In a recent Letter, Bergsten and co-authors have studied the resistance oscillations with gate voltage and magnetic field in arrays of semiconductor rings and interpreted the oscillatory magnetic field dependence as Altshuler-Aronov-Spivak (AAS) oscillations and oscillatory dependence on gate voltage as the Aharonov-Casher (AC) effect. This Comment shows that Bergsten and co-authors incorrectly identified AAS effect as a source of resistance oscillations in magnetic field, that spin relaxation in their experimental setting is strong enough to destroy oscillatory effects of spin origin, and that the oscillations are caused by changes in carrier density and the Fermi energy by gate, and are unrelated to spin.
We briefly review the theoretical formulations and applications of the Aharonov--Bohm effect and the Aharonov--Casher effect with emphasis on mesoscopic physics. Topics relating to the Aharonov--Bohm effect include: locality, periodicity, non-integrable phase factors, Abelian gauge theory, interference, the spectrum and persistent current of electrons on a ring pierced by a magnetic field, Onsager reciprocity relations, and Aharonov--Bohm interferometer. Topics relating to the Aharonov--Casher effect include: a magnetic dipole in an electric field, locality, periodicity, non-Abelian gauge inva…
We investigate electron transport under the two impurity Kondo problem with the Aharonov--Bohm and Aharonov--Casher effects. These interference effects induce the Ising-coupled Ruderman--Kittel--Kasuya--Yosida (RKKY) interaction. We discuss the inter- and intra-site spin conductance as well as charge conductance in the Kondo and the mixed-valence regimes using the slave boson mean field approximation.
It is shown that an Aharonov-Casher vector potential in a two-dimensional geometry can lead to helical edge states. The Aharonov-Casher vector potential is the electromagnetic dual of the magnetic vector potential, and leads to traveling states at the sample edge in analogy to the integer quantum Hall effect. The helical edge states are predicted to appear in a narrow channel geometry with parabolic or sufficiently symmetric confinement potential. The implications of the helical Aharonov-Casher edge states and experimental considerations in specific materials systems are discussed.
We study combined interference effects due to the Aharonov-Bohm (AB) and Aharonov-Casher (AC) phases in a Josephson supercurrent of local and nonlocal (split) Cooper pairs. We analyze a junction between two superconductors interconnected through a normal-state nanostructure with either (i) a ring, where single-electron interference is possible, or (ii) two parallel nanowires, where the single-electron interference can be absent, but the cross Andreeev reflection can occur. In the low-transmission regime in both geometries the AB and AC effects can be related to only local or nonlocal Cooper pa…
Ring structures fabricated from HgTe/HgCdTe quantum wells have been used to study Aharonov-Bohm type conductance oscillations as a function of Rashba spin-orbit splitting strength. We observe non-monotonic phase changes indicating that an additional phase factor modifies the electron wave function. We associate these observations with the Aharonov-Casher effect. This is confirmed by comparison with numerical calculations of the magneto-conductance for a multichannel ring structure within the Landauer-Büttiker formalism.
