Local density of states in mesoscopic samples from scanning gate microscopy

作者：Marco G. Pala, Benoit Hackens, Frederico Martins, H. Sellier, V. Bayot, S. Huant, T. Ouisse · 发表于：Physical Review B · 年份：2008 · DOI：10.1103/physrevb.77.125310 · 被引用次数：51 · 研究领域：Quantum and electron transport phenomena、Advancements in Semiconductor Devices and Circuit Design、Molecular Junctions and Nanostructures

We study the relationship between the local density of states (LDOS) and the conductance variation $\ensuremath{\Delta}G$ in scanning-gate-microscopy experiments on mesoscopic structures as a charged tip scans above the sample surface. We present an analytical model showing that in the linear-response regime the conductance shift $\ensuremath{\Delta}G$ is proportional to the Hilbert transform of the LDOS and hence a generalized Kramers--Kronig relation holds between LDOS and $\ensuremath{\Delta}G$. We analyze the physical conditions for the validity of this relationship both for one-dimensional and two-dimensional systems when several channels contribute to the transport. We focus on realistic Aharonov--Bohm rings including a random distribution of impurities and analyze the LDOS-$\ensuremath{\Delta}G$ correspondence by means of exact numerical simulations, when localized states or semiclassical orbits characterize the wave function of the system.