Localization in a Quantum Spin Hall System

We extend the Yao-Kivelson decorated honeycomb lattice Kitaev model [Phys. Rev. Lett. 99, 247203 (2007)] of an exactly solvable chiral spin liquid by including disordered exchange couplings. We have determined the phase diagram of this system and found that disorder enlarges the region of the topological non-Abelian phase with finite Chern number. We study the energy level statistics as a function of disorder and other parameters in the Hamiltonian, and show that the phase transition between the non-Abelian and Abelian phases of the model at large disorder can be associated with pair annihilation of extended states at zero energy. Analogies to integer quantum Hall systems, topological Anderson insulators, and disordered topological Chern insulators are discussed.

Section: Energy Level Statisticssupporting

confidence: 83%

Exactly solvable topological chiral spin liquid with random exchange

Chua

Fiete

2011

“…The computer simulations have already began this process (note that these are all zero-temperature finitesize scaling simulations). [49][50][51][52][53][54][55][56][57][58][59][60] One question that received great attention from these works is if the scaling exponents of the symplectic models at the metal-to-normal insulator and at the metal-to-topological insulator are the same. So far, the answer seems to be affirmative.…”

Section: Introductionmentioning

confidence: 99%

Quantum criticality at the Chern-to-normal insulator transition

Xue

Prodan

2013

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.

“…This robustness against disorder can be the key to many technological applications, [9][10][11] and because of that, a great deal of effort has been dedicated to understanding the behavior of the topological materials in the presence of disorder. [13][14][15][16][17][18][19][20][21][22][23][24][25][26] One important question, which is still opened for 3D topological insulators, is if the robustness against disorder extends into the strong disorder regime, particularly into the regime where the insulating gap is filled with dense localized spectrum. The theoretical argument based on the time-reversal symmetry is perturbative and therefore it breaks down in this regime.…”

mentioning

confidence: 99%

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

Leung

Prodan

2012

We study the effect of strong disorder in a 3-dimensional topological insulators with time-reversal symmetry and broken inversion symmetry. Firstly, using level statistics analysis, we demonstrate the persistence of delocalized bulk states even at large disorder. The delocalized spectrum is seen to display the levitation and pair annihilation effect, indicating that the delocalized states continue to carry the Z2 invariant after the onset of disorder. Secondly, the Z2 invariant is computed via twisted boundary conditions using an efficient numerical algorithm. We demonstrate that the Z2 invariant remains quantized and non-fluctuating even after the spectral gap becomes filled with dense localized states. In fact, our results indicate that the Z2 invariant remains quantized until the mobility gap closes or until the Fermi level touches the mobility edges. Based on such data, we compute the phase diagram of the Bi2Se3 topological material as function of disorder strength and position of the Fermi level.