Higher order topology in a Creutz ladder

TL;DR

This paper explores higher order topological phases in a two-dimensional extension of the Creutz ladder, revealing phases with robust corner modes and edge modes, characterized by topological invariants, in different boundary configurations.

Contribution

It introduces a 2D version of the Creutz ladder to study higher order topology, identifying phases with corner and edge modes and analyzing their topological invariants.

Findings

Identification of higher order topological phases with corner modes

Presence of first order edge modes in certain phases

Phase diagram showing distinct topological sectors

Abstract

A Creutz ladder, is a quasi one dimensional system hosting robust topological phases with localized edge modes protected by different symmetries such as inversion, chiral and particle-hole symmetries. Non-trivial topology is observed in a large region of the parameter space defined by the horizontal, diagonal and vertical hopping ampitudes and a transverse magnetic flux that threads through the ladder. In this work, we investigate higher order topology in a two dimensional extrapolated version of the Creutz ladder. To explore the topological phases, we consider two different configurations, namely a torus (periodic boundary) and a ribbon (open boundary) to look for hints of gap closing phase transitions. We also associate suitable topological invariants to characterize the non-trivial sectors. Further, we find that the resultant phase diagram hosts two different topological phases, one where the higher order topological excitations are realized in the form of robust corner modes, along with (usual) first order excitations demonstrated via the presence of edge modes in a finite lattice, for the other.