We have calculated the persistent spin current of an open ring induced by the Aharonov-Casher phase. For unpolarized electrons there exist no persistent charge currents, but persistent spin currents. We show that, in general, the magnitude of the persistent spin current in a ring depends on the direction of the direct current flow from one reservoir to another. The persistent spin current is modulated by the cosine function of the spin precession angle. The nonadiabatic Aharonov-Casher phase gives anomalous behaviors. The Aharonov-Anandan phase is determined by the solid angle of spin precessi…
We investigate quantum spin transport in a structure of conducting ring, embedded in textured electric field, with two leads, and obtain an exact solution for the problem. The spin precession induced by the Aharonov-Casher phase is studied. It is shown that the spin-polarized current and its polarizability can be controlled by the electric field. As a result the polarizability is a function of the geometric phase which originates from the spin-orbital interaction in the ring. 72.25.-b, 03.65.Vf
After obtaining an exact analytical time-varying solution for the Aharonov-Casher conducting ring embedded in a textured static/dynamic electric field, we investigate the spin-resolved quantum transport in the structure. It is shown that the interference patterns are governed by not only the Aharonov-Casher geometry phase but also the instantaneous phase difference of spin precession through different traveling paths. This dynamic phase is determined by the strength of applied electric field and can have substantial effects on the charge/spin conductances, especially in the weak field regime a…
We analyze a Josephson junction between two superconductors interconnected through a normal-state nanostructure made of two parallel nanowires with embedded quantum dots. We study the influence of interference effects due to the Aharonov-Bohm (AB) and Aharonov-Casher (AC) phases for local and nonlocal (split) Cooper pairs. In the AB effect the phase of electron is affected by magnetic flux, while in the AC effect the phase of the electron in solid state can be modified due to the Rashba spin-orbit coupling. In the low-transmission regime the AB and AC effects can be related to only local or no…
The time reversal Aharonov-Casher (AC) interference effect in the mesoscopic ring structures, based on the experiment in Phys. Rev. Lett. \textbf{97}, 196803 (2006), is studied theoretically. The transmission curves are calculated from the scattering matrix formalism, and the time reversal AC interference frequency is singled out from the Fourier spectra in numerical simulations. This frequency is in good agreement with analytical result. It is also shown that in the absent of magnetic field, the Altshuler-Aronov-Spivak type (time reversal) AC interference retains under the influence of strong…
A mesoscopic ring subject to the Rashba spin-orbit interaction and sequentially coupled to an interacting quantum dot, in the presence of Aharonov-Bohm flux, is proposed as a flux tunable tunneling diode. The analysis of the conductance by means of the nonequilibrium Green's function technique, shows an intrinsic bistability at varying the Aharonov-Bohm flux when 2U > πΓ, U being the charging energy on the dot and Γthe effective resonance width. The bistability properties are discussed in connection with spin-switch effects and logical storage device applications.
We study the time-dependent transport of charge and spin through a ring-shaped region sequentially coupled to a weakly interacting quantum dot in the presence of an Aharonov-Bohm flux and spin-orbit interaction. The time-dependent modulation of the spin-orbit interaction, or of the corresponding Aharonov-Casher flux, together with the modulation of the dot-level induces an electrically pumped spin current even in absence of a charge current. The results beyond the adiabatic regime show that an additional rectification current proportional to \cos(ϕ), being ϕthe relative phase between the time …
We study the transport of electrons through a single-mode quantum ring with electric field induced Rashba spin-orbit interaction that is subjected to an in-plane magnetic field and weakly coupled to electron reservoirs. Modelling a ring array by ensemble averaging over a Gaussian distribution of energy level positions, we predict slow conductance oscillations as a function of the Rashba interaction and electron density due to spin-orbit interaction-induced beating of the spacings between the levels crossed by the Fermi energy. Our results agree with experiments by Nitta c.s., thereby providing…
Electrical control of spin dynamics in Bi$_{\rm 2}$Se$_{\rm 3}$ was investigated in ring-type interferometers. Aharonov-Bohm and Altshuler-Aronov-Spivak resistance oscillations against magnetic field, and Aharorov-Casher resistance oscillations against gate voltage were observed in the presence of a Berry phase of $π$. A very large tunability of spin precession angle by gate voltage has been obtained, indicating that Bi$_{\rm 2}$Se$_{\rm 3}$-related materials with strong spin-orbit coupling are promising candidates for constructing novel spintronic devices.
