Anomalous topological edge modes in a periodically-driven trimer lattice

Periodically driven systems have a longstanding reputation for establishing rich topological phenomena beyond their static counterpart. In this work, we propose and investigate a periodically driven extended Su-Schrieffer-Heeger model with three sites per unit cell, obtained by replacing the Pauli matrices with their $3\times 3$ counterparts. The system is found to support a number of edge modes over a range of parameter windows, some of which have no static counterparts. Among these edge modes, of particular interest are those which are pinned at a specific quasienergy value. Such quasienergy-fixed edge modes arise due to the interplay between topology and chiral symmetry, which are typically not expected in a three-band static model due to the presence of a bulk band at the only chiral-symmetric energy value, i.e., zero. In our time-periodic setting, another chiral-symmetric quasienergy value exists at half the driving frequency, which is not occupied by a bulk band and could then host chiral-symmetry-protected edge modes ($\pi$ modes). Finally, we verify the robustness of all edge modes against spatial disorder and briefly discuss the prospect of realizing our system in experiments.