Thermal-field electron emission from three-dimensional Dirac and Weyl semimetals

Abstract

A model is constructed to describe the thermal-field emission of electrons from a three-dimensional (3D) Dirac and Weyl semimetal hosting Dirac/Weyl node(s). The traditional thermal-field electron emission model is generalized to accommodate the 3D nonparabolic energy band structures in the Dirac/Weyl semimetals, such as cadmium arsenide $({\mathrm{Cd}}_{3}{\mathrm{As}}_{2})$, sodium bismuthide $({\mathrm{Na}}_{3}\mathrm{Bi})$, tantalum arsenide (TaAs), and tantalum phosphide (TaP). Due to the nontrivial energy decomposition of the energy dispersion and the vanishing transverse density of states, an unusual dual-peak feature is observed in the total energy distribution spectrum. This nontrivial dual-peak feature, absent from traditional materials, plays a critical role in manipulating the magnitude of the emission current through the variation of an applied field, temperature, and Fermi level. This feature suggests that a higher Fermi level will achieve a larger current density (apart from low work function). At zero temperature limit, a ${F}^{3}$ scaling law for pure field emission is derived and it is different from the well-known Fowler-Nordheim ${F}^{2}$ scaling law. Furthermore, these new behaviors have shown to exist beyond the Dirac cone approximated model. This model expands the recent understandings of electron emission studied for the Dirac two-dimensional (2D) materials into the 3D regime, and thus offers a theoretical foundation for the exploration in using Dirac semimetallic materials as novel electrodes.