Topography inversion in scanning tunneling microscopy of single-atom-thick materials from penetrating substrate states

Scanning tunneling microscopy (STM) is one of the indispensable tools to characterize surface structures, but the distinction between atomic geometry and electronic effects based on the measured tunneling current is not always straightforward. In particular, for single-atomic-thick materials (graphene or boron nitride) on metallic substrates, counterintuitive phenomena such as a larger tunneling current for insulators than for metal and a topography opposite to the atomic geometry are reported. Using first-principles density functional theory calculations combined with analytical modeling, we reveal the critical role of penetrating states of metallic substrates that surpass 2D material states, hindering the measurement of intrinsic 2D materials states and leading to topography inversion. Our finding should be instrumental in the interpretation of STM topographies of atomic-thick materials and in the development of 2D material for (opto)electronic and various quantum applications.