Interaction-Induced Criticality in<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>Topological Insulators

Ostrovsky, P. M.; Gornyi, I. V.; Mirlin, A. D.

doi:10.1103/physrevlett.105.036803

Cited by 137 publications

(192 citation statements)

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“…If the bulk were simply a trivial insulator it would be inert and no further considerations would be required. However, it is known that topological insulators react to the presence of thin flux tubes 13,14 , which can generate a "worm-hole" effect that traps low-energy states on the flux tube. This is of particular concern as the simplest approach to create vortices in a 3D topological insulator -s-wave superconductor would be to coat the surface of the 3D topological insulator with a type-II s-wave superconductor and then use magnetic flux tubes generated by an applied magnetic field to proliferate the vortices, which would then contain the Majorana states.…”

Section: Introductionmentioning

confidence: 99%

Vortex lines in topological insulator-superconductor heterostructures

2011

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3D topological insulator/s-wave superconductor heterostructures have been predicted as candidate systems for the observation of Majorana fermions in the presence of superconducting vortices. In these systems, Majorana fermions are expected to form at the interface between the topological insulator and the superconductor while the bulk plays no role. Yet the bulk of a 3D topological insulator penetrated by a magnetic flux is not inert and can gap the surface vortex modes destroying their Majorana nature. In this work, we demonstrate the circumstances under which only the surface physics is important and when the bulk physics plays an important role in the location and energy of the Majorana modes.

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Section: Introductionmentioning

confidence: 99%

Vortex lines in topological insulator-superconductor heterostructures

2011

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“…Recently, there has been considerable interest in understanding the nature of such topological transition in the two-dimensional HgCdTe quantum well [7] and three dimensional materials such as BiTl(S 1−δ Se δ ) 2 [8,9] and (Bi 1−x In x ) 2 Se 3 [10,11]. Although the phase diagram of noninteracting, disordered systems has been investigated in many analytical and numerical works [12][13][14][15][16][17][18][19][20] and the interplay of disorder and long range Coulomb interactions has also been studied perturbatively for both two [14] and three dimensions [16], the effects of strong short range electronic interactions on the phase diagram of clean AII insulators is not well understood. The investigation of this fundamental problem is the central theme of this Rapid Communication.…”

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confidence: 99%

Continuous and discontinuous topological quantum phase transitions

Roy

Goswami

2016

Phys. Rev. B

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The continuous quantum phase transition between noninteracting, time-reversal symmetric topological and trivial insulators in three dimensions is described by the massless Dirac fermion. We address the stability of this quantum critical point against short range electronic interactions by using renormalization group analysis and mean field theory. For sufficiently weak interactions, we show that the nature of the direct transition remains unchanged. Beyond a critical strength of interactions we find that either (i) there is a direct first order transition between two time reversal symmetric insulators or (ii) the direct transition is eliminated by an intervening time reversal and inversion odd "axionic" insulator. We also demonstrate the existence of an interaction driven first order quantum phase transition between topological and trivial gapped states in lower dimensions. Introduction: The spin-orbit coupled, time reversal symmetric insulators in two and three dimensions belong to the Altland-Zirnbauer class AII [1,2]. Due to the existence of nontrivial Z 2 topological invariants in both spatial dimensions, a band insulator can be classified either as a strong topological insulator (TI) or a trivial/normal insulator (NI). The four component massive Dirac fermion provides an efficient low energy description of Kramers degenerate conduction and valence bands in such systems [3][4][5][6]. The sign of the Dirac mass provides the topological distinction between two insulating states. In a clean, noninteracting system the universality class of a continuous topological quantum phase transition (QPT) between them (where the Dirac mass vanishes) is described by a massless Dirac Hamiltonian. Recently, there has been considerable interest in understanding the nature of such topological transition in the two-dimensional HgCdTe quantum well [7] and three dimensional materials such as BiTl(S 1−δ Se δ ) 2 [8,9] and (Bi 1−x In x ) 2 Se 3 [10,11]. Although the phase diagram of noninteracting, disordered systems has been investigated in many analytical and numerical works [12][13][14][15][16][17][18][19][20] and the interplay of disorder and long range Coulomb interactions has also been studied perturbatively for both two [14] and three dimensions [16], the effects of strong short range electronic interactions on the phase diagram of clean AII insulators is not well understood. The investigation of this fundamental problem is the central theme of this Rapid Communication.

