Phase dependent differential thermopower ofs-wave-superconductor–normal-metal–d-wave-superconductor junctions: Pair-breaking effects and Gaussian fluctuations

Abstract

We start with revisiting our previous results on thermoelectric response of s-wave-superconductor--normal-metal--$s$-wave-superconductor $(\mathrm{SNS})$ configuration in a C-shaped ${\mathrm{Bi}}_{x}{\mathrm{Pb}}_{1\ensuremath{-}x}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{y}$ sample in order to include strong fluctuation effects. Then, by appropriate generalization of the Ginzburg-Landau theory based on admixture of s-wave $(S)$ and d-wave $(D)$ superconductors, we consider a differential thermoelectric power (TEP) of s-wave-superconductor--normal-metal--$d$-wave-superconductor $(\mathrm{SND})$ junction. In addition to its strong dependence on the relative phase $\ensuremath{\theta}={\ensuremath{\varphi}}_{s}\ensuremath{-}{\ensuremath{\varphi}}_{d}$ between the two superconductors, two major effects are shown to influence the behavior of the predicted TEP. One, based on the chemical imbalance at $\mathrm{SD}$ interface, results in a pronounced maximum of the TEP peak near $\ensuremath{\theta}=\ensuremath{\pi}/2$ (where the so-called $s+id$ mixed pairing state is formed) for two identical superconductors with ${T}_{\mathrm{cd}}{=T}_{\mathrm{cs}}\ensuremath{\equiv}{T}_{c}.$ Another effect, which should manifest itself at $\mathrm{SD}$ interface comprising an s-wave low-${T}_{c}$ superconductor and a d-wave high-${T}_{c}$ superconductor with ${T}_{\mathrm{cd}}\ensuremath{\ne}{T}_{\mathrm{cs}},$ predicts ${S}_{p}\ensuremath{\propto}{T}_{\mathrm{cd}}\ensuremath{-}{T}_{\mathrm{cs}}$ for the TEP peak value. The experimental conditions under which the predicted behavior of the induced differential TEP can be measured are discussed.