Phase shifts and phaseπjumps in four-terminal waveguide Aharonov-Bohm interferometers

Abstract

Quantum coherent properties of electrons can be studied in Aharonov-Bohm (AB) interferometers. We investigate both experimentally and theoretically the transmission phase evolution in a four-terminal quasi-one-dimensional AlGaAs/GaAs-based waveguide AB ring. As main control parameter besides the magnetic field, we tune the Fermi wave number along the pathways using a top-gate. Our experimental results and theoretical calculations demonstrate the strong influence of the measurement configuration upon the AB-resistance-oscillation phase in a four-terminal device. While the non-local setup displays continuous phase shifts of the AB oscillations, the phase remains rigid in the local voltage-probe setup. Abrupt phase jumps are found in all measurement configurations. We analyze the phase shifts as functions of the magnetic field and the Fermi energy and provide a detailed theoretical model of the device. Scattering and reflections in the arms of the ring are the source of abrupt phase jumps by π.

Thermal energy and charge currents in multi-terminal nanorings

“…We use a wave-packet approach well-suited for the simultaneous evaluation of the transmission across the complete transport window. [17][18][19] This approach has been used before to accurately describe Aharonov-Bohm oscillations in a similar device probed over several transverse mode openings and magnetic fields. 17 The channels of the interferometer are modelled with a harmonic confinement.…”

“…[17][18][19] This approach has been used before to accurately describe Aharonov-Bohm oscillations in a similar device probed over several transverse mode openings and magnetic fields. 17 The channels of the interferometer are modelled with a harmonic confinement. 5,17 The harmonic confinement results in an equidistant spacing of mode-openings as a function of Fermi energy.…”

“…17 The channels of the interferometer are modelled with a harmonic confinement. 5,17 The harmonic confinement results in an equidistant spacing of mode-openings as a function of Fermi energy. For a linear relationship between Fermi energy and applied gate-voltage, the equidistant spacing is in line with the experimental data probing the mode-openings as a function of applied gate-voltage, Fig.…”

“…is determined from the frequency-independent part of the power spectral density of the thermal noise. 10,15 The phase coherence of interfering electrons in a similar device has been characterized before in theory and experiment 16,17 and thermal transport data measured in the same device have been reported. 10,15 The presence of junctions and crossings in a multi-terminal device requires to calculate the electric and thermal transport for the specific sample geometry across a range of Fermi energies.…”

Mesoscopic behavior of the transmission phase through confined correlated electronic systems

“…10 The phase of a QD in the Kondo regime was measured by Ji et al 11,12 Highly controlled experiments coupled with detailed theoretical modeling for an AB device without QD also found phase lapses for some parameter values due to scattering and reflections in the arms of the ring. 13 The puzzles posed by the experimental data attracted a sustained theoretical interest. Refs.…”