Wiedemann-Franz law violation domain for graphene and nonrelativistic systems

TL;DR

This work analyzes violations of the Wiedemann–Franz law across graphene and nonrelativistic systems by developing a systematic non-fluid to fluid transition framework for the Lorenz ratio $L=\kappa/(\sigma T)$ with $L_0=\frac{\pi^2}{3}(k_B/e)^2$. It first derives non-fluid transport expressions for multiple cases (2D graphene, 3D NR, 3D graphene, etc.) and then introduces a fluid description via a relaxation-time Boltzmann approach, incorporating two CV definitions and a transition to enthalpy-per-electron to better capture Dirac-fluid behavior. A switching-function (sandwich) model interpolates between non-fluid and fluid regimes, yielding a four-region map in $\epsilon_F/T$ that qualitatively matches experimental graphene data (Crossno et al.) and highlights a nontrivial NF→F transition linked to electron–hole hydrodynamics. The findings suggest that WF-law violations in graphene arise from a fluid-dominated Dirac fluid sector and provide a pathway to connect theory with measurements, with potential extensions to other Dirac-like materials and doped graphene under various conditions.

Abstract

A systematic non-fluid to fluid transition framework and comparative research on Lorenz ratios for graphene and nonrelativistic systems have been studied to identify their Wiedemann-Franz law violation domain. Here, Lorenz ratio is defined as thermal conductivity divided by electrical conductivity times temperature times Lorenz number. In non-fluid framework, Lorenz ratio become exactly one, which means that the Wiedemann-Franz is obeyed within a Fermi Liquid domain. When one enters from Fermi Liquid to Dirac Fluid domain, Lorenz ratio becomes less than one in non-fluid framework but in fluid framework, it always remain greater than one for both domain. By compiling our outcomes and connecting with experimental data, a non-fluid to fluid transition framework is expected during the transition from Fermi Liquid to Dirac Fluid domain.

Figures (6)

• Figure 1: The Lorenz ratio regarding the chemical potential for non-fluid descriptions of graphene case (a) for 3D and (b) for 2D expressions
• Figure 2: The Lorenz ratio regarding the chemical potential for non-fluid descriptions of nonrelativistic case (a) for 3D and (b) for 2D expressions
• Figure 3: Lorenz ratio of 2D-G system by using fluid-type expression versus $\epsilon_F/T$ (LEFT) and comparison of specific heat and fluid aspect in 2D-G system versus $\epsilon_F/T$ (RIGHT)
• Figure 4: Lorenz ratio of fluid and non-fluid for 2D-G system versus $\epsilon_F/T$ (LEFT) and Lorenz ratio of the mixture of fluid and non-fluid with fitting parameters for 2D-G system versus $\epsilon_F/T$ (RIGHT)
• Figure 5: Lorenz ratio of 2D-G system versus number density for different theoretical works by Rycerz rycerz2021wiedemann, Tu et al.tu_Yin_23_the, Lucus et al.Theory_G_WF, including present work