Non-uniqueness of the heat-current operator and the hopping thermoelectric and thermomagnetic phenomena

Abstract

The Hardy's corrections to the Maradudin's lattice part of the total heat current operator are shown to yield no corrections to the hopping thermoelectric coefficients of amorphous solids and glasses in the lowest (minus-first) order of the electron phonon coupling constant. But even after including the magnetic field ℋ≡ (0, 0,ℋ), the lowest non-zero (zeroth order) contributions to the Peltier and Seebeck tensors are shown to be diagonal, yielding thus no contribution to the Nernst and Ettingshaussen coefficients. Therefore, the Hardy corrections, which might yield the next (first) order contributions to these coefficients, appear to be crucial for treating the thermomagnetic phenomena in amorphous and glassy materials.