Fragile topological phase on the triangular kagome lattice and its bulk-boundary correspondence

TL;DR

This paper investigates fragile topological states and their bulk-boundary correspondence in a 2D triangular kagome lattice, revealing new topological phases and transitions using theoretical models and topological quantum chemistry.

Contribution

It introduces the diagnosis of fragile topology in TKL, explores the bulk-boundary relation, and predicts a magnetic-field-induced topological phase transition.

Findings

Fragile topological states confirmed via Wilson-loop and Hofstadter spectra.

Obstructed-atomic-limit insulators can host fractional corner states without fragile topology.

A magnetic field induces a transition from second-order to first-order topological phases.

Abstract

We predict and examine various topological states on a two-dimensional (2D) triangular kagome lattice (TKL) using the tight-binding (TB) models and theory of topological quantum chemistry (TQC). Firstly, on the basis of TQC, we diagnose band structures with fragile topology and calculate Wilson-loop spectra and Hofstadter butterfly spectra to confirm their non-trivial nature. Secondly, we examine the bulk-boundary correspondence and find that an obstructed-atomic-limit (OAL) insulator hosts fractional corner states without being accompanied by fragile topological band structures, which implies that the presence of OALs and corner states is not a sufficient condition to fragile topology. Last but not least, we predict a topological phase transition from a second-order topological phase to a first-order topological phase that can be realized in the TKL under the action of a magnetic field.