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 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-ED|eb|E-ED|, rather than the commonly assumed |E-ED| scaling, where E and ED refer to the energy of the electrons and the Dirac point, respectively. The parameter b is inversely proportional to the Fermi velocity.