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 (Cd3As2), sodium bismuthide (Na3Bi), 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.