Electron interferometry in the quantum Hall regime: Aharonov-Bohm effect of interacting electrons

Abstract

An apparent h/fe Aharonov-Bohm flux period, where f is an integer, has been reported in coherent quantum Hall devices. Such sub-period is not expected for non-interacting electrons and thus is thought to result from interelectron Coulomb interaction. Here we report experiments in a Fabry-Perot interferometer comprised of two wide constrictions enclosing an electron island. By carefully tuning the constriction front gates, we find a regime where interference oscillations with period h/2e persist throughout the transition between the integer quantum Hall plateaus 2 and 3, including half-filling. In a large quantum Hall sample, a transition between integer plateaus occurs near half-filling, where the bulk of the sample becomes delocalized and thus dissipative bulk current flows between the counterpropagating edges ("backscattering"). In a quantum Hall constriction, where conductance is due to electron tunneling, a transition between forward-and back-scattering is expected near the half-filling. In our experiment, neither period nor amplitude of the oscillations show a discontinuity at half-filling, indicating that only one interference path exists throughout the transition. We also present experiments and an analysis of the front-gate dependence of the phase of the oscillations. The results point to a single physical mechanism of the observed conductance oscillations: Aharonov-Bohm interference of interacting electrons in quantum Hall regime.The Aharonov-Bohm effect demonstrates the primacy of the potentials, rather than fields in quantum mechanics. Electron interaction usually does not affect the e h / Aharonov-Bohm flux period observed in conductance of normal metal and semiconductor rings with two leads. The situation is more complex in quantum Hall devices. An apparent e f h / Aharonov-Bohm flux period, where f is the integer quantum Hall effect (QHE) filling in the constrictions, has been reported in quantum antidot 4,5 and Fabry-Perot interferometer 6-8 devices. In quantum antidots, the closed AharonovBohm path follows an equipotential around the lithographically-defined potential hill in the twodimensional (2D) electron plane. In interferometer devices, the interference path follows an equipotential at device's edges, and is closed by two tunneling links.The experiments are done in a uniform magnetic field, so that a well-defined interference path enclosing an area is needed to translate the field into flux. This Aharonov-Bohm sub-period is accompanied by an e charge period as a function of a gate voltage, and is not affected by the 2D bulk filling outside the device. In quantum antidots, previously reported e h 2 / period 9,10 was tentatively attributed to spin-splitting of a Landau level. However, subsequent work has concluded that no model of non-interacting electrons can consistently explain this sub-period. 11,12 On the other hand, it seems apparent that the strong interelectron Coulomb interaction, present in

Robust electron pairing in the integer quantum hall effect regime

“…In these examples, the nonlinear conductance exhibited the ubiquitous Coulomb 28,31 , and the oscillation periodicity with respect to magnetic field scaled inversely with the number of fully transmitted channels through the device 6,30,[32][33][34] . These two features clearly differ from our observation in the AB-FPI.…”

“…Observation of h/2e periodicity (and higher harmonics) in other electronic systems, such as a CD FPI 6,7 and a CD quantum anti-dot [28][29][30] , have been reported in the past. In these examples, the nonlinear conductance exhibited the ubiquitous Coulomb 28,31 , and the oscillation periodicity with respect to magnetic field scaled inversely with the number of fully transmitted channels through the device 6,30,[32][33][34] .…”

Quantum Hall Mach-Zehnder interferometer at fractional filling factors

“…Low-size interferometers [10][11][12][13][14][15][16] are subject [15,16] to Coulomb blockade effects [17] because the size-induced Coulomb gap becomes comparable with the corresponding spectrum (cyclotron, Zeeman or fractional) one.…”

“…(ii) By contrast, low-size Fabry-Perot interferometers clearly demonstrate interference oscillations even in the fractional regime [10][11][12][13][14][15][16]. On the other hand, the interference pattern was shown [15,16] to be determined by Coulomb blockade effects [17] at fractional fillings.…”

Quantum Hall Mach-Zehnder interferometer far beyond equilibrium

“…Recent investigations of quantum Hall (QH) interferometers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] give rise to several fundamental puzzles even in the integer QH regime. The major ones are the influence of the electron-electron interaction on the interference pattern 10,15,17 and the nature of the decoherence 2,7,16 .…”