Universal model for electron thermal-field emission from two-dimensional semimetals

We present the theory of out-of-plane (or vertical) electron thermal-field emission from 2D semimetals. show that current-voltage-temperature characteristic is well-captured by a universal scaling relation applicable for broad classes semimetals, including graphene and its few-layer, nodal point semimetal, Dirac semimetal at verge topological phase transition line semimetal. Here an important consequence behavior revealed: in contrast to common expectation band topology shall manifest differently physical observables, topologies two spatial dimension are indistinguishable each others bear no special signature characteristics. Our findings represent quantum extension semiclassical thermionic law materials, provide theoretical foundations understanding cathode charge interface transport design 2D-material-based vacuum nanoelectronics.