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An algebraic approach to the Aharonov-Bohm effect is considered. The constructed mathematical scheme agrees with experimental data and provides a clear physical interpretation of this effect that does not contradict classical concepts.
The phase of the wave function of charged matter is sensitive to the value of the electric potential, even when the matter never enters any region with nonvanishing electromagnetic fields. Despite its fundamental character, this archetypal electric Aharonov-Bohm effect has evidently never been observed. Here, we propose an experiment to detect the electric potential through its coupling to the superconducting order parameter. A potential difference between two superconductors will induce a relative phase shift that is observable via the DC Josephson effect even when no electromagnetic fields ever act on the superconductors, and even if the potential difference is later reduced to zero. This is a type of electromagnetic memory effect, and would directly demonstrate the physical significance of the electric potential.
Quantum coherence of electrons can produce striking behaviors in mesoscopic conductors, including weak localization and the Aharonov-Bohm effect. Although magnetic order can also strongly affect transport, the combination of coherence and magnetic order has been largely unexplored. Here, we examine quantum coherence-driven universal conductance fluctuations in the antiferromagnetic, canted antiferromagnetic, and ferromagnetic phases of a thin film of the topological material MnBi 2 Te 4 . In each magnetic phase we extract a charge carrier phase coherence length of about 100 nm. The conductance magnetofingerprint is repeatable when sweeping applied magnetic field within one magnetic phase, but changes when the applied magnetic field crosses the antiferromagnetic/canted antiferromagnetic magnetic phase boundary. Surprisingly, in the antiferromagnetic and canted antiferromagnetic phase, but not in the ferromagnetic phase, the magnetofingerprint depends on the direction of the field sweep. Finally, to explain these observations, we suggest that conductance fluctuation measurements are sensitive to the motion and nucleation of magnetic domain walls in MnBi 2 Te 4 .
Semiconductor quantum rings are topological structures that support fascinating phenomena such as the Aharonov-Bohm effect and persistent current, which are of high relevance in the research of quantum information devices. The annular shape of quantum rings distinguishes them from other low-dimensional materials, and enables topologically induced properties such as geometry-dependent spin manipulation and emission. While optical transition dipole moments (TDMs) in zero to two-dimensional optical emitters have been well investigated, those in quantum rings remain obscure despite their utmost relevance to the quantum photonic applications of quantum rings. Here, we study the dimensionality and orientation of TDMs in CdSe quantum rings. In contrast to those in other two-dimensional optical emitters, we find that TDMs in CdSe quantum rings show a peculiar in-plane linear distribution. Our theoretical modeling reveals that this uniaxial TDM originates from broken rotational symmetry in the quantum ring geometries.
We demonstrate a tunable path-separated electron interferometer using a single amplitude-dividing beamsplitter to prepare multiple spatially isolated, coherent electron probe beams. We place four electrostatic bi-prisms in the optical column of a scanning transmission electron microscope (STEM) to achieve path separations of up to 25 μ m, the largest demonstrated within amplitude-division electron interferometers while maintaining fringe visibility of the directly observed interference fringes at the detector. We characterize the fringe visibility of this setup over a range of path separations and perform STEM holography to reconstruct the full object wave of a fabricated Si ramp test phase object. We report a quantitative object-wave measurement in this configuration and confirm with an independent off-axis electron holography measurement. This experimental design can potentially be applied to high-resolution phase imaging and fundamental physics experiments, such as an exploration of the electron wave packet coherence length and the Aharonov-Bohm effect.
This is a brief review on the theoretical interpretation of the Aharonov–Bohm effect, which also contains our new insight into the problem. A particular emphasis is put on the unique role of electron orbital angular momentum, especially viewed from the novel concept of the physical component of the gauge field, which has been extensively discussed in the context of the nucleon spin decomposition problem as well as the photon angular momentum decomposition problem. Practically, we concentrate on the frequently discussed idealized setting of the Aharonov–Bohm effect, i.e. the interference phenomenon of the electron beam passing around the infinitely-long solenoid. One of the most puzzling observations in this Aharonov–Bohm solenoid effect is that the pure-gauge potential outside the solenoid appears to carry non-zero orbital angular momentum. Through the process of tracing its dynamical origin, we try to answer several fundamental questions of the Aharonov–Bohm effect, which includes the question about the reality of the electromagnetic potential, the gauge-invariance issue, and the non-locality interpretation, etc.
