Intrinsic violation of the Wiedemann-Franz law in interacting systems

Abstract

The Wiedemann-Franz (WF) law dictates a universal ratio between thermal and electrical conductivities, is widely obeyed by Fermi liquid systems. Here, we identify a fundamental yet often overlooked, thermodynamic mechanism for the violation of WF law: the temperature-dependent renormalization of the electronic band structure. We demonstrate that the interaction-induced energy drift $\partialε_k/\partial T$, acts as an effective driving force that fundamentally decouples heat transport from charge transport. We derive a generalized transport relation linking the Lorenz ratio deviation directly to the thermoelectric response. Our findings provide a unified framework for understanding thermal transport in interacting topological phases and suggest the Lorenz ratio as a probe for distinguishing topological robustness from Fermi liquid instabilities.

Figures (3)

• Figure 1: Schematic of the interaction-induced force. The orange-to-blue gradient represents the thermal excitation density, fully covering the band below the Fermi level. (a) Rigid band: The statistical force $F_{\text{stat}}$ drives transport. (b) Interacting system: The band tilt $\nabla \varepsilon$ generates an opposing interaction force $F_{\text{int}}$, modifying the heat current.
• Figure 2: (a) Sublattice magnetization $m_A$ and $-m_B$ versus Hubbard interaction $U$ at zero temperature. (b)-(e) Sublattice magnetization, interaction-induced energy drift, longitudinal Mott ratio, and the longitudinal WF law deviation $\gamma_{xx}(T) -1$ as a function of temperature for different $U$. (f) A color density plot showing $\gamma_{xx}-1$, in the U-T plane. The magnitude of $\gamma_{xx}-1$ is represented by the color density, which is superimposed with white contour lines denoting the sublattice magnetization $m$. The parameters are $t=1$, $\lambda_R = 0.1$, $M=0.1$, and particle filling number is set to $2.1$.
• Figure 3: (a) Anomalous Hall conductivity and (b) transverse WF deviation versus temperature for a metal state with filling number $n=2.1$. (c)-(f) Topological protection of the transverse Wiedemann-Franz (WF) law against electron-electron interactions. Dependence of transport quantities on the chemical potential $\mu/t$ for Rashba spin-orbit coupling strengths $\lambda_R=0.1$ and $\lambda_R=0.2$. (c) Transverse electrical conductivity $\sigma_{xy}$. (d) Transverse thermoelectric conductivity $\alpha_{xy}$. (e) The interaction-induced energy drift at the Fermi level, $(\partial\epsilon/\partial T)_{\mu}$. (f) The relative deviation of the transverse Lorenz ratio, $\gamma_{xy}-1$.