Thermopower and thermophase in a $d$-wave superconductor

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.

11 pages, 6 figures

References in corpus (9)

• The Josephson heat interferometer
• Nonlocal Thermoelectric Effects and Nonlocal Onsager Relations in a Three-Terminal Proximity-Coupled Superconductor-Ferromagnet Device
• Phase Modulated Thermal Conductance of Josephson Weak Links
• Very large thermophase in ferromagnetic Josephson junctions
• Theory of a large thermoeffect in superconductors doped with magnetic impurities
• Seebeck coefficient in a cuprate superconductor: particle-hole asymmetry in the strange metal phase and Fermi surface transformation in the pseudogap phase
• Electron-hole imbalance and large thermoelectric effect in superconducting hybrids with spin-active interfaces
• Effect of Quasiparticles Injection on the AC Response of a Superconductor
• Quasiclassical theory of charge transport across mesoscopic normal metal-superconducting heterostructures with current conservation

Cited by in corpus (7)

• Robust and tunable coreless vortices and fractional vortices in chiral $d$-wave superconductors
• A finite element method for the quasiclassical theory of superconductivity
• Enhanced chiral edge currents and orbital magnetic moment in chiral $d$-wave superconductors from mesoscopic finite-size effects
• Phase-dependent charge and heat current in thermally biased short Josephson junctions formed at helical edge states
• Impurity strength-temperature phase diagram with phase crystals and competing time-reversal symmetry breaking states in nodal $d$-wave superconductors
• Designing edge currents using mesoscopic patterning in chiral d-wave superconductors
• Self-consistent theory of current injection into $d$ and $d+is$ superconductors