Hidden Fermi Liquid, Scattering Rate Saturation, and Nernst Effect: A Dynamical Mean-Field Theory Perspective

We investigate the transport properties of a correlated metal within dynamical mean-field theory. Canonical Fermi liquid behavior emerges only below a very low temperature scale $T_{\mathrm{FL}}$. Surprisingly the quasiparticle scattering rate follows a quadratic temperature dependence up to much higher temperatures and crosses over to saturated behavior around a temperature scale $T_{\mathrm{sat}}$. We identify these quasiparticles as constituents of the hidden Fermi liquid. The non-Fermi-liquid transport above $T_{\mathrm{FL}}$, in particular the linear-in-$T$ resistivity, is shown to be a result of a strongly temperature dependent band dispersion. We derive simple expressions for the resistivity, Hall angle, thermoelectric power and Nernst coefficient in terms of a temperature dependent renormalized band structure and the quasiparticle scattering rate. We discuss possible tests of the dynamical mean-field theory picture of transport using ac measurements.

Figure 1

Spectral function $A_{\mathbf{k}}(\omega )$ along $\Gamma -X-M-\Gamma$ in Brillioun zone at (a) $T=0.0075$, (b) $T=0.025$, (c) $T=0.1$, and (d) $T=0.125$. (e) Local density of states. (f) Roots of Eq. (3) at different temperatures.

Figure 2

Transport properties. (a) Resistivity. (b) Hall angle. (c) Seebeck coefficient. (d) Nernst coefficient. Points labeled “exact exp.” are obtained using Eqs. (6). Points labeled “QP approx.” are obtained using Eqs. (8). Points labeled “expansion” are obtained using the general Sommerfeld expansion detailed in Supplemental Material [24]. The units are expressed in terms of universal constants, $\hslash$, $k_B$, $e$, the in-plane lattice constant $a$, and the out-of-plane lattice constant $c$.

Figure 3

(a) Quasiparticle scattering rate ${\Gamma }_{{\mathbf{k}}_F}^{*}$. The inset shows the estimation of $(k_F{l}^{*}{)}^{-1}$. (b) ${\Gamma }_{{\mathbf{k}}_F}^{*}$ as a function of $T^2$ for $T\lesssim T_{\mathrm{sat}}/2$. (c) Quasiparticle renormalization factor $Z_{{\mathbf{k}}_F}$ for $T\lesssim T_{\mathrm{sat}}/2$.