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“…The 3D topological insulators (TIs) discovered in recent years [6,7] provide novel types of 2D electron systems that are of particular interest for study of the localization-delocalization problem. The Dirac surface states of 3D TIs are believed to be topologically protected from localization due to its special symmetry class [8][9][10][11][12]. Moreover, when a 3D TI thin film is sufficiently thin, the hybridization between the top and the bottom surface states opens an energy gap near the Dirac point [13], and it is suggested theoretically that the hybridization gap would drive the electron system to topologically different phase, such as a quantum spin Hall insulator or a trivial band insulator [14][15][16].…”

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confidence: 99%

Observation of Anderson Localization in Ultrathin Films of Three-Dimensional Topological Insulators

Liao

Feng

et al. 2015

Phys. Rev. Lett.

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Anderson localization, the absence of diffusive transport in disordered systems, has been manifested as hopping transport in numerous electronic systems, whereas in recently discovered topological insulators it has not been directly observed. Here we report experimental demonstration of a crossover from diffusive transport in the weak antilocalization regime to variable range hopping transport in the Anderson localization regime with ultrathin (Bi1−xSbx)2Te3 films. As disorder becomes stronger, negative magnetoconductivity due to the weak antilocalization is gradually suppressed, and eventually positive magnetoconductivity emerges when the electron system becomes strongly localized. This works reveals the critical role of disorder in the quantum transport properties of ultrathin topological insulator films, in which theories have predicted rich physics related to topological phase transitions.The concept of Anderson localization has profoundly influenced our understanding of electron conductivity [1]. While examples for disorder driven metal-insulator transition are abundant in three-dimensions (3D), the question of whether Anderson transitions exist in 2D has posed a lot of theoretical and experimental challenges. Scaling theory proposed by Abrahams et al. predicts that there are no truly metallic states in non-interacting 2D electron systems [2,3]. It was, however, discovered later that extended electron states may exist when electronelectron (e-e) interaction, spin-orbit coupling (SOC) or magnetic field comes in to play [4,5]. The 3D topological insulators (TIs) discovered in recent years [6,7] provide novel types of 2D electron systems that are of particular interest for study of the localization-delocalization problem. The Dirac surface states of 3D TIs are believed to be topologically protected from localization due to its special symmetry class [8][9][10][11][12]. Moreover, when a 3D TI thin film is sufficiently thin, the hybridization between the top and the bottom surface states opens an energy gap near the Dirac point [13], and it is suggested theoretically that the hybridization gap would drive the electron system to topologically different phase, such as a quantum spin Hall insulator or a trivial band insulator [14][15][16]. Even though a lot of work has been carried out on electron transport properties of TI thin films [17][18][19][20], the fate of such electron systems under the condition of strong disorder (or in other words, whether Anderson localization could take place), still remains unclear.In this work, we have studied electron transport in a large number of highly gate-tunable TI thin films with various thicknesses and chemical compositions. We found that only in ultrathin TI films in which surface hybridization and disorder effects are significant, hopping transport, a hallmark of strong localization [21][22][23], can be observed. The observed temperature and magnetic field dependences of conductivity suggest that electron transport can be driven from the diffusive transport governed by we...

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Interaction-Induced Criticality inZ2Topological Insulators

Cited by 137 publications

References 59 publications

Vortex lines in topological insulator-superconductor heterostructures

Vortex lines in topological insulator-superconductor heterostructures

Continuous and discontinuous topological quantum phase transitions

Observation of Anderson Localization in Ultrathin Films of Three-Dimensional Topological Insulators

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