Magnetic field symmetry and phase rigidity of the nonlinear conductance in a ring

Abstract

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. 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 con-nected 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 coefficients are asymm...

Wigner time delay and related concepts: Application to transport in coherent conductors

“…Note also the study for a ring made of strictly 1D wires [111]. (iii) Several experimental groups have analysed the non-linear transport in mesoscopic structures and specifically the asymmetry in magnetic field [128,137,215,9,8]. (iv) The case of disordered wires in the diffusive regime was analysed in Ref.…”

What can we learn from noise? — Mesoscopic nonequilibrium statistical physics —

“…What is the microscopic mechanism to break the Onsager-Casimir reciprocity in the nonlinear transport regime? Actually this phenomenon was known before [87,[91][92][93] and is attributed to electron-electron interactions in mesoscopic conductors [91,92]. As the magnetic field changes, the electronic property inside the ring and hence G 2 and S 1 are modulated at finite bias through the interaction.…”

“…(16), (29), and (30)) in the quantum regime. To this end, we used an electronic interferometer, or Aharonov-Bohm (AB) ring [87,88], as a typical mesoscopic conductor. While other mesoscopic systems, such as a quantum dot or a quantum wire, can be used for the same purpose, an AB ring has an advantage in that it is easy to prove that the coherent transport takes place as signaled by the AB oscillation.…”

Nonlinear conductance in weakly disordered mesoscopic wires: Interaction and magnetic field asymmetry

“…The symmetry with respect to magnetic field reversal is of special interest here, as it is related to the renewal of the interest for non-linear transport in normal metals [14][15][16][17][18]29,37,39,70 . Before discussing this matter, we come back to the important question of current conservation and gauge invariance, which introduce two types of constraints on the non-linear conductance.…”

“…Magnetic field symmetry of the electric conduction in the non-linear regime was addressed in several experiments : on quantum dots 14,17,37 , carbon nanotubes 38 , mesoscopic 2D metallic rings 18,[39][40][41][42] and monolayer graphene sheets 43 . Motivated by the early experiments, the first theoretical works on ballistic 15 and diffusive 16 quantum dots were completed by investigating the role of dephasing, thermal smearing, etc [28][29][30]44 .…”