Local Density of States in Mesoscopic Samples from Scanning Gate Microscopy

Details Local Density of States in Mesoscopic Samples from Scanning Gate Microscopy Local Density of States in Mesoscopic Samples from Scanning Gate Microscopy

2007-11-21

arxiv.org/abs/0711.3370v1

Phys. Rev. B 77, 125310 (2008)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

8 pages, 8 figures

Scientific paper

10.1103/PhysRevB.77.125310

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.

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