We demonstrate the time reversal Aharonov-Casher (AC) effect in small arrays of mesoscopic semiconductor rings. By using an electrostatic gate we can control the spin precession rate and follow the AC phase over several interference periods. We show that we control the precession rate in two different gate voltage ranges; in the lower range the gate voltage dependence is strong and linear and in the higher range the dependence in almost an order of magnitude weaker. We also see the second harmonic of the AC interference, oscillating with half the period. We finally map the AC phase to the spin…
We considered the circulating current induced by the current magnification and the persistent current induced by Aharonov-Casher flux. The persistent currents have directional dependence on the direct current flow, but the circulating currents have no directional dependence. Hence in the equilibrium, only the persistent current can survives on the ring. For the charge current, the persistent charge current cancelled between spin up and down states, because of the time reversal symmetry of the Hamiltonian on the ring. So there are only circulating charge currents on the ring for electrons with …
We study the quantum interference effects induced by the Aharonov-Casher phase in a ring structure in a two-dimensional heavy hole (HH) system with spin-orbit interaction realizable in narrow asymmetric quantum wells. The influence of the spin-orbit interaction strength on the transport is investigated analytically. These analytical results allow us to explain the interference effects as a signature of the Aharonov-Casher Berry phases. Unlike previous studies on the electron two-dimensional Rashba systems, we find that the frequency of conductance modulations as a function of the spin-orbit st…
We study theoretically the combined effect of the spin-orbit and Zeeman interactions on the tunneling electron transport through a single-channel quantum ring threaded by magnetic flux. We focus on the high temperature case (temperature is much higher than the level spacing in the ring) and demonstrate that spin-interference effects are not suppressed by thermal averaging. In the absence of the Zeeman coupling the high-temperature tunneling conductance of the ring exhibits two types of oscillations: Aharonov-Bohm oscillations with magnetic flux and Aharonov-Casher oscillations with the strengt…
Spin interference due to Rashba spin-orbit interaction (SOI) in a ballistic two-dimensional electron gas (2DEG) ring conductor submitted to a bias voltage is investigated theoretically. We calculate the scattering matrices and differential conductance with lead-ring junction coupling as an adjustable parameter. Due to the interference of electronic waves traversing the ring, the differential conductance modulated by both bias voltage and SOI exhibits a diamond-shaped pattern, thus termed as \ti{Rashba diamond}. This feature offers a supplementary degree of freedom to manipulate phase interfere…
In this study, Rashba coupling induced Aharonov-Casher effect in a graphene based nano ring is investigated theoretically. The graphene based nano ring is considered as a central device connected to semi-infinite graphene nano ribbons. In the presence of the Rashba spin-orbit interaction, two armchair shaped edge nano ribbons are considered as semi-infinite leads. The non-equilibrium Green's function approach is utilized to obtain the quantum transport characteristics of the system. The relaxation and dephasing mechanisms within the self-consistent Born approximation is scrutinized. The Lopez-…
The matrix-valued Aharonov-Casher phase factor $F_{\text{AC}}$ (related to the c-number Aharonov-Casher phase $λ_{\text{AC}}$) plays an important role in the physics of mesoscopic systems in which spin-orbit coupling is relevant. Yet, its relation to experimental observables is rather elusive. Based on the SU(2)-gauge-invariant formulation of the Schroedinger equation, we relate $F_{\text{AC}}$ to measurable quantities in electronic interferometers subject to electric fields that generate Rashba or Dresselhaus spin-orbit coupling. Specifically, we consider electron transmission through (i) a s…
In this Reply we argue that (i) the Hamiltonian, Eq. (17) in our paper (Phys. Rev. Lett. 108, 070405 (2012)), is definitely Lorentz invariant; (ii) the conditions of generating topological Aharonov-Casher(AC) and Scalar Aharonov-Bohm (SAB) effects are essential and physically meaningful; (iii) the Hamiltonians both in Phys. Rev. Lett. 74, 2847 (1995) and arXiv:1311.4011 are not suitable to describe the polarized spinor particles.
