A unified ballistic transport relation for anisotropic dispersions and generalized dimensions

TL;DR

This paper presents a unified analytical formula for particle and energy transport in anisotropic dispersions across various dimensions, simplifying the analysis of ballistic transport phenomena in multiple systems.

Contribution

It introduces a generalized formula that unifies the description of ballistic transport for fermions and bosons in anisotropic dispersions and various dimensions, covering diverse physical systems.

Findings

Unified formula for ballistic transport in anisotropic dispersions.

Predicted novel thermoelectric power factor behavior in 3D Dirac bands.

Demonstrated applications to blackbody radiation, ballistic transistors, and thermoelectric effects.

Abstract

An analytical formula is derived for particle and energy densities of fermions and bosons, and their ballistic momentum and energy currents for anisotropic energy dispersions in generalized dimensions. The formulation considerably simplifies the comparison of the statistical properties and ballistic particle and energy transport currents of electrons, acoustic phonons, and photons in various dimensions in a unified manner. Assorted examples of its utility are discussed, ranging from blackbody radiation to Schottky diodes and ballistic transistors, quantized electrical and thermal conductance, generalized ballistic Seebeck and Peltier coefficients, their Onsager relations, the generalized Wiedemann-Franz law and the robustness of the Lorenz number, and ballistic thermoelectric power factors, all of which are obtained from the single formula. The new formulation predicts a thermoelectric power factor behaviour of 3D Dirac bands which has not been observed yet.