Conductivity of a compensated metal near a Pomeranchuk quantum critical point: the absence of mass renormalization

The role of mass renormalization, m^*/m_b, in electron transport near a quantum critical point (QCP) is a nontrivial issue. According to a naive interpretation of the Drude formula, as electrons get heavier near a QCP, their electrical and thermal conductivities decrease. However, this picture has never been supported by an actual calculation. In this work, we employ a model case of a compensated metal near a Pomeranchuk-type criticality. The advantage of this model is that it allows one to treat electrical and thermal conductivities on the same footing, without invoking umklapp scattering or any other channels of momentum relaxation which are extraneous to the electron system. By solving exactly the kinetic equation, we obtain explicit results for the electrical and thermal conductivities, and also for the viscosity of a two-band compensated metal. We show that mass renormalization factors cancel out with the Z factors, which renormalize the scattering probability, such that all the transport quantities contain the bare rather than renormalized electron masses. We also demonstrate how the same cancelation happens diagrammatically, on an example of the optical conductivity of a compensated metal.