Topological phase detection through high-harmonic spectroscopy in extended Su-Schrieffer-Heeger chains

Abstract

Su-Schrieffer-Heeger (SSH) chains are paradigmatic examples of one-dimensional topological insulators hosting zero-energy edge modes when the bulk of the system has a nonzero topological winding invariant. Recently, high-harmonic spectroscopy has been suggested as a tool for detecting the topological phase. Specifically, it has been shown that when the SSH chain is coupled to an external laser field of a frequency much smaller than the band gap, the emitted light at harmonic frequencies strongly differs between the trivial and the topological phase. However, it remains unclear whether various nontrivial topological phases---differing in the number of edge states---can also be distinguished by the high-harmonic generation (HHG). In this paper, we investigate this problem by studying an extended version of the SSH chain with extended-range hoppings, resulting in a topological model with different topological phases. We explicitly show that HHG spectra are a sensitive and suitable tool for distinguishing topological phases when there is more than one topological phase. We also propose a quantitative scheme based on tuning the filling of the system to precisely locate the number of edge modes in each topological phase of this chain.