Two-dimensional spin-filtered chiral network model for theZ2quantum spin-Hall effect

Abstract

The effects of static disorder on the Z 2 quantum spin-Hall effect for non-interacting electrons propagating in two-dimensional space are studied numerically. A two-dimensional time-reversal symmetric network model is constructed to account for the effects of static disorder on the propagation of non-interacting electrons subjected to spin-orbit couplings. This network model is different from past network models belonging to the symplectic symmetry class in that the propagating modes along the links of the network can be arranged into an odd number of Kramers doublet. It is found that (1) a two-dimensional metallic phase of finite extent is embedded in a Z 2 insulating phase in parameter space and (2) the quantum phase transitions between the metallic and Z 2 insulating phases belong to the conventional symplectic universality class in two space dimensions.

Network models of photonic Floquet topological insulators

“…Indeed, the CC network model concept has been generalized to study quantum spin Hall insulators by imposing fermionic time-reversal symmetries on the links and nodes [44][45][46] . However, bosonic edge states are not protected from backscattering by time-reversal symmetric perturbations, so topologically non-trivial behavior can only occur if mixing into time-reversed modes is negligible.…”

Quantum criticality at the Chern-to-normal insulator transition

“…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.…”

Stability of Z2topological order in the presence of vacancy-induced impurity band

“…Since topological order is protected by associated symmetries [4], surface states and edge states in TIs are considered to be robust against bulk disorders that do not break the time-reversal symmetry that is associated with Z 2 topological order. The robustness against disorders is the key to potential technological applications and hence a great effort has been dedicated to understanding the behavior of the topological materials in the presence of disorders [5][6][7][8][9][10]12]. Indeed, surface states or edge states are shown to persist in the presence of weak disorders [5].…”

“…In addition, using the fact that edge states are described by the effective Hamiltonian given in Eq. (8) and their energies must be poles of T , it implies that…”