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

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