Four-band insulator on a ℤ₂ domain wall: an analytically solvable model for the interface between trivial and topological 2D insulators

2017/12/07 by Felipe Lopes de Freitas, Freitas, F. L.
Materials Science · Physics and Astronomy · #Chemical and Physical Properties of Materials #FOS: Physical sciences #Graphene research and applications #Materials Science (cond-mat.mtrl-sci) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Topological Materials and Phenomena

paper · pdf · doi:10.48550/arxiv.1712.02525

openalex publication_date 2017/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A phenomenological model for the interface between trivial and topological two-dimensional insulators possessing the same band gap is presented. The model depends on three measurable parameters, the energy gap E_g, the Fermi velocity of the metallic edge states v_F and the thickness of the interface Δ where the gap inversion occurs, and can be reduced to the Schrödinger equation for the modified Pöschl-Teller potential, which admits an analytical solution. It is demonstrated that the underlying physics is determined by the adimensional parameter α=E_gΔ/2ℏ v_F, whose integral part determines the number of massive bound states at the interface. Furthermore, when α is exactly an integer, waves incident on the interface are never reflected. Results for parameters chosen in the typical scale of condensed matter systems are briefly discussed.

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