations, xc is around 17% for (Bi1−xInx)2Se3, but as high as 78%-83% for (Bi1−xSbx)2Se3. In (Bi1−xSbx)2Se3, we find that the phase transition is dominated by the decrease of SOC, with a crossover or "critical plateau" observed from around 78% to 83%. On the other hand, for (Bi1−xInx)2Se3, the In 5s orbitals suppress the topological band inversion at low impurity concentration, therefore accelerating the phase transition. In (Bi1−xInx)2Se3 we also find a tendency of In atoms to segregate.

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confidence: 88%

Topological phase transitions in (Bi1−xInx)2Se
Liu
¹
,
Vanderbilt
²

2013
Phys. Rev. B

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“…This characteristic has been indeed observed numerically for several symmetry classes. [11][12][13][14][15][16] However, a recent study 1 on the AIII symmetry class revealed that, in this particular case, the entire energy spectrum becomes localized as soon as the disorder is turned on, and it stays localized until an Anderson localization-delocalization transition builds up (from this entirely localized spectrum!) while crossing from one topological phase to another.…”

Section: Introductionmentioning

confidence: 99%

AIII and BDI topological systems at strong disorder

Song

Prodan

2014

Phys. Rev. B

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Using an explicit 1-dimensional model, we provide direct evidence that the one-dimensional topological phases from the AIII and BDI symmetry classes follow a Z-classification, even in the strong disorder regime when the Fermi level is embedded in a dense localized spectrum. The main tool for our analysis is the winding number ν, in the non-commutative formulation introduced in I. Mondragon-Shem, J. Song, T. L. Hughes, and E. Prodan, arXiv:1311.5233. For both classes, by varying the parameters of the model and/or the disorder strength, a cascade of sharp topological transitions ν = 0 → ν = 1 → ν = 2 is generated, in the regime where the insulating gap is completely filled with the localized spectrum. We demonstrate that each topological transition is accompanied by an Anderson localization-delocalization transition. Furthermore, to explicitly rule out a Z 2 classification, a topological transition between ν = 0 and ν = 2 is generated. These two phases are also found to be separated by an Anderson localization-delocalization transition, hence proving their distinct identity.

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“…As noted by several authors, 22,23,[28][29][30][31] disorder produces a phase transition between the topological insulator phase and a gapless metallic phase. This can be seen most directly using the self-consistent Green function, given by Eqs.…”

Section: Gapless Topological Phasementioning

confidence: 99%

“…[19][20][21][22][23] Studies of disorder led to additional surprises: It was shown that disorder can induce topological behavior in some trivial insulators, [24][25][26][27] and (more importantly for the current work) that disorder may close the gap in topological insulators, leading to a metallic phase. [28][29][30][31][32] In our work, we focus on the disorder-induced metallic phase in a simple test case of the Kane-Mele-Haldane honeycomb model. 1,33 Naively, once the disorder destroys the gap of a topological insulator, a simple metal emerges.…”

Section: Introductionmentioning

confidence: 99%

Disordered topological metals

Meyer

Refael

2013

Phys. Rev. B

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Topological behavior can be masked when disorder is present. A topological insulator, either intrinsic or interaction induced, may turn gapless when sufficiently disordered. Nevertheless, the metallic phase that emerges once a topological gap closes retains several topological characteristics. By considering the self-consistent disorder-averaged Green function of a topological insulator, we derive the condition for gaplessness. We show that the edge states survive in the gapless phase as edge resonances and that, similar to a doped topological insulator, the disordered topological metal also has a finite, but nonquantized topological index. We then consider the disordered Mott topological insulator. We show that within mean-field theory, the disordered Mott topological insulator admits a phase where the symmetry-breaking order parameter remains nonzero but the gap is closed, in complete analogy to "gapless superconductivity" due to magnetic disorder.

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Effect of strong disorder in a three-dimensional topological insulator: Phase diagram and maps of theZ2invariant

Cited by 36 publications

References 58 publications

Topological phase transitions in (Bi1−xInx)2Se
Liu
¹
,
Vanderbilt
²

2013
Phys. Rev. B

Topological phase transitions in (Bi1−xInx)2Se
Liu
¹
,
Vanderbilt
²

2013
Phys. Rev. B

AIII and BDI topological systems at strong disorder

Disordered topological metals

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Effect of strong disorder in a three-dimensional topological insulator: Phase diagram and maps of theZ2invariant

Cited by 36 publications

References 58 publications

Topological phase transitions in (Bi1−xInx)2SeLiu1, Vanderbilt2 2013Phys. Rev. B

Topological phase transitions in (Bi1−xInx)2SeLiu1, Vanderbilt2 2013Phys. Rev. B

AIII and BDI topological systems at strong disorder

Disordered topological metals

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Product

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About

Topological phase transitions in (Bi1−xInx)2Se
Liu
¹
,
Vanderbilt
²

2013
Phys. Rev. B

Topological phase transitions in (Bi1−xInx)2Se
Liu
¹
,
Vanderbilt
²

2013
Phys. Rev. B