Absence of localization in a class of topological systems

Castro, Eduardo V.; Gail, R. de; Sancho, M. P. López; Vozmediano, María A. H.

doi:10.1103/physrevb.93.245414

Cited by 17 publications

(19 citation statements)

References 37 publications

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“…Disorder initially closes the gap between the bands and smears out the Van Hove singularities, thereby erasing any of the remaining band features. For large disorder the extended states contributing to the Chern number annihilate and the system becomes localized 35,36 . At this stage we expect no signif- icant difference in the density of states of the four points as seen in Fig.…”

Section: Disorder-averaged Entanglement Entropy and Density Of Stmentioning

confidence: 99%

Interplay between topology and disorder in a two-dimensional semi-Dirac material

2018

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We investigate the role of disorder in a two-dimensional semi-Dirac material characterized by a linear dispersion in one direction and a parabolic dispersion in the orthogonal direction. Using the self-consistent Born approximation, we show that disorder can drive a topological Lifshitz transition from an insulator to a semi metal, as it generates a momentum-independent off-diagonal contribution to the self-energy. Breaking time-reversal symmetry enriches the topological phase diagram with three distinct regimes-single-node trivial, two-node trivial, and two-node Chern. We find that disorder can drive topological transitions from both the single-and two-node trivial to the two-node Chern regime. We further analyze these transitions in an appropriate tight-binding Hamiltonian of an anisotropic hexagonal lattice by calculating the real-space Chern number. Additionally, we compute the disorder-averaged entanglement entropy which signals both the topological Lifshitz and Chern transition as a function of the anisotropy of the hexagonal lattice. Finally, we discuss experimental aspects of our results.

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Section: Disorder-averaged Entanglement Entropy and Density Of Stmentioning

confidence: 99%

Interplay between topology and disorder in a two-dimensional semi-Dirac material

2018

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“…Even though topological phases are robust against weak disorder, strong disorder in general induces localization of wave functions [1,2]. Localized wave-functions are not expected to contribute to the non-trivial topology, so the fate of the topological phase in the presence of strong disorder has attracted interest [3][4][5][6][7][8][9]. Naively one would expect that increasing disorder leads to complete electronic localization and trivial topology.…”

Section: Introductionmentioning

confidence: 99%

Static and Dynamic Disorder in Topological Systems: Localized, Critical and Extended States

2019

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Topological properties may be induced or changed by the action of disorder. We investigate two examples of this scenario: in the first, by showing that either trivial or topological two-dimensional superconductors, as a result of a static random distribution of magnetic impurities, display topological phases. The second one involves using timedependent perturbations, which also have the general effect of inducing topology and, under appropriate conditions, the appearance of topological properties is shown. In this case, we consider the effect on the topology of onedimensional systems, of time periodic or aperiodic perturbations consisting of kicks of spatially non-homogeneous potentials. One finds different regimes characterized by localized, critical, or extended non-equilibrium states, as a result of the time dependent perturbation. We further carry out the existence and characterization of the topological edge states that occur both in the case of a static and dynamic perturbations. In the case of the static disorder, the topological phases are characterized calculating the real space Chern number and various regimes for the low energy density of states are identified and explained in the context of general properties of the symmetry classes D and C. In the case of a time periodic perturbation (the Floquet regime) we contrast the dynamical localization, and its properties, when using kicks either in the quasiperiodic spatially inhomogeneous potentials of the Aubry-André type or in the case of kicks on the pairing amplitude in the presence of static Aubry-André quasi-disorder. In both, we make use of lattice sizes drawn from the Fibonacci sequence. We also show that aperiodicity in the sequence of time perturbations leads in general to delocalization, a regime characterized by a fully random matrix Hamiltonian with the appropriate symmetry.

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“…The interplay of disorder-induced localization [56] and topological order, in both one and two dimensions has formed a significant area of research. [57][58][59][60][61][62][63][64][65][66][67][68][69][70] Although in a static two-dimensional system, disorder localizes all bulk states, systems with quantum Hall-like topological order necessarily have a narrow window of energy possessing delocalized states, which can be further argued from the response of the system to gauge flux insertion. [71] The Floquet system considered in this work also has a similar behavior, however quasienergies of the delocalized states depend on the particular underlying topological phase.…”

Section: Introductionmentioning

confidence: 99%

Disordered Chern insulator with a two-step Floquet drive

Roy¹,

Sreejith²

2016

Phys. Rev. B

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We explore the physics of a Chern insulator subjected to a two step Floquet drive. We analytically obtain the phase diagram and show that the system can exhibit different topological phases characterized by presence and chirality of edge-modes in the two bulk gaps of the Floquet quasienergy spectrum, around 0 and π. We find that the phase of the system depends on the mean but not on the amplitude of the drive. The bulk topological invariants characterizing the phases can be extracted by mapping the unitary evolution within a time period to an energetically trivial but topologically non-trivial time evolution. An extensive numerical study of the bulk topological invariants in the presence of quenched disorder reveals new transitions induced by strong disorder (i) from the different topological to trivial insulator phases and (ii) from a trivial to a topological Anderson insulator phase at intermediate disorder strengths. Careful analysis of level statistics of the quasienergy spectrum indicates a 'levitation-annihilation' mechanism near these transitions.

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Absence of localization in a class of topological systems

Cited by 17 publications

References 37 publications

Interplay between topology and disorder in a two-dimensional semi-Dirac material

Interplay between topology and disorder in a two-dimensional semi-Dirac material

Static and Dynamic Disorder in Topological Systems: Localized, Critical and Extended States

Disordered Chern insulator with a two-step Floquet drive

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