Topological Phases of Tight-Binding Trimer Lattice in the BDI Symmetry Class

TL;DR

This paper explores a modified SSH model with a three-site unit cell, revealing new topological phases and edge states protected by multiple symmetries, with potential experimental realizations.

Contribution

It introduces a novel trimer lattice model with higher-dimensional Hamiltonian matrices, leading to unique symmetries and topological features not present in traditional SSH models.

Findings

Presence of multiple edge states protected by combined symmetries

Emergence of next-nearest neighbor hopping terms

Potential realization in superconducting circuits and waveguide arrays

Abstract

In this work, we theoretically study a modified Su-Schrieffer-Heeger (SSH) model in which each unit cell consists of three sites. Unlike existing extensions of the SSH model which are made by enlarging the periodicity of the (nearest-neighbor) hopping amplitudes, our modification is obtained by replacing the Pauli matrices in the system's Hamiltonian by their higher dimensional counterparts. This, in turn, leads to the presence of next-nearest neighbor hopping terms and the emergence of different symmetries than those of other extended SSH models. Moreover, the system supports a number of edge states that are protected by a combination of particle-hole, time-reversal, and chiral symmetry. Finally, our system could be potentially realized in various experimental platforms including superconducting circuits as well as acoustic/optical waveguide arrays.