Effective model for massless Dirac electrons on a surface of weak topological insulators

Abstract

In a typical situation, gapless surface states of a three-dimensional (3D) weak topological insulator (WTI) appear only on sides, leaving the top and bottom surfaces gapped. To describe massless Dirac electrons emergent on such side surfaces of a WTI, a two-dimensional (2D) model consisting of a series of one-dimensional helical channels is usually employed. Yet, explicit derivation of such a model from a 3D bulk Hamiltonian has been lacking. Here, we explicitly derive an effective 2D model for the WTI surface states starting from a Wilson-Dirac Hamiltonian for the bulk WTI and establish a firm basis to the hitherto hypothesized 2D model. We show that the resulting 2D model accurately reproduces the excitation spectrum of surface Dirac electrons determined by the 3D model. We also show that the 2D model is applicable to a side surface with atomic steps.

arXiv comment8 pages, 9 figures

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Cited by in corpus (7)

• Disorder effect on chiral edge modes and anomalous Hall conductance in Weyl semimetals
• Manipulating quantum channels in weak topological insulator nanoarchitectures
• Chiral surface states on the step edge in a Weyl semimetal
• Engineering Dirac electrons emergent on the surface of a topological insulator
• 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