Superconducting fluctuations and the Nernst effect: A diagrammatic approach

Abstract

We calculate the contribution of superconducting fluctuations above the critical temperature ${T}_{c}$ to the transverse thermoelectric response ${\ensuremath{\alpha}}_{\mathrm{xy}},$ the quantity central to the analysis of the Nernst effect. The calculation is carried out within the microscopic picture of BCS, and to linear order in magnetic field. We find that as $\stackrel{\ensuremath{\rightarrow}}{T}{T}_{c},$ the dominant contribution to ${\ensuremath{\alpha}}_{\mathrm{xy}}$ arises from the Aslamazov-Larkin diagrams, and is equal to the result previously obtained from a stochastic time-dependent Ginzburg-Landau equation [I. Ussishkin, S. L. Sondhi, and D. A. Huse, Phys. Rev. Lett. 89, 287001 (2002)]. We present an argument which establishes this correspondence for the heat current. Other microscopic contributions, which generalize the Maki-Thompson and density of states terms for the conductivity, are less divergent as $\stackrel{\ensuremath{\rightarrow}}{T}{T}_{c}.$