Scanning tunneling spectroscopy of two-dimensional Dirac materials on substrates with a band gap

Abstract

In this paper we show that conventional current-voltage spectroscopy can provide quantitative information on the dispersion relation of the low-energy electrons of monoelemental group-IV two-dimensional (2D) Dirac materials provided that (1) the 2D material is placed on a substrate with a band gap and (2) the density of states of the scanning tunneling microscopy tip is constant. We have derived an expression for the differential conductivity of a monoelemental group-IV 2D Dirac material that is placed on a substrate with a band gap. The differential conductivity scales as $|E\ensuremath{-}{E}_{D}|{e}^{b|E\ensuremath{-}{E}_{D}|},$ rather than the commonly assumed $|E\ensuremath{-}{E}_{D}|$ scaling, where $E$ and ${E}_{D}$ refer to the energy of the electrons and the Dirac point, respectively. The parameter $b$ is inversely proportional to the Fermi velocity.