Tunable Aharonov-Bohm effect in an electron interferometer

Vegvar, P. G. N. de; Timp, G.; Mankiewich, P. M.; Behringer, R. E.; Cunningham, J. E.

doi:10.1103/physrevb.40.3491

Cited by 80 publications

(38 citation statements)

References 15 publications

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“…13,[34][35][36] Due to the ring's geometrical asymmetry, a change in k F evokes an AB oscillation phase shift. At a fixed magnetic field and neglecting constant phases i , the interference of partial electron waves ⌿ s 1 = ͉⌿ s 1 ͉ · e ik F s 1 propagating along the waveguide s 1 and ⌿ s 2 = ͉⌿ s 2 ͉ · e ik F s 2 propagating along s 2 is ͉⌿ s 1 + ⌿ s 2 ͉ 2 = ͉⌿ s 1 ͉ 2 + ͉⌿ s 2 ͉ 2 +2͉⌿ s 1 ͉͉⌿ s 2 ͉cos͓k F ⌬s͔, where ⌬s = s 1 − s 2 is the geometrical difference between the paths.…”

Section: B Electrostatic Ab Phase Shiftmentioning

confidence: 99%

Control of the transmission phase in an asymmetric four-terminal Aharonov-Bohm interferometer

et al. 2010

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Phase sensitivity and thermal dephasing in coherent electron transport in quasi-one-dimensional ͑1D͒ waveguide rings of an asymmetric four-terminal geometry are studied by magnetotransport measurements. We demonstrate the electrostatic control of the phase in Aharonov-Bohm resistance oscillations and investigate the impact of the measurement circuitry on decoherence. Phase rigidity is broken due to the ring geometry: orthogonal waveguide cross junctions and 1D leads minimize reflections and resonances between leads allowing for a continuous electron transmission phase shift. The measurement circuitry influences dephasing: thermal averaging dominates in the nonlocal measurement configuration while additional influence of potential fluctuations becomes relevant in the local configuration.

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Section: B Electrostatic Ab Phase Shiftmentioning

confidence: 99%

Control of the transmission phase in an asymmetric four-terminal Aharonov-Bohm interferometer

et al. 2010

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“…Since the latter suggests the phase induced by the vector potential associated to a magnetic flux penetrating the system, 49 we prefer to avoid that denomination in the present system, which preserves time-reversal invariance. There is literature on the Aharonov-Bohm effect induced by the scalar potential, [50][51][52] which could eventually justify the use of that term in the present context. However, it is not clear in those systems whether the effect is due to the extra phase acquired by electrons according to the Aharonov-Bohm mechanism 53,54 or simply due to the change of the electron trajectories 50 or the electron density.…”

Section: B Two Point Contactsmentioning

confidence: 99%

Transport phenomena in helical edge state interferometers: A Green's function approach

2013

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We analyze the current and the shot-noise of an electron interferometer made of the helical edge states of a two-dimensional topological insulator within the framework of non-equilibrium Green's functions formalism. We study in detail setups with a single and with two quantum point contacts inducing scattering between the different edge states. We consider processes preserving the spin as well as the effect of spin-flip scattering. In the case of a single quantum point contact, a simple test based on the shot-noise measurement is proposed to quantify the strength of the spin-flip scattering. In the case of two single point contacts with the additional ingredient of gate voltages applied within a finite-size region at the top and bottom edges of the sample, we identify two type of interference processes in the behavior of the currents and the noise. One of such processes is analogous to that taking place in a Fabry-Pérot interferometer, while the second one corresponds to a configuration similar to a Mach-Zehnder interferometer. In the helical interferometer these two processes compete.

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“…1(a)] to modify locally the electron density in the ring. Earlier experiments have shown that a gate voltage can tune the electronic phase accumulated along the arms of the ring through the product k F L, where k F is the Fermi wave vector and L the length of the ring affected by the gate [4,7,21,22,23]. Here we use either the gates PG2 and PG3 (right arm of the ring), or the gate PG1 (left arm of the ring), in order to change the phase only in a selected part of the ring.…”

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confidence: 99%

Magnetic Field Symmetry and Phase Rigidity of the Nonlinear Conductance in a Ring

et al. 2006

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We have performed nonlinear transport measurements as a function of a perpendicular magnetic field in a semiconductor Aharonov-Bohm ring connected to two leads. While the voltage-symmetric part of the conductance is symmetric in magnetic field, the voltage-antisymmetric part of the conductance is not symmetric. These symmetry relations are compatible with the scattering theory for nonlinear mesoscopic transport. The observed asymmetry can be tuned continuously by changing the gate voltages near the arms of the ring, showing that the phase of the nonlinear conductance in a two-terminal interferometer is not rigid, in contrast to the case for the linear conductance.PACS numbers: 73.50.Fq, A mesoscopic ring can be used as an electron interferometer in order to compare the electronic phase of electrons traveling through both arms of the ring using the Aharonov-Bohm (AB) effect. However, it has been shown that a two-terminal ring does not allow to measure directly this phase difference in the linear transport [1]: the two-terminal conductance shows AB oscillations with a phase constrained to 0 or π [2,3,4]. This phase rigidity is a consequence of microreversibility [5] showing that the linear conductance of a two-terminal system must be symmetric in magnetic field [1,6]. A direct measurement of the phase difference is possible only in an open multi-terminal geometry [7,8].While the Onsager-Casimir relations hold close to equilibrium (linear conductance), there is no fundamental reason why far from equilibrium the nonlinear conductance should still follow this symmetry, i.e., one could expect G(V, B) = G(V, −B). It is then natural to ask whether the phase rigidity would still hold for the nonlinear transport in a two-terminal ring.In a phase coherent diffusive system, nonlinear conductance is expected when the bias voltage is larger than E T /e, where E T is the Thouless energy [9]. Models developed for non-interacting electrons predict an effect symmetric in magnetic field, which has been observed experimentally through bias voltage induced universal conductance fluctuations [10,11]. The possibility to observe magnetic field asymmetric nonlinear transport has been addressed only very recently both theoretically [12,13] and experimentally [14,15,16,17]. The models proposed there rely on effects of electron-electron interactions in noncentrosymmetric systems. Such behavior could be also expected in AB rings, for which symmetry breaking occurs due to asymmetries in the phase accumulated in each arm of the ring.Here we address the question of the magnetic field symmetries of the nonlinear conductance in a ring used as an Aharonov-Bohm interferometer. We have performed nonlinear d.c. transport measurements in a ring connected to two terminals. The current is fitted by a polynomial function of the bias voltage, with each coefficient of the decomposition showing AB oscillations as a function of magnetic field. While the odd coefficients are symmetric in magnetic field and show strong h/2e oscillations, the even coefficient...

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Tunable Aharonov-Bohm effect in an electron interferometer

Cited by 80 publications

References 15 publications

Control of the transmission phase in an asymmetric four-terminal Aharonov-Bohm interferometer

Control of the transmission phase in an asymmetric four-terminal Aharonov-Bohm interferometer

Transport phenomena in helical edge state interferometers: A Green's function approach

Magnetic Field Symmetry and Phase Rigidity of the Nonlinear Conductance in a Ring

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