A neutral quantum particle with magnetic moment encircling a static electric charge acquires a quantum mechanical phase (Aharonov-Casher effect). In superconducting electronics the neutral particle becomes a fluxon that moves around superconducting islands connected by Josephson junctions. The full understanding of this effect in systems of many junctions is crucial for the design of novel quantum circuits. Here we present measurements and quantitative analysis of fluxon interference patterns in a six Josephson junction chain. In this multi-junction circuit the fluxon can encircle any combinat…
The coexistence of Rashba and Dresselhaus spin-orbit interactions (SOIs) in semiconductor quantum wells leads to an anisotropic effective field coupled to carriers' spins. We demonstrate a gate-controlled anisotropy in Aharonov-Casher (AC) spin interferometry experiments with InGaAs mesoscopic rings by using an in-plane magnetic field as a probe. Supported by a perturbation-theory approach, we find that the Rashba SOI strength controls the AC resistance anisotropy via spin dynamic and geometric phases and establish ways to manipulate them by employing electric and magnetic tunings. Moreover, a…
The Aharonov-Casher (AC) oscillations of spin current through a 2D ballistic ring in the presence of Rashba spin-orbit interaction and external magnetic field has been calculated using the semiclassical path integral method. For classically chaotic trajectories the Fokker-Planck equation determining dynamics of the particle spin polarization has been derived. On the basis of this equation an analytic expression for the spin conductance has been obtained taking into account a finite width of the ring arms carrying large number of conducting channels. It was shown that the finite width results i…
The spin-orbit interaction is a key tool for manipulating and functionalizing spin-dependent electron transport. However, the precise value of the spin-orbit coupling constant is hard to determine and control. Here we propose a measurement of the geometric (Aharonov-Casher) phase of the electron wavefunction generated by the spin-orbit coupling as a means to deduce the spin-orbit coupling strength in weak links. Unlike other proposed measurements of geometric phases, which rely on interference, we show that the anisotropy of the magnetoconductance, measured at different directions of an extern…
The Aharonov Casher effect predicts the existence in two dimensions of ceil(Phi/2pi) -1 bounded zero modes associated with a magnetic flux Phi. Aharonov and Casher discussed the case of gyromagnetic factor equals 2, we will discuss the general case of any gyromagnetic factor. As a simple model, we study the case where the magnetic field lies in a thin annulus. First we examine the wavefunctions of the zero-energy bounded states, predicted by the Aharonov Casher Effect for electrons with gyromagnetic ratio equal 2. We then calculate the wave function and energies for a gyromagnetic ratio g not …
We study the interference effect induced by the Aharonov-Casher phase on the Josephson current through a semiconducting ring attached to superconducting leads. Using a 1D model that incorporates spin-orbit coupling in the semiconducting ring, we calculate the Andreev levels analytically and numerically, and predict oscillations of the Josephson current due to the AC phase. This result is valid from the point contact limit to the long channel length limit, as defined by the ratio of the junction length and the BCS healing length. We show in the long channel length limit that the impurity scatte…
Phase slips in a one-dimensional closed array of Josephson junctions hybridize the persistent current states (PCS) and plasmon branches of excitations. The interference between phase slips passing through different junctions of the array makes the hybridization sensitive to the charges of the superconducting islands comprising the array. This in turn results in the Aharonov-Casher effect for plasmons, which in absence of phase slips are insensitive to island charges.
In this Comment we point out (i) that the Hamiltonian, Eq. (17) in the Letter(Phys. Rev. Lett. 108, 070405 (2012)), is not a relativistic Hamiltonian, (ii) then that the conditions in the Letter are irrelevant for a topological AC and SAB effects, and (iii) conclusively that the non-relativistic Hamiltonian employed by Peshkin and Lipkin (Phys. Rev. Lett. 74, 2847 (1995)) has the same $U(1)_{mm}$ gauge structure for a fixed spin and then is not wrong, but their incorrect interpretation of the spin autocorrelations led to the incorrect conclusion.
We study the persistent currents induced by both the Aharonov-Bohm and Aharonov-Casher effects in a one-dimensional mesoscopic ring coupled to a side-branch quantum dot at Kondo resonance. For privileged values of the Aharonov-Bohm-Casher fluxes, the problem can be mapped onto an integrable model, exactly solvable by a Bethe ansatz. In the case of a pure magnetic Aharonov-Bohm flux, we find that the presence of the quantum dot has no effect on the persistent current. In contrast, the Kondo resonance interferes with the spin-dependent Aharonov-Casher effect to induce a current which, in the str…
We study the effect of an electric charge in the middle of a ring of electrons in a magnetic field such as $ν= 1/2$. In the absence of the central charge, a residual current should appear due to an Aharanov-Bohm effect. As the charge varies, periodic currents should appear in the ring. We evaluate the amplitude of these currents, as well as their period as the central charge varies. The presence of these currents should be a direct signature of the existence of a statistical gauge field in the $ν=1/2$ quantum Hall effect. Numerical diagonalizations for a small number of electrons on the sphere…
We establish systematic consolidation of the Aharonov-Bohm and Aharonov-Casher effects including their scalar counterparts. Their formal correspondences in acquiring topological phases are revealed on the basis of the gauge symmetry in non-simply connected spaces and the adiabatic condition for the state of magnetic dipoles. In addition, investigation of basic two-body interactions between an electric charge and a magnetic dipole clarifies their appropriate relative motions and discloses physical interrelations between the effects. Based on the two-body interaction, we also construct an exact …
We consider a model describing a spin field-effect transistor based on a quantum nanowire with a tunable spin-orbit interaction embedded between two ferromagnetic leads with anticollinear magnetization. We investigate a regime of a strong interplay between resonance Kondo scattering and interference associated with the Aharonov-Casher effect. Using the Keldysh technique at weak coupling regime we calculate perturbatively the charge current. It is predicted that the effects of the spin-orbit interaction result in a non-vanishing current for any spin polarization of the leads including the case …
We theoretically study the effects of spin-orbit coupling on spin exchange in a low-density Wigner crystal. In addition to the familiar antiferromagnetic Heisenberg exchange, we find general anisotropic interactions in spin space if the exchange paths allowed by the crystal structure form loops in real space. In particular, it is shown that the two-electron exchange interaction can acquire ferromagnetic character.
