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R. G. Herb Condensed Matter Seminar
Transport properties of a compensated metal: the Lorentz ratio and the absence of mass renormalization near a Pomeranchuk quantum critical point
Date: Thursday, September 12th
Time: 11:00 am
Place: 5310 Chamberlin Hall
Speaker: Songci Li , UW-Madison
Abstract: A violation of the Wiedemann-Franz law in a metal can be quantified by comparing the Lorentz ratio, $L=kapparho/T$. We obtain the Lorentz ratio of a clean compensated metal with intercarrier interaction as the dominant scattering mechanism by solving exactly the system of coupled integral Boltzmann equations. The Lorentz ratio is shown to assume a particular simple form in the forward-scattering limit: $L/L_0=overline{Theta^2}/2$, where $Theta$ is the scattering angle. In this limit, $L/L_0$ can be arbitrarily small. We discuss how a strong downward violation of the Wiedemann-Franz law in a type-II Weyl semimetal WP$_2$ can be explained within our model. In the second part of the talk, we discuss the role of mass renormalization in electron transport of a compensated metal near a QCP. 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. We employ a model case of a compensated metal near a Pomeranchuk-type QCP. 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 the kinetic equations, we obtain explicit results for the electrical and thermal conductivities of a two-band compensated metal. We show that mass renormalization factors cancel out with the $Z$ factors, which renormalize the scattering probability, so that all the transport quantities contain the bare rather than renormalized electron masses. We also demonstrate how the same conclusion can be drawn by diagrammatically calculating the optical conductivity.
Host: Alex Levchenko
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