Dependence of topological Anderson insulator on the type of disorder

Song, Juntao; Liu, Haiwen; Jiang, Hua; Sun, Qing-Feng; Xie, X. C.

doi:10.1103/physrevb.85.195125

Cited by 86 publications

(70 citation statements)

References 45 publications

(62 reference statements)

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“…3, while disorder closes the gap and destroys the Chern insulator in the system with inversion symmetry (panel b), the QAHE with ∆ AB = 0 is insensitive to increasing Anderson disorder (panel c). As illustrated in panel (c), large disorder can localize carriers and extend the topological phase to energies in the vicinity of the bulk gap, similarly to what is observed in topological Anderson insulators [39,40]. For illustration purposes, the values of ∆ T and ∆ AB used in panel (c) are large in comparison with values in (b).…”

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confidence: 67%

Real-Space Calculation of the Conductivity Tensor for Disordered Topological Matter

2015

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We describe an efficient numerical approach to calculate the longitudinal and transverse Kubo conductivities of large systems using Bastin's formulation [1]. We expand the Green's functions in terms of Chebyshev polynomials and compute the conductivity tensor for any temperature and chemical potential in a single step. To illustrate the power and generality of the approach, we calculate the conductivity tensor for the quantum Hall effect in disordered graphene and analyze the effect of the disorder in a Chern insulator in Haldane's model on a honeycomb lattice.PACS numbers: 71.23. An,72.15.Rn,71.30.+h One of the most important experimental probes in condensed matter physics is the electrical response to an external electrical field. In addition to the longitudinal conductivity, in specific circumstances, a system can present a transverse conductivity under an electrical perturbation. The Hall effect [2] and the anomalous Hall effect in magnetic materials [3] are two examples of this type of response. Paramagnetic materials with spin-orbit interaction can also present transverse spin currents [4]. There are also the quantized versions of the three phenomena: while the quantum Hall effect (QHE) was observed more than 30 years ago [5], the quantum spin Hall effect (QSHE) and the quantum anomalous Hall effect (QAHE) could only be observed [6, 7] with the recent discovery of topological insulators, a new class of quantum matter [8].In the linear response regime, the conductivity tensor can be calculated using the Kubo formalism [9]. The Hall conductivity can be easily obtained in momentum space in terms of the Berry curvature associated with the bands [10]. The downside of working in momentum space, however, is that the robustness of a topological state in the presence of disorder can only be calculated perturbatively [11]. Real-space implementations of the Kubo formalism for the Hall conductivity, on the other hand, allow the incorporation of different types of disorder in varying degrees, while providing flexibility to treat different geometries. Real-space techniques, however, normally require a large computational effort. This has generally restricted their use to either small systems at any temperature [12,13], or large systems at zero temperature [14].In this Letter, we propose a new efficient numerical approach to calculate the conductivity tensor in solids. We use a real space implementation of the Kubo formalism where both diagonal and off-diagonal conductivities are treated in the same footing. We adopt a formulation of the Kubo theory that is known as Bastin formula [1] and expand the Green's functions involved in terms of Chebyshev polynomials using the kernel polynomial method [16]. There are few numerical methods that use Chebyshev expansions to calculate the longitudinal DC conductivity [17][18][19][20] and transverse conductivity [14,21] at zero temperature. An advantage of our approach is the possibility of obtaining both conductivities for large systems in a single calculation step, independe...

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confidence: 67%

Real-Space Calculation of the Conductivity Tensor for Disordered Topological Matter

2015

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“…1a). The existence of such delocalized quantum states can be demonstrated 44 with mathematical rigor using the theory of non-commutative Chern number, 64 while numerically, it has been demonstrated using recursive Green's function and transfer matrix calculations, 51,74,99,100 level statistics analysis, 44,67,101 simulations of the edge currents and computations of the edge conductance. [102][103][104] Near the transitions, the field-theoretic arguments developed by Pruisken and collaborators [105][106][107][108] for IQHE predict the T-driven flowdiagram shown in Fig.…”

Section: Quantum Criticality In the Spin-up Sector Of The Kane-mmentioning

confidence: 99%

Quantum criticality at the Chern-to-normal insulator transition

Xue

Prodan

2013

Phys. Rev. B

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Using the non-commutative Kubo formula for aperiodic solids and a recently developed numerical implementation, we study the conductivity σ and resistivity ρ tensors as functions of Fermi level E F and temperature T, for models of strongly disordered Chern insulators. The formalism enabled us to converge the transport coefficients at temperatures low enough to enter the quantum critical regime at the Chern-to-trivial insulator transition. We find that the ρ xx -curves at different temperatures intersect each other at one single critical point, and that they obey a single-parameter scaling law with an exponent close to the universally accepted value for the unitary symmetry class. However, when compared with the established experimental facts on the plateau-insulator transition in the Integer Quantum Hall Effect, we find a universal critical conductance σ c xx twice as large, an ellipse rather than a semi-circle law, and absence of the Quantized Hall Insulator phase.

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“…Using the self-consistent Born approximation (SCBA), we first show that disorder can drive topological Lifshitz transition from a gapless (single-node SN) or gapped semi-Dirac phase to a semi metallic semi-Dirac phase with two nodes (TN) of Dirac type. This is a consequence of the electronic self-energy containing a finite off-diagonal part, a feature absent in typical topological insulators 18 or isotropic Dirac 25,26 systems. Furthermore, we show that breaking time-reversal symmetry in a SD system results in three distinct topological regimes: single-node trivial, two-node trivial, and two-node Chern.…”

Section: Introductionmentioning

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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Dependence of topological Anderson insulator on the type of disorder

Cited by 86 publications

References 45 publications

Real-Space Calculation of the Conductivity Tensor for Disordered Topological Matter

Real-Space Calculation of the Conductivity Tensor for Disordered Topological Matter

Quantum criticality at the Chern-to-normal insulator transition

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

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