The conventional unpolarized current injected into a {\em quantum-coherent} semiconductor ring attached to two external leads can be modulated from perfect conductor to perfect insulator limit via Rashba spin-orbit (SO) coupling. This requires that ballistic propagation of electrons, whose spin precession is induced by the Aharonov-Casher phase, takes place through a single conducting channel ensuring that electronic quantum state remains a pure separable one in the course of transport. We study the fate of such spin interference effects as more than one orbital conducting channel becomes avai…
Zero-modes, their topological degeneracy and relation to index theorems have attracted attention in the study of single- and bilayer graphene. For negligible scalar potentials, index theorems explain why the degeneracy of the zero-energy Landau level of a Dirac hamiltonian is not lifted by gauge field disorder, for example due to ripples, whereas other Landau levels become broadened by the inhomogenous effective magnetic field. That also the bilayer hamiltonian supports such protected bulk zero-modes was proved formally by Katsnelson and Prokhorova to hold on a compact manifold by using the At…
We have observed the effect of the Aharonov-Casher (AC) interference on the spectrum of a superconducting system containing a symmetric Cooper pair box (CPB) and a large inductance. By varying the charge $n_{g}$ induced on the CPB island, we observed oscillations of the device spectrum with the period $Δn_{g}=2e$. These oscillations are attributed to the charge-controlled AC interference between the fluxon tunneling processes in the CPB Josephson junctions. Total suppression of the tunneling (complete destructive interference) has been observed for the charge $n_{g}=e(2n+1)$. The CPB in this r…
We investigate parametric pumping of spin and charge currents in a mesoscopic ring interrupted by a tunnel barrier in presence of Aharonov-Casher (AC) effect and Aharonov-Bohm (AB) flux along the axis of the same ring. Generation of a dc current is achieved by tuning the tunnel barrier strength and modulating in time either a radial(transverse) electric field or the magnetic flux. A pure spin current is generated by the interplay of breaking spin reversal symmetry, due to AC effect, and time-reversal symmetry breaking, intrinsic in parametric pumping procedure. We analyze the conditions for op…
A periodic network of connected rhombii, mimicking a spintronic device, is shown to exhibit an intriguing spin selective extreme localization, when submerged in a uniform out of plane electric field. The topological Aharonov Casher phase acquired by a travelling spin is seen to induce a complete caging, triggered at a special strength of the spin orbit coupling, for half odd integer spins s \ge n\hbar/2, with n odd, sparing the integer spins. The observation finds exciting experimental parallels in recent literature on caged, extreme localized modes in analogous photonic lattices. Our results …
We propose a two-path vortex interferometry experiment based on the Aharonov-Casher effect for detecting the non-Abelian nature of vortices in a chiral p-wave superconductor. The effect is based on observing vortex interference patterns upon enclosing a finite charge of externally controllable magnitude within the interference path. We predict that when the interfering vortices enclose an odd number of identical vortices in their path, the interference pattern disappears only for non-Abelian vortices. When pairing involves two distinct spin species, we derive the mutual statistics between half…
We calculate the conductance through a system of three quantum dots under two different sets of conditions that lead to spin filtering effects under an applied magnetic field. In one of them, a spin is localized in one quantum dot, as proposed by Delgado et al. [Phys. Rev. Lett. 101, 226810 (2008)]. In the other one, all dots are equivalent by symmetry and the system is subject to a Rashba spin-orbit coupling. We solve the problem using a simple effective Hamiltonian for the low-energy subspace, improving the accuracy of previous results. We obtain that correlation effects related to the Kondo…
We suggest a system in which the amplitude of macroscopic flux tunneling can be modulated via the Aharonov-Casher effect. The system is an rf-SQUID with the Josephson junction replaced by a Bloch transistor -- two junctions separated by a small superconducting island on which the charge can be induced by an external gate voltage. When the Josephson coupling energies of the junctions are equal and the induced charge is q=e, destructive interference between tunneling paths brings the flux tunneling rate to zero. The device may also be useful as a qubit for quantum computation.
