Theory of the Nernst Effect Caused by Fluctuations of the Superconducting Order Parameter

Abstract

We show that the strong Nernst effect observed recently in amorphous superconducting films far above the critical temperature is caused by the fluctua- tions of the superconducting order parameter. We present here the main steps of the calculation and discuss some subtle issues in the theoretical study of thermal phenomena that we have encountered while calculating the Nernst coefficient. Un- like the calculation of the electric conductivity, the use of the Kubo formula for the thermal and thermoelectric transport coefficients meets with certain complications in the presence of interactions - the interaction enters the heat current operator. In practice a simplified expression for the heat current operator ignoring interactions is commonly used. Since in the presence of superconducting fluctuations there is no justification for the simplified form of the Kubo formula, we preferred to derive the expression for the Nernst coefficient in the quantum kinetic equation approach. The Nernst effect provides an excellent opportunity to test the use of the quantum kinetic equation in the description of thermoelectric transport phenomena. We show how the third law of thermodynamics constrains the magnitude of the Nernst signal. In particular, we demonstrate the cancellation of the non-vanishing quantum contri- butions in the limit T → 0 by the magnetization current. As a result, we obtained a striking agreement between our theoretical calculations and the experimental data in a broad region of temperatures and magnetic fields.