Nonlocal Thermoelectricity in a S-TI-S Junction in Contact with a N-Metal Probe: Evidence for Helical Edge States

TL;DR

This paper demonstrates a non-local thermoelectric effect in a Josephson junction with helical edge states, showing how magnetic flux can control thermoelectric response, providing a new method to probe topological edge states.

Contribution

It introduces a novel thermoelectric effect in a topological Josephson junction, linking magnetic flux control to helical edge state detection.

Findings

Thermoelectric current is induced by temperature bias in the hybrid junction.

Magnetic flux (Doppler shift) controls thermoelectric response.

The effect serves as a signature of helical edge states.

Abstract

We consider a Josephson junction hosting a Kramers pair of helical edge states of a quantum spin Hall bar in contact with a normal-metal probe. In this hybrid system, the orbital phase induced by a small magnetic field threading the junction known as Doppler shift (DS), combines with the conventional Josephson phase difference and originates an effect akin to a Zeeman field in the spectrum. As a consequence, when a temperature bias is applied to the superconducting terminals, a thermoelectric current is established in the normal probe. We argue that this purely non-local thermoelectric effect is a unique signature of the helical nature of the edge states coupled to superconducting leads and it can constitute a useful tool for probing the helical nature of the edge states in systems where the Hall bar configuration is difficult to achieve. We fully characterize thermoelectric response and performance of this hybrid junction in a wide range of parameters, demonstrating that the external magnetic flux inducing the DS can be used as a knob to control the thermoelectric response and the heat flow in a novel device based on topological junctions.