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arXiv:1201.4224 · Physical Review B

Phase structure of the topological Anderson insulator

Dongwei Xu, Junjie Qi, Jie Liu, Vincent Sacksteder, X. C. Xie, Hua Wei Jiang

Published May 25, 2012• 38 citations
arXivHTMLPDF

Abstract

We study the disordered topological Anderson insulator in a two-dimensional (square not strip) geometry. We first report the phase diagram of finite systems and then study the evolution of phase boundaries when the system size is increased to a very large $1120\ifmmode\times\else\texttimes\fi{}1120$ area. We establish that conductance quantization can occur without a bulk band gap, and that there are two distinct scaling regions with quantized conductance: TAI-I with a bulk band gap, and TAI-II with localized bulk states. We show that there is no intervening insulating phase between the bulk conduction phase and the TAI-I and TAI-II scaling regions, and that there is no metallic phase at the transition between the quantized and insulating phases. Centered near the quantized-insulating transition there are very broad peaks in the eigenstate size and fractal dimension ${d}_{2}$; in a large portion of the conductance plateau eigenstates grow when the disorder strength is increased. The fractal dimension at the peak maximum is ${d}_{2}\ensuremath{\approx}1.5$. Effective-medium theory (Coherent Potential Approximation, self-consistent Born approximation) predicts well the boundaries and interior of the gapped TAI-I scaling region, but fails to predict all boundaries save one of the ungapped TAI-II scaling region. We report conductance distributions near several phase transitions and compare them with critical conductance distributions for well-known models.

DOI
10.1103/physrevb.85.195140

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We study the disordered topological Anderson insulator in a two-dimensional (square not strip) geometry. We first report the phase diagram of finite systems and then study the evolution of phase boundaries when the system size is increased to a very large 1120\ifmmode×\else\texttimes\fi11201120\ifmmode\times\else\texttimes\fi{}11201120\ifmmode×\else\texttimes\fi1120 area. We establish that conductance quantization can occur without a bulk band gap, and that there are two distinct scaling regions with quantized conductance: TAI-I with a bulk band gap, and TAI-II with localized bulk states. We show that there is no intervening insulating phase between the bulk conduction phase and the TAI-I and TAI-II scaling regions, and that there is no metallic phase at the transition between the quantized and insulating phases. Centered near the quantized-insulating transition there are very broad peaks in the eigenstate size and fractal dimension d2{d}_{2}d2​; in a large portion of the conductance plateau eigenstates grow when the disorder strength is increased. The fractal dimension at the peak maximum is d2\ensuremath≈1.5{d}_{2}\ensuremath{\approx}1.5d2​\ensuremath≈1.5. Effective-medium theory (Coherent Potential Approximation, self-consistent Born approximation) predicts well the boundaries and interior of the gapped TAI-I scaling region, but fails to predict all boundaries save one of the ungapped TAI-II scaling region. We report conductance distributions near several phase transitions and compare them with critical conductance distributions for well-known models.
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We study the critical properties of the topological Anderson phase transition in a strongly disordered Chern insulator, separating the topological phase from a trivial Anderson insulator. We show that the transition is characterized by a non-zero electrical conductance and by the emergence of a critical length scale in the real-space profile of the local Chern marker. From this, we extract the correlation-length and the dynamical critical exponents, which are consistent with those of non-interacting models of the integer quantum Hall effect. We then ramp the disorder strength across the transition and study the ensuing dynamics. In contrast to clean topological systems, we find that the excitation density does not follow the Kibble-Zurek scaling. The non-equilibrium length scale associated with the local Chern marker is decoupled from the generation of excitations. For studied system sizes, we find it to be close to the Kibble-Zurek prediction for the topological-to-trivial quench, while it deviates from it for the reverse direction.
The density of states, the dynamic (optical) conductivity, and the phase diagram of the paramagnetic two-dimensional Anderson-Hubbard model with strong correlations and disorder are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are accounted by the DMFT, while disorder is taken into account via the appropriate generalization of the self-consistent theory of localization. We consider the two-dimensional system with the rectangular “bare” density of states (DOS). The DMFT effective single-impurity problem is solved by numerical renormalization group (NRG). The “correlated metal,” Mott insulator, and correlated Anderson insulator phases are identified from the evolution of the density of states, optical conductivity, and localization length, demonstrating both Mott-Hubbard and Anderson metal-insulator transitions in two-dimensional systems of finite size, allowing us to construct the complete zero-temperature phase diagram of the paramagnetic Anderson-Hubbard model. The localization length in our approximation is practically independent of the strength of Hubbard correlations. But the divergence of the localization length in a finite-size two-dimensional system at small disorder signifies the existence of an effective Anderson transition.