Electrostatic theory of irregular conductance oscillations through a quantum constriction under quantized Hall conditions

Abstract

Abstract We propose a semi-classical explanation to the conductance oscillations ( δ G ) observed at gate-controlled quantum dots under quantized Hall conditions. Our approach is based on the self-consistent screening theory of the quantum Hall effect and δ G originates either from the interference of electrons or from charging effects. In the interference regime electrons acquire an Aharonov–Bohm phase while propagating coherently along the evanescent incompressible stripes at a particular filling factor, where the stripes enclose a magnetic flux. The charging regime finds its ground in Coulomb blocked, where the transport electron generates an additional energy scale to conductance oscillations. Combining these two regimes, we found that the period of conductance oscillations in magnetic field ( Δ B ) may increase, decrease or remain constant at different filling factors, as observed in the experiments. In addition it is shown that, a gate potential can shift the incompressible stripe along the gated edge spatially, thereby changing the enclosed flux, and can induce δ G with a period Δ V g . We demonstrate that our formulation is able to generate the superimposed Δ B - Δ V g interferences in stripe or checkerboard patterns in agreement with experiments. We can account for further salient and peculiar features of experimental observations for example the surprising absence of oscillations at certain filling factors.