Stability of surface states of weak ${\mathbb{Z}}_2$ topological insulators and superconductors

Abstract

We study the stability against disorder of surface states of weak ${\mathbb{Z}}_2$ topological insulators (superconductors) which are stacks of strong ${\mathbb{Z}}_2$ topological insulators (superconductors), considering representative Dirac Hamiltonians in the Altland-Zirnbauer symmetry classes in various spatial dimensions. We show that, in the absence of disorder, surface Dirac fermions of weak ${\mathbb{Z}}_2$ topological insulators (superconductors) can be gapped out by a Dirac mass term which couples surface Dirac cones and leads to breaking of a translation symmetry (dimerization). The dimerization mass is a unique Dirac mass term in the surface Dirac Hamiltonian, and the two dimerized gapped phases which differ in the sign of the Dirac mass are distinguished by a ${\mathbb{Z}}_2$ index. In other words the dimerized surfaces can be regarded as a strong ${\mathbb{Z}}_2$ topological insulator (superconductor). We argue that the surface states are not localized by disorder when the ensemble average of the Dirac mass term vanishes.

8 pages

References in corpus (7)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Topological classification with additional symmetries from Clifford algebras
• Two-dimensional spin-filtered chiral network model for the Z_2 quantum spin-Hall effect
• Quantum Hall Effect of Massless Dirac Fermions in a Vanishing Magnetic Field

Cited by in corpus (19)

• Floquet topological phases protected by time glide symmetry
• Weyl and Dirac semimetals with Z_2 topological charge
• Dislocation Non-Hermitian Skin Effect
• Anderson localization and the topology of classifying spaces
• Higher-order topological superconductors based on weak topological insulators
• Bott periodicity for the topological classification of gapped states of matter with reflection symmetry
• Space group constraints on weak indices in topological insulators
• Bosonic symmetry protected topological phases with reflection symmetry
• Theory of weak symmetry breaking of translations in ${\mathbb{Z}}_2$ topologically ordered states and its relation to topological superconductivity from an exact lattice ${\mathbb{Z}}_2$ charge-flux attachment
• Translation symmetry-enriched toric code insulator
• Correlation between topological band character and chemical bonding in a $\mathbf{B}{\mathbf{i}}_{14}\mathbf{R}{\mathbf{h}}_3{\mathbf{I}}_9$-based family of insulators
• Delocalization of surface Dirac electrons in disordered weak topological insulators
• Effective model for massless Dirac electrons on a surface of weak topological insulators
• Control of Edge Currents at a Ferromagnet - Triplet Superconductor Interface by Multiple Helical Majorana Modes
• A spin pump characterized by entanglement Chern numbers
• Majorana edge states and topological properties in 1D/2D Rashba semiconductor proximity coupled to iron-based superconductor
• Weak topological insulators with step edges: Subband engineering and its effect on electron transport
• Landau levels on a surface of weak topological insulators
• Finite-size scaling analysis of the conductivity of Dirac electrons on a surface of disordered topological insulators