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

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