Identifying Bogoliubov Fermi surfaces via thermoelectric response in a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi></mml:math>-wave superconductor heterostructure

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 a normal-$d$-wave superconductor hybrid junction, we compute the thermoelectric coefficients including thermal conductance, Seebeck coefficient, and figure of merit ($zT$), and examine the validation of the Widemann-Franz law in the presence of both voltage and temperature bias. Importantly, as a signature of the 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 the Seebeck coefficient ($\ensuremath{\sim}200\phantom{\rule{0.16em}{0ex}}\textmu{}\mathrm{V}/\phantom{\rule{0.16em}{0ex}}\mathrm{K}$) and $zT$ ($\ensuremath{\sim}3.5$) 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.