Identifying Bogoliubov Fermi surfaces via thermoelectric response in a $d$-wave superconductor heterostructure

TL;DR

This paper theoretically explores how Bogoliubov Fermi surfaces in a $d$-wave superconductor heterostructure influence thermoelectric responses, revealing significant enhancements in thermoelectric efficiency due to interface states and topological protection.

Contribution

It introduces a theoretical framework for detecting BFSs via thermoelectric measurements in $d$-wave superconductors, highlighting the role of Andreev bound states and topological protection.

Findings

Enhanced Seebeck coefficient (~200 μV/K) observed.

High figure of merit ($zT$ ~ 3.5) indicating potential for thermoelectric devices.

Validation of Wiedemann-Franz law in the studied heterostructure.

Abstract

We theoretically investigate the thermoelectric response of Bogoliubov Fermi surfaces (BFSs) generated in a two dimensional unconventional $d$-wave superconductor subjected to an external in-plane Zeeman field. These BFSs exhibiting the same dimension as the underlying normal state Fermi surface are topologically protected by combinations of discrete symmetries. Utilizing the Blonder-Tinkham-Klapwijk formalism and considering normal-$d$-wave superconductor hybrid junction, we compute the thermoelectric coefficients including thermal conductance, Seebeck coefficient, figure of merit ($zT$), and examine the validation of Widemann-Franz law in the presence of both voltage and temperature bias. Importantly, as a signature of anisotropic nature of $d$-wave pairing, Andreev bound states (ABSs) formed at the normal-superconductor interface play a significant role in the thermoelectric response. In the presence of ABSs, we observe a substantial enhancement in Seebeck coefficient ($\sim 200\,\mu$V/K) and $zT$ ($\sim 3.5$) due to the generation of the BFSs and thus making such setup a potential candidate for device applications. Finally, we strengthen our continuum model results by computing the thermoelectric coefficients based on a lattice-regularized version of our continuum model.