Scanning gate microscopy as a tool for extracting electronic properties in quantum transport

The scanning gate microscopy (SGM) technique consists in measuring the conductance of a two dimensional electron gas (2DEG) under the influence of a scanning tip. In this work, an analytical approach complemented by numerical simulations is developed to study the connection between SGM measurements and local electronic properties in mesoscopic devices. The connection between the SGM response and the partial local density of states (PLDOS) is studied for the case of a quantum point contact surrounded by clean or disordered 2DEG for perturbative or non-perturbative, local or extended tips. An SGM-PLDOS correspondence is found for integer transmissions and local tips. The degradation of this correspondence out of these conditions is studied. Moreover, a presumed link between the SGM response and the Hilbert transform of the LDOS is discussed. To study the role of the tip strength, an analytical formula giving the full conductance in the case of local tips is obtained. Furthermore, a Green function method enabling to calculate the quantum conductance in the presence of a finite size tip in terms of the unperturbed properties is proposed. Finally the dependence of the PLDOS branches on the Fermi energy is studied.