Aharonov-Casher Effect Research Articles

Theory of topological exciton insulators and condensates in flat Chern bands

Excitons are the neutral quasiparticles that form when Coulomb interactions create bound states between electrons and holes. Due to their bosonic nature, excitons are expected to condense and exhibit superfluidity at sufficiently low temperatures. In interacting Chern insulators, excitons may inherit the nontrivial topology and quantum geometry from the underlying electron wavefunctions. We theoretically investigate the excitonic bound states and superfluidity in flat-band insulators pumped with light. We find that the exciton wavefunctions exhibit vortex structures in momentum space, with the total vorticity being equal to the difference of Chern numbers between the conduction and valence bands. Moreover, both the exciton binding energy and the exciton superfluid density are proportional to the Brillouin-zone average of the quantum metric and the Coulomb potential energy per unit cell. Spontaneous emission of circularly polarized light from radiative decay is a detectable signature of the exciton vorticity. We propose that the vorticity can also be experimentally measured via the nonlinear anomalous Hall effect, whereas the exciton superfluidity can be detected by voltage-drop quantization through a combination of quantum geometry and Aharonov-Casher effect. Topological excitons and their superfluid phase could be realized in flat bands of twisted Van der Waals heterostructures.

Controlled refraction and focusing of spin waves determined by the Aharonov-Casher effect

The influence of an external static electric field on spin wave (SW) dynamics leads to an additional topological phase called the Aharonov-Casher (AC) phase. It is manifested as a shift in dispersion and the group velocity direction of the spin wave under the electric field. Within a linear approximation, the AC effect can be considered by including the Dzyaloshinskii-Moriya-like interaction between neighboring spins, which is proportional to the applied electric field. In this paper, we use these findings to examine the possibility of the electric field control of the refraction of coherently propagating SWs. This is done by studying the propagation SWs across the boundary between two regions of a homogeneous ferromagnetic film under the influence of different external electric fields. We have derived an analytical expression for a magnetic Snell's law and performed micromagnetic simulations to demonstrate how the AC phase shift can control SW refraction. This effect enables us to quantify the topological AC phase action. It presents a promising approach for guiding and manipulating the phase and energy flow of SWs using an external electric field, opening a way to control magnonic devices. Published by the American Physical Society 2024

Exact solutions of the Dirac oscillator under the influence of the Aharonov–Casher effect in the cosmic string background

Exact solutions of the Dirac oscillator under the influence of the Aharonov–Casher effect in the cosmic string background

Towards an experimental proof of the magnonic Aharonov-Casher effect

Towards an experimental proof of the magnonic Aharonov-Casher effect

Disentangling electric field effect on spin waves in ferromagnetic insulators

In this paper we extend the micromagnetic theory of magnetostatic surface waves in insulating ferromagnetic thin films to include the applied electric field effects. We start by identifying the two main effects on the dispersion relation: the first one is of relativistic nature and emerges as a consequence of the Aharonov–Casher effect, while the second one is a consequence of the electric field induced symmetry breaking operating at the level of magnetic exchange interactions. We support our theory by comparing its predictions with experimental data on ittrium iron garnet thin films taken from the literature. The main result is to evidence the limitations of using the same value of the applied electric field to address both effects and to emphasize that crystal symmetry breaking due to the applied electric field brings about the contributions of the crystal field and determines different amplitudes for the two effects.

Phase detection of electron vortex beams on structured charge distribution

Recent advances in the production of so-called twisted electron (electron vortex) beams with sub-nanometer spot size offer unique opportunities to explore the role of orbital angular momentum (OAM) on electromagnetic microstructures. We address here the interaction between the OAM and an external electric field based on the Aharonov–Casher effect. Taking an inhomogeneous electric field generated by a point charge as an example, we show that the deformation of twisted electron's wavefront is very sensitive to the location and orientation of point charges and can be clearly visualized by interference patterns with a spherical wave. This phase shifting detection provides a high resolution representation for the structure and distribution of charged nanoparticles.

Time-dependent Aharonov–Casher effect on noncommutative space

In this paper, we study the time-dependent Aharonov–Casher effect and its corrections due to spatial noncommutativity. Given that the charge of the infinite line in the Aharonov–Casher effect can adiabatically vary with time, we show that the original Aharonov–Casher phase receives an adiabatic correction, which is characterized by the time-dependent charge density. Based on Seiberg–Witten map, we show that noncommutative corrections to the time-dependent Aharonov–Casher phase contains not only an adiabatic term but also a constant contribution depending on the frequency of the varying electric field.

