Anomalous Lorenz Number In Massive And Tilted Dirac Systems

We analytically calculate the anomalous transverse electric and thermal currents in massive and tilted Dirac systems, using beta -borophene as a representative material, and report on conditions under which the corresponding Lorenz number(La n ) deviates from its classically accepted value(L 0 ). The deviations in the high-temperature regime are shown to be an outcome of the quantitative difference in the respective kinetic transport expressions for electric( sigma ) and thermal( kappa ) conductivity and are further weighted through a convolution integral with a non-linearly energy-dependent Berry curvature that naturally arises in a Dirac material. In addition, the tilt and anisotropy of the Dirac system that are amenable to change via an external stimulus are found to quantitatively influenceLa n. The reported deviations fromL 0 hold practical utility inasmuch as they allow an independent tuning of sigma and kappa, useful in optimizing the output of thermoelectric devices.