Weak-localization effect on thermomagnetic phenomena

The quantum transport equation (QTE) is extended to study weak localization (WL) effects on galvanomagnetic and thermomagnetic phenomena. QTE has many advantages over the linear response method (LRM): (i) particle-hole asymmetry, which is necessary for the Hall effect is taken into account by the nonequilibrium distribution function, while the LRM requires expansion near the Fermi surface, (ii) when calculating response to the temperature gradient, the problem of WL correction to the heat current operator is avoided, (iii) the magnetic field is directly introduced to the QTE, while the LRM deals with the vector potential and special attention should be paid to maintain gauge invariance, e.g., when calculating the Nernst-Ettingshausen effect the heat current operator should be modified to include the external magnetic field. We reproduce in a very compact form known results for the conductivity, the Hall and the thermoelectric effects and then we study our main problem, WL correction to the Nernst-Ettingshausen coefficient (transverse thermopower). We show that in a quasi-two-dimensional film the Nernst-Ettingshausen coefficient has a large logarithmic factor similar to that of the conductivity and the Hall conductivity, while the thermoelectric coefficient does not have such a factor.