ИСТИНА

Our study is related to the question: how much the tip of a scanning tunneling microscope (STM) affects the measured values. We study the influence of the potential induced by the microscope tip on the electronic states in a two-dimensional crystal. We consider the two-dimensional stationary Schrodinger and Dirac equations with a radial symmetric potential that simulates the STM tip. We construct semiclassical asymptotic forms for generalized eigenfunctions and study the local density of states that corresponds to the microscope measurements. We show that in the case of the Dirac equation, the tip distorts the measured density of states for all energies. Financial support by RFBR–CNRS project 17-51-150006.