The influence of Aharonov–Casher effect on the generalized Dirac oscillator in the cosmic string space-time

In this paper, we investigate the influence of the Aharonov–Casher (A–C) effect on the generalized Dirac oscillator containing the Coulomb-type potential function related to a relativistic neutral particle having a permanent magnetic dipole moment interacting with the external electromagnetic fields in (1 + 2)-dimensional cosmic string space-time. The eigenfunctions and energy eigenvalues of such a Dirac oscillator are derived by using the Nikiforov–Uvarov method. We indicate that implementing the scenario gives the relativistic modified exact analytical solutions. In this way, we can see that the degeneracy of the relevant relativistic energy eigenvalues is broken by depending on the Coulomb strength parameter under the influence of the curvature effect and the A–C effect.

Non-Abelian Braiding in Spin Superconductors Utilizing the Aharonov-Casher Effect.

Spin superconductor (SSC) is an exciton condensate state where the spin-triplet exciton superfluidity is charge neutral while spin 2(ℏ/2). In analogy to the Majorana zero mode (MZM) in topological superconductors, the interplay between SSC and band topology will also give rise to a specific kind of topological bound state obeying non-Abelian braiding statistics. Remarkably, the non-Abelian geometric phase here originates from the Aharonov-Casher effect of the "half-charge" other than the Aharonov-Bohm effect. Such topological bound state of SSC is bound with the vortex of electric flux gradient and can be experimentally more distinct than the MZM for being electrically charged. This theoretical proposal provides a new avenue investigating the non-Abelian braiding physics without the assistance of MZM and charge superconductor.

Investigation of the Aharonov-Bohm and Aharonov-Casher topological phases for quantum entangled states

Aharonov-Bohm (AB) and Aharonov-Casher (AC) effects are treated fully relativistically in 2+1 dimensions. The influences of the relevant geometric and topological phases on an entangled spin-1/2 system are studied. It is shown that for the AC case the correlation function of the Clauser-Horne-Shimony-Holt (CHSH) inequality for certain choices of the spin measurements depends on the AC phase explicitly.

Aharonov-Casher and shielded Aharonov-Bohm effects with a quantum electromagnetic field

We use a covariant formalism that is capable of describing the electric and magnetic versions of the Aharonov-Bohm effect, as well as the Aharonov-Casher effect, through local interactions of charges and currents with the quantum electromagnetic field. By considering that only local interactions of a quantum particle with the quantum field can affect its behavior, we show that the magnetic Aharonov-Bohm effect must be present even if the solenoid generating the magnetic field is shielded by a perfect conductor, as experimentally demonstrated.

Algebraic solution and coherent states for the Dirac oscillator interacting with the Aharonov–Casher system in the cosmic string background

In this paper, we introduce an SU(1, 1) algebraic approach to study the (2 + 1)-Dirac oscillator in the presence of the Aharonov–Casher effect coupled to an external electromagnetic field in the Minkowski spacetime and the cosmic string spacetime. This approach is based on a quantum mechanics factorization method that allows us to obtain the su(1, 1) algebra generators, the energy spectrum and the eigenfunctions. We obtain the coherent states and their temporal evolution for each spinor component of this problem. Finally, for these problems, we calculate some matrix elements and the Schrödinger uncertainty relationship for two general SU(1, 1) operators.

Enhanced Coherence in Superconducting Circuits via Band Engineering.

In superconducting circuits interrupted by Josephson junctions, the dependence of the energy spectrum on offset charges on different islands is 2e periodic through the Aharonov-Casher effect and resembles a crystal band structure that reflects the symmetries of the Josephson potential. We show that higher-harmonic Josephson elements described by a cos(2φ) energy-phase relation provide an increased freedom to tailor the shape of the Josephson potential and design spectra featuring multiplets of flat bands and Dirac points in the charge Brillouin zone. Flat bands provide noise-insensitive energy levels, and consequently, engineering band pairs with flat spectral gaps can help improve the coherence of the system. We discuss a modified version of a flux qubit that achieves, in principle, no decoherence from charge noise and introduce a flux qutrit that shows a spin-1 Dirac spectrum and is simultaneously quite robust to both charge and flux noise.

Three-phase Majorana zero modes at tiny magnetic fields

Proposals for realizing Majorana fermions in condensed matter systems typically rely on magnetic fields, which degrade the proximitizing superconductor and plague the Majoranas' detection. We propose an alternative scheme to realize Majoranas based only on phase-biased superconductors. The phases (at least three of them) can be biased by a tiny magnetic field threading macroscopic superconducting loops, focusing and enhancing the effect of the magnetic field onto the junction, or by supercurrents. We show how a combination of the superconducting phase winding and the spin-orbit phase induced in closed loops (Aharonov-Casher effect) facilitates a topological superconducting state with Majorana end states. We demontrate this scheme by an analytically tractable model as well as simulations of realistic setups comprising only conventional materials.

