Abstract
In an unconventional superconductor, the interplay of scattering off impurities and Andreev processes may lead to different scattering times for electronlike and holelike quasiparticles. Such electron-hole asymmetry appears when the impurity scattering phase shift is intermediate between the Born and unitary limits and leads to an expectation for large thermoelectric effects. Here, we examine the thermoelectric response of a $d$-wave superconductor connected to normal-metal reservoirs under a temperature bias using a fully self-consistent quasiclassical theory. The thermoelectrically induced quasiparticle current is cancelled by superflow in an open circuit setup, but at the cost of a charge imbalance induced at the contacts and extending across the structure. We investigate the resulting thermopower and thermophase and their dependencies on scattering phase shift, mean free path, and interface transparency. For crystal-axis orientations such that surface-bound zero-energy Andreev states are formed, the thermoelectric effect is reduced as a result of locally reduced electron-hole asymmetry. For a semiballistic superconductor with good contacts, we find thermopowers of order several ${\mu}V/K$, suggesting a thermovoltage measurement as a promising path to investigate thermoelectricity in unconventional superconductors.
Highlights
The interest in thermal currents and thermoelectric effects in superconductors has been revived in recent years, partly because the response to temperature gradients in superconductors is phase coherent [1–8]
The temperature bias leads to a thermal current from hot to cold jth = 1.45 · 10−3 j0th, that in the absence of inelastic scattering is conserved across the device
We have studied the stationary nonlinear thermoelectric response of a d-wave superconductor connected to normal-metal reservoirs under a temperature bias
Summary
The interest in thermal currents and thermoelectric effects in superconductors has been revived in recent years, partly because the response to temperature gradients in superconductors is phase coherent [1–8]. The thermoelectric effect and the contact thermopower are small, since they require electron-hole asymmetry Such asymmetry is very small in most metals because the density of states near the Fermi level is approximately constant and, in addition, the scattering time is to a good approximation energy independent. In addition to the impurity band in the density of states, electron-hole asymmetric scattering rates appear, which leads to the possibility of large thermoelectric effects that to the best of our knowledge have not been measured experimentally. The induced voltage leads to a charge imbalance extending into the bulk of the superconductor and is large by the combined effects of the electron-hole asymmetric impurity scattering and the abundance of quasiparticle states around the nodes of the superconducting order parameter.
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