Electron-electron interaction corrections to the thermal conductivity in disordered conductors

We evaluate the electron-electron interaction corrections to the electronic thermal conductivity in a disordered conductor in the diffusive regime. We use a diagrammatic many-body method analogous to that of Altshuler and Aronov for the electrical conductivity. We derive results in one, two, and three dimensions for both the singlet and triplet channels, and in all cases find that the Wiedemann-Franz law is violated.

Figure 1

Feynman diagram for the Drude contribution to the heat response kernel. The black circles represent the Matsubara heat current vertex given in Eq. (4).

Figure 2

Feynman diagrams for the leading order interaction corrections to the heat response kernel. Diagrams (A)–(E) are identical to those considered by Alshuler and Aronov for the electrical response; diagram (F) is the heat-drag contribution discussed in the text.