Local Density of States in Mesoscopic Samples from Scanning Gate Microscopy

• Published in: arXiv.org
• Main Authors: Pala, M G, Hackens, B, Martins, F, Sellier, H, Bayot, V, Huant, S, Ouisse, T
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 21.11.2007
• Subjects: Computer simulation; Density of states; Hilbert transformation; Mathematical models; Microscopy; Physics - Mesoscale and Nanoscale Physics; Resistance
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.0711.3370

We study the relationship between the local density of states (LDOS) and the conductance variation \(\Delta G\) 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 \(\Delta G\) is proportional to the Hilbert transform of the LDOS and hence a generalized Kramers-Kronig relation holds between LDOS and \(\Delta G\). 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-\(\Delta G\) correspondence by means of exact numerical simulations, when localized states or semi-classical orbits characterize the wavefunction of the system.