Aharonov-Casher effect in quantum ring ensembles

Joibari, Fateme K.; Blanter, Ya. M.; Bauer, G.

doi:10.1103/physrevb.88.115410

Cited by 8 publications

(9 citation statements)

References 13 publications

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“…3c,d, equation (3) reproduces the observed phase shift within the energy range of small Zeeman energy (due to ) compared with the kinetic and Rashba SO-coupling energies. A similar quadratic shift in the interference peak positions has been recently calculated also for weakly coupled rings27.…”

Section: Resultssupporting

confidence: 79%

Control of the spin geometric phase in semiconductor quantum rings

et al. 2013

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Since the formulation of the geometric phase by Berry, its relevance has been demonstrated in a large variety of physical systems. However, a geometric phase of the most fundamental spin-1/2 system, the electron spin, has not been observed directly and controlled independently from dynamical phases. Here we report experimental evidence on the manipulation of an electron spin through a purely geometric effect in an InGaAs-based quantum ring with Rashba spin-orbit coupling. By applying an in-plane magnetic field, a phase shift of the Aharonov–Casher interference pattern towards the small spin-orbit-coupling regions is observed. A perturbation theory for a one-dimensional Rashba ring under small in-plane fields reveals that the phase shift originates exclusively from the modulation of a pure geometric-phase component of the electron spin beyond the adiabatic limit, independently from dynamical phases. The phase shift is well reproduced by implementing two independent approaches, that is, perturbation theory and non-perturbative transport simulations.

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Section: Resultssupporting

confidence: 79%

Control of the spin geometric phase in semiconductor quantum rings

et al. 2013

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“…2. The fit with the calculated wavefronts is very good despite the fact that actual spin dynamics is nonadiabatic (some deviations are visible for ∆ 1, where wavefronts are best described by geometric phase shifts [11,23]). The critical line corresponds to the frontier where the field texture changes topology, which coincides with the spineigenstate texture only in the adiabatic regime.…”

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confidence: 83%

Topological transitions in spin interferometers

et al. 2015

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We show that topological transitions in electronic spin transport are feasible by a controlled manipulation of spin-guiding fields. The transitions are determined by the topology of the fields texture through an effective Berry phase (related to the winding parity of spin modes around poles in the Bloch sphere), irrespective of the actual complexity of the nonadiabatic spin dynamics. This manifests as a distinct dislocation of the interference pattern in the quantum conductance of mesoscopic loops. The phenomenon is robust against disorder, and can be experimentally exploited to determine the magnitude of inner spin-orbit fields.PACS numbers: 71.70. Ej, 75.76.+j, In the early 1980s Berry showed that quantum states in a cyclic motion may acquire a phase component of geometric nature [1]. This opened a door to a class of topological quantum phenomena in optical and material systems [2]. With the development of quantum electronics in semiconducting nanostructures, a possibility emerged to manipulate electronic quantum states via the control of spin geometric phases driven by magnetic field textures [3]. After several experimental attempts An early proposal for the topological manipulation of electron spins by Lyanda-Geller involved the abrupt switching of Berry phases in spin interferometers [12]. These are conducting rings of mesoscopic size subject to Rashba spin-orbit (SO) coupling, where a radial magnetic texture B SO steers the electronic spin (Fig. 1a). For relatively large field strengths (or, alternatively, slow orbital motion) the electronic spins follow the local field direction adiabatically during transport, acquiring a Berry phase factor π of geometric origin (equal to half the solid angle subtended by the spins in a roundtrip) leading to destructive interference effects. By introducing an additional in-plane uniform field B, it was assumed that the spin geometric phase undergoes a sharp transition at the critical point beyond which the corresponding solid angle vanishes together with the Berry phase, and interference turns constructive. The transition should manifest as a step-like characteristic in the ring's conductance as a function of the coupling fields (so far unreported). However, this reasoning appears to be oversimplified: the adiabatic condition can not be satisfied in the vicinity of the transition point, since the local steering field vanishes and reverses direction abruptly at the rim of the ring. Moreover, typical experimental conditions correspond to moderate field strengths, resulting in nonadiabatic effects in analogy to the case of spin transport in helical magnetic fields [13]. Hence, a more sophisticated approach is required. This includes identifying the role played by nonadiabatic Aharonov-Anandan (AA) geometric phases [14].Here, we report transport simulations showing that a topological phase transition is possible in loop-shaped spin interferometers away from the adiabatic limit. The transition is determined by the topology of the field texture through an effective Berry phase ...

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“…Similarly, the Hamiltonian of the ring reads [46,48,49] As for the pairing potential, it is given by…”

Section: Model and Formalismmentioning

confidence: 99%

“…Here, V n (with n = x or z) stands for the Zeeman splitting from the magnetic field along the n-axis; σ stand for the Pauli matrices; L is the number of sites at each wire; µ = −1 (1) stands for the left (right) wire; t = /(2m * a 2 0 ) represents the hopping energy with a 0 denoting the distance between the nearest neighbors in the wire; V i = 2t stands for the on-site energy; i, j represents a pair of the nearest neighbors; v x ij = e x • d ij with d ij = (r i − r j )/|r i − r j |; E R is the Rashba spinorbit-coupling constant. The Hamiltonian of the ring reads 46,48,49 Ĥring =…”

Section: Model and Formalismmentioning

confidence: 99%

Majorana fermions in semiconductor nanostructures with two wires connected through a ring

Sun

2014

New J. Phys.

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We investigate the Majorana fermions in a semiconductor nanostructure with two wires connected through a ring. The nanostructure is mirror symmetric and in the proximity of a superconductor. The Rashba spin-orbit coupling and a magnetic field parallel to the wires or perpendicular to the ring are included. Moreover, a magnetic flux is applied through the center of the ring, which makes the phase difference of the superconducting order parameters in the two wires being zero or π due to the fluxoid quantization and the thermodynamic equilibrium of the supercurrent in the superconducting ring. If the phase difference is π, two Majorana modes are shown to appear around the ring without interacting with each other. On contrast, if the phase difference is zero, these Majorana modes disappear and the states localized around the ring have finite energies. These states can be detected via the conductance measurement by connecting two normal leads to the wires and a third one directly to the ring. It is shown in the bias dependence of the differential conductance from one of the leads connected to the wire to the one connected directly to the ring that the tunnelings through the Majorana modes (i.e., in the case with π phase difference) leads to two peaks very close to the zero bias, while the tunneling through the states with finite energies (i.e., in the case with zero phase difference) leads to peaks far away from the zero bias if the ring radius is small. This difference for the cases with and without the Majorana modes in small ring radius is distinct and hence can be used to identify the Majorana modes. In addition, we also find that, because of the mirror inversion symmetry of the nanostructure, the Andreev reflection through the lead connected at the ring (which is along the inversion axis) is forbidden around the zero bias if the magnetic flux is zero and the magnetic field is parallel to the wires.

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Aharonov-Casher effect in quantum ring ensembles

Cited by 8 publications

References 13 publications

Control of the spin geometric phase in semiconductor quantum rings

Control of the spin geometric phase in semiconductor quantum rings

Topological transitions in spin interferometers

Majorana fermions in semiconductor nanostructures with two wires connected through a ring

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