Comment on “Energy Spectrum of a Dirac Particle with Position-Dependent Mass Under the Influence of the Aharonov-Casher Effect”

It is shown that the paper “Energy spectrum of a Dirac particle with position-dependent mass under the influence of the Aharonov-Casher effect,” by Oliveira et al. (Braz. J. Phys. 49, 801 2019), is based on a series of ingredients clearly incorrect.

Dual Fraunhofer interference and charge fluctuations in long quantum phase slip wires

Charge interference (Aharonov-Casher effect) in a long superconducting quantum phase slip wire is considered, and from this the ``dual'' Fraunhofer interference effect (dual to the critical current modulation of a short Josephson junction in an external magnetic field) is derived. The device that can be used to observe this effect is proposed. Furthermore, the impact of wire inhomogeneities, charge disorder, and noise on the phase slip amplitude is investigated. Although intrinsically protected against small fluctuations, the Aharonov-Casher interference resulting from jumps of random offset charges and quasiparticles can result in significant fluctuations of the measured current-voltage characteristics of the quantum phase slip wire, similar to the effects of Joule heating when averaged out over many fluctuations. Possible ways to identify and mitigate such disorder are discussed.

Aharonov–Casher effect in the presence of spin-dependent potential

We study the quantum description of a neutral particle that has a permanent magnetic dipole moment that interacts with the Aharonov–Casher-type field configuration and a nonuniform magnetic field. From the interaction of the magnetic dipole moment with the magnetic field, an effective scalar potential arises in the Schrödinger–Pauli equation, which is characterized by being spin-dependent and proportional to the inverse of the square of the radial distance. We thus study the analytical solutions to the Schrödinger–Pauli equation for the two cases where the spin-dependent potential can be attractive and repulsive.

Universal Voltage Fluctuations in Disordered Superconductors.

The Aharonov-Casher effect is the analogue of the Aharonov-Bohm effect that applies to neutral particles carrying a magnetic moment. This effect can be manifested by vortices or fluxons flowing in trajectories that encompass an electric charge. These vortices have been predicted to result in a persistent voltage that fluctuates for different sample realizations. Here, we show that disordered superconductors exhibit reproducible voltage fluctuation, which is antisymmetrical with respect to the magnetic field, as a function of various parameters such as the magnetic field amplitude, field orientations, and gate voltage. These results are interpreted as the vortex equivalent of the universal conductance fluctuations typical of mesoscopic disordered metallic systems. We analyze the data in the framework of random matrix theory and show that the fluctuation correlation functions and curvature distributions exhibit behavior that is consistent with Aharonov-Casher physics. The results demonstrate the quantum nature of the vortices in highly disordered superconductors, both above and below T_{c}.

Aharonov–Casher effect and persistent spin currents in a Coulomb-type potential induced by Lorentz symmetry breaking effects

We investigate quantum effects on a nonrelativistic neutral particle with a permanent magnetic dipole moment that interacts with an electric field. This neutral particle is also under the influence of a background that breaks the Lorentz symmetry. We focus on the Lorentz symmetry violation background determined by a space-like vector field. Then, we show that the effects of the violation of Lorentz symmetry can yield an attractive Coulomb-type potential. Furthermore, we obtain the bound state solutions to the Schrödinger–Pauli equation and show that the spectrum of energy is a function of the Aharonov–Casher geometric quantum phase. Finally, we discuss the arising of persistent spin currents.

Aharonov–Casher effect and electric field control of magnetization dynamics

A spin wave (SW) propagating in an external electric field acquires an extra phase, the so-called Aharonov– Casher phase. To linear order, that is equivalent the SW frequency shift linear in both the applied electric field and the wave vector of SW’s and can be described by adding effective Dzyaloshinskii–Moriya-like interaction between spins. This effect is a promising way to control and manipulate magnetization precession dynamics by electric field and opens up a new way of SWs steering in magnonic devices. The goal of the report is to emphasize a fundamental physical difference in the nature of external electric field effect through the Aharonov–Casher phase shift and of a voltage control of magnetic anisotropy (VCMA). In the context of an experimental performance, we deal with almost identical experimental conditions. Yet, from the quantum physics point of view, we deal with different effects and this is important to understand the experimental results. In the case of the Aharonov–Casher phase shift it is a global nonlocal (topological) effect and in the case of VCMA it is the influence on a system’s local (Landau) magnetic parameters (e.g., magnetic anisotropy).