Non-uniqueness of the heat current operator and the hopping thermoelectric and Nernst-Ettingshausen effects in amorphous semiconductors

The Hardy correction in the heat current operator is generalized to the case of non-zero electron-phonon coupling constantg. It is then shown that not only the lowest (minus first) order but also the fist order contribution ing to the thermoelectric power of amorphous semiconductors in the hopping regime disappears. Consequently, since the lowest (zero) order contribution to the thermoelectric effects in the magnetic field yields no Nernst-Ettingshausen effect in these materials, the last effect is of the second order ing, at least.