Spin thermoelectric effects in an Aharnov-Bohm ring with a magnetic impurity quantum dot (QD) are theoretically investigated by using the nonequilibrium Green's function method. It is found that due to the exchange coupling between the impurity and the electrons in QD, spin output power, and efficiency can be significant and be further modulated by the gate voltage. The spin thermoelectric effect can be modulated effectively by adjusting the Rashba spin-orbit interaction (RSOI) and the magnetic flux. The spin power and efficiency show zigzag oscillations, and thus spin thermoelectric effect can be switched by adjusting the magnetic flux phase factor and RSOI ones. In addition, the spin efficiency can be significantly enhanced by the coexistence of the RSOI and the magnetic flux, and the maximal value of normalized spin efficiency η{sub max}/η{sub C} = 0.35 is obtained. Our results show that such a QD ring device may be used as a manipulative spin thermoelectric generator.
We point out that the known quantum phases for an electric/magnetic dipole moving in an electromagnetic (EM) field must be presented as the superposition of more fundamental quantum phases emerging for elementary charges. Using this idea, we find two new fundamental quantum phases for point-like charges, next to the known electric and magnetic Aharonov–Bohm (A–B) phases, named by us as the complementary electric and magnetic phases, correspondingly. We further demonstrate that these new phases can indeed be derived via the Schrödinger equation for a particle in an EM field, where however the operator of momentum is re-defined via the replacement of the canonical momentum of particle by the sum of its mechanical momentum and interactional field momentum for a system “charged particle and a macroscopic source of EM field”. The implications of the obtained results are discussed.
The Aharonov–Bohm elastic scattering with incident particles described by plane waves is revisited by using the phase-shifts method. The formal equivalence between the cylindrical Schrödinger equation and the one-dimensional Calogero problem allows us to show that up to two scattering phase-shifts modes in the cylindrical waves expansion must be renormalized. The renormalization procedure introduces new length scales giving rise to spontaneous breaking of the conformal symmetry. The knowledge of the exact beta function permits us to describe the renormalization group flows within the two-parametric family of renormalized Aharonov–Bohm scattering amplitudes.
In this work, we study the (2+1)-dimensional Dirac oscillator in the presence of a homogeneous magnetic field in an Aharonov-Bohm-Coulomb system. To solve our system, we apply the left-handed and right-handed projection operators in the Dirac oscillator to obtain a biconfluent Heun equation. Next, we explicitly determine the energy spectrum for the bound states of the system and their exact dependence on the cyclotron frequency ω{sub c} and on the parameters Z and Φ{sub AB} that characterize the Aharonov-Bohm-Coulomb system. As a result, we observe that by adjusting the frequency of the Dirac oscillator to resonate with the cyclotron half-frequency the energy spectrum reduces to the rest energy of the particle. Also, we determine the exact eigenfunctions, angular frequencies, and energy levels of the Dirac oscillator for the ground state (n=1) and the first excited state (n=2). In this case, the energy levels do not depend on the homogeneous magnetic field, and the angular frequencies are real and positive quantities, increase quadratically with the energy and linearly with ω{sub c}.
Highlights: •Effectively rotate the so-coupled condensate by an external magnetic field. •New effects of the Aharonov–Bohm geometric phase in ultracold atomic gases. •Many novel vortex structures have been studied. •A new stabilization mechanism for multiquantum vortices in spinor BECs. -- Abstract: We investigate the vortex states generated by the gauge-potential-induced rotation in spin-1 Bose–Einstein condensates with spin–orbit coupling. An external magnetic field coupling with spin equivalently imprints a non-zero gauge angular momentum, which induces an equivalent canonical angular momentum in the opposite direction, accompanied by the generation of quantized vortices. The competition between interatomic interactions, spin–orbit coupling and magnetic field leads to a variety of vortex structures. In the weakly interatomic interacting regime, as the increase of SO coupling strength, the condensate with a weak magnetic field gradient experiences the transition from polar-core vortex to Mermin–Ho vortex then to vortex cluster , and the three-vortex structures are found in the vortex cluster. As the SO coupling increases further, the condensate presents symmetrical density domains separated by radial vortex arrays. With the increase of magnetic field gradient, the number of density domains increases, and the condensate eventually turns into a giant vortex. In the relatively strong interatomic interacting regime, vortex sheets are formed when the magnetic field gradient is weak, and the increasing of magnetic field gradient makes the vortex arrangement orderly. Compared with the cases of weak interatomic interacting regime, density domain structures are broken because of the strong interatomic interactions, and the vortices are