Theory of scanning gate microscopy

Abstract

A systematic theory of the conductance measurements of noninvasive (weak probe) scanning gate microscopy is presented that provides an interpretation of what precisely is being measured. A scattering approach is used to derive explicit expressions for the first-and second-order conductance changes due to the perturbation by the tip potential in terms of the scattering states of the unperturbed structure. In the case of a quantum point contact, the first-order correction dominates at the conductance steps and vanishes on the plateaux where the second-order term dominates. Both corrections are nonlocal for a generic structure. Only in special cases, such as that of a centrally symmetric quantum point contact in the conductance quantization regime, can the second-order correction be unambiguously related with the local current density. In the case of an abrupt quantum point contact, we are able to obtain analytic expressions for the scattering eigenfunctions and thus evaluate the resulting conductance corrections.

Scanning-gate-induced effects in nonlinear transport through nanostructures

“…For a QPC r m t m = 0 on a conductance plateau [21,22], yielding a vanishing μ. Moreover, away from the edges of the plateau the V and U derivatives of r m t m also vanish, and thus 115414-2 g (1) i = 0.…”

“…On one hand, from various experimental and theoretical works focused on a QPC probed by a strongly charged tip, the conductance change appears to be closely related to the local current density [15,16,23,24]. On the other, it has been shown [22] that only under quite restrictive conditions (a spatially symmetric QPC tuned to a conductance plateau) the tip-induced conductance change is directly related to the current density at the tip position.…”

“…The last equality of Eq. (3) is obtained by a change into the basis of scattering eigenstates (built from the eigenmodes of t † t) [22], where the reflection and transmission submatrices are diagonal with nonzero elements r m (r m ) and t m (t m ) for l = 1,2. N is the number of channels in the leads and U 21 m m is the matrix element of the perturbing potential between the m th left-and the mth right-moving scattering eigenstates.…”

“…Even in the linear regime, the interpretation of the resulting scans is delicate [21,22]. On one hand, from various experimental and theoretical works focused on a QPC probed by a strongly charged tip, the conductance change appears to be closely related to the local current density [15,16,23,24].…”

“…Firstly, what is the local potential of a QPC operating in the nonlinear regime [1,[25][26][27][28][29]? Secondly, what is actually measured in the scanning gate microscopy of a QPC in the linear and nonlinear regimes [13,18,21,22]?…”