We propose an experiment that would produce and measure a large Aharonov-Casher (A-C) phase in a solid-state system under macroscopic motion. A diamond crystal is mounted on a spinning disk in the presence of a uniform electric field. Internal magnetic states of a single NV defect, replacing interferometer trajectories, are coherently controlled by microwave pulses. The A-C phase shift is manifested as a relative phase, of up to 17 radians, between components of a superposition of magnetic substates, which is two orders of magnitude larger than that measured in any other atom-scale quantum sys…
We explore the influence of a circularly polarized cavity photon field on the transport properties of a finite-width ring, in which the electrons are subject to spin-orbit and Coulomb interaction. The quantum ring is embedded in an electromagnetic cavity and described by ``exact'' numerical diagonalization. We study the case that the cavity photon field is circularly polarized and compare it to the linearly polarized case. The quantum device is moreover coupled to external, electrically biased leads. The time propagation in the transient regime is described by a non-Markovian generalized maste…
We derive a non-perturbative solution to the Floquet-nonequilibrium Green function (Floquet-NEGF) describing open quantum systems periodically driven by an external field of arbitrary strength of frequency. By adopting the reduced-zone scheme, we obtain expressions rendering conserved charge currents for any given maximum number of photons, distinguishable from other existed Floquet-NEGF-based expressions where, less feasible, infinite number of photons needed to be taken into account to ensure the conservation. To justify our derived formalism and to investigate spin-charge conversions by spi…
We study the quantum interference effects induced by the Aharonov-Casher phase in asymmetrically confined two-dimensional electron and heavy-hole ring structures systems taking into account the electrically tunable spin-orbit (SO) interaction. We have calculated the non-adiabatic transport properties of charges (heavy-holes and electrons) in two-probe thin ring structures and compare how the form of the SO coupling of the carries affects it. We show that both the SO splitting of the bands and the carrier density can be used to modulate the conductance through the ring. We show that the depende…
A recent Letter [1] has proposed a device, consisting of an rf SQUID with the junction replaced by a double one, i.e. a Bloch transistor. For symmetric Josephson couplings, and for specific flux bias and gate voltage applied to the transistor's island, the tunneling of encircled flux between its two local potential minima is claimed to be suppressed completely due to destructive interference. This comment purports to show that this claim in general is not valid. Namely, the very Hamiltonian (1) in [1], from which the effect is derived, describes the circuit only under an additional condition. …
The 2-dimensional charge transport with parallel (in plane) magnetic field is considered from the physical and mathematical point of view. To this end, we start with the magnetic field parallel to the plane of charge transport, in sharp contrast to the configuration described by the theorems of Aharonov and Casher where the magnetic field is perpendicular. We explicitly show that the specific form of the arising equation enforce the respective field solution to fulfil the Majorana condition. Consequently, as soon any physical system is represented by this equation, the rise of fields with Majo…
We consider a neutral particle with permanent magnetic dipole moment in an elastic medium with the presence of a uniform distribution of screw dislocations interacting with a radial electric field. We show that the uniform distribution of dislocations plays the role of an effective uniform magnetic field, and obtain a spectrum of energy which depends on the Aharonov-Casher geometric phase [Y. Aharonov and A. Casher, Phys. Rev. Lett. 53, 319 (1984)]. Moreover, from the dependence of energy levels on the Aharonov-Casher geometric phase, we calculate the persistent spin currents in this elastic L…
