Probing topological protected transport in finite-sized Su-Schrieffer-Heeger chains

TL;DR

This paper experimentally investigates the transport properties of topological edge states in finite-sized SSH chains, revealing a characteristic transport length and demonstrating edge state coupling through transmission spectroscopy.

Contribution

It introduces the concept of a transport length in finite SSH chains and experimentally verifies edge state coupling and transport using split-ring resonator arrays.

Findings

Existence of a characteristic transport length $L_c$ for edge states.

Edge state transport persists even when lattice size exceeds penetration depth.

Direct measurement of transport velocity via transmission spectroscopy.

Abstract

In order to transport information with topological protection, we reveal and demonstrate experimentally the existence of a characteristic length $L_c$, coined as the transport length, in the bulk size for edge states in one-dimensional Su-Schrieffer-Heeger (SSH) chains. In spite of the corresponding wavefunction amplitude decays exponentially, characterized by the penetration depth $\xi$, the transport between two edge states remains possible even when the lattice size $L$ is much larger than the penetration depth, i.e., $\xi \ll L \le L_c$. Due to the non-zero coupling energy in a finite-size system, the supported SSH edge states are not completely isolated at the two ends, giving an abrupt change in the wave localization, manifested through the inverse participation ratio to the lattice size. To verify such a non-exponential scaling factor to the system size, we implement a chain of split-ring resonators and their complementary ones with controllable hopping strengths. By performing the measurements on the group velocity from the transmission spectroscopy of non-trivially topological edge states with pulse excitations, the transport velocity between two edge states is directly observed with the number of lattices up to $20$. Along the route to harness topology to protect optical information, our experimental demonstrations provide a crucial guideline for utilizing photonic topological devices.