Local density of states in mesoscopic samples from scanning gate microscopy

Abstract

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

Extracting the density profile of an electronic wave function in a quantum dot

“…This technique compliments earlier methods to image the electron probability density in quantum rings. [10][11][12][13] Access to this fundamental information about the electron system will advance designs and applications of quantum devices.…”

“…4 The conducting tip of a cooled SPM has been used as a moveable gate to capacitively probe electrons inside nanostructures to image the flow of electron waves from a quantum point contact [5][6][7][8][9] and through a quantum ring [10][11][12] and to measure the energy of quantum states. [13][14][15][16][17][18] Semiconductor nanostructures are attractive for quantum devices.…”

Scanning-Gate Microscopy of Semiconductor Nanostructures: An Overview

“…It results in distortions of the SGM images, which can also be simulated (see Fig. 2 in [12]). For large distortions, it may even happen that the respective roles of the electron system and of the tip are reversed, as suggested by the SGM image in Fig.…”

“…Since its introduction in the late nineties [1][2][3], SGM has proven powerful to unravel the local details of electron behavior inside modulation--doped nanostructures whose active electron systems are, in contrast to surface electron-systems [4], not accessible to scanning-tunneling microscopy (STM) because they are located too deep below the surface. After a brief description of the technique as well as of some instructive achievements found in the literature [2,3,[5][6][7][8][9], this paper contains a selection of our own research dealing with the imaging of electron transport across GaInAs quantum rings (QRs) both in the (low-field) AharonovBohm (AB) [10][11][12][13] regime and in the (high-field) quantum Hall [14] regime.…”

Signatures of spin-orbit coupling in scanning gate conductance images of electron flow from quantum point contacts

“…The perturbation induced by the floating gate was used to map scarred wave functions in quantum billiards, 1,2 local density of states in quantum rings, [3][4][5] magnetic focusing of electrons 6 or for demonstration of a mesoscopic analogue to the Braess paradox. 7 Mapping of conductance of quantum point contacts (QPCs) allowed for observation of spatial maps of the coherent electron flow [8][9][10][11][12][13][14] and signatures of interference involving the presence of the tip.…”