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

TL;DR

This paper reveals that in a dimerized Hofstadter model, topologically protected edge states can exist with zero Hall conductivity, enabled by inversion symmetry, expanding the understanding of topological phases in lattice systems.

Contribution

It introduces a new topological phase in the dimerized Hofstadter model where edge states appear without a non-zero Chern number, protected by inversion symmetry.

Findings

Edge states appear with zero Chern number in the dimerized Hofstadter model.

Inversion symmetry protects these edge states at specific momenta.

Potential platform identified for experimental detection of these states.

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.