Thermoelectric effects arising from particle-hole symmetry breaking near vortices in type-II superconductors

We numerically study the Bogoliubov-de-Gennes (BdG) equation to derive the thermoelectric response of a single vortex in a low magnetic field regime. Using the cylindrical symmetry of a vortex, we solve the BdG equations using the Fourier-Bessel expansion and impose particle number conservation in a self-consistent manner. We find that the particle-hole symmetry is broken near a vortex due to the presence of bound states and this asymmetry is manifested in density of states. This asymmetry also results into a finite Seebeck coefficient (in the order of mV/K at low temperatures). We also study the electrical and thermal conductance, power factor, and the figure of merit.