Comprehensive tunneling spectroscopy of quasi-freestanding MoS$_2$ on graphene on Ir(111)

We apply scanning tunneling spectroscopy to determine the bandgaps of mono-, bi- and trilayer MoS$_2$ grown on a graphene single crystal on Ir(111). Besides the typical scanning tunneling spectroscopy at constant height, we employ two additional spectroscopic methods giving extra sensitivity and qualitative insight into the $k$-vector of the tunneling electrons. Employing this comprehensive set of spectroscopic methods in tandem, we deduce a bandgap of $2.53\pm0.08$ eV for the monolayer. This is close to the predicted values for freestanding MoS$_2$ and larger than is measured for MoS$_2$ on other substrates. Through precise analysis of the `comprehensive' tunneling spectroscopy we also identify critical point energies in the mono- and bilayer MoS$_2$ band structures. These compare well with their calculated freestanding equivalents, evidencing the graphene/Ir(111) substrate as an excellent environment upon which to study the many feted electronic phenomena of monolayer MoS$_2$ and similar materials. Additionally, this investigation serves to expand the fledgling field of the comprehensive tunneling spectroscopy technique itself.