Topological Edge States with Zero Hall Conductivity in a Dimerized Hofstadter Model

Abstract

The Hofstadter model is a simple yet powerful Hamiltonian to study quantum Hall physics in a lattice system, manifesting its essential topological states. Lattice dimerization in the Hofstadter model opens an energy gap at half filling. Here we show that even if the ensuing insulator has a Chern number equal to zero, concomitantly a doublet of edge states appear that are pinned at specific momenta. We demonstrate that these states are topologically protected by inversion symmetry in specific one-dimensional cuts in momentum space, define and calculate the corresponding invariants and identify a platform for the experimental detection of these novel topological states.

5 pages, 3 figures + Supplemental Material (6 pages)

References in corpus (7)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
• Stacked topological insulator built from bismuth-based graphene sheet analogues
• Sub-nm wide electron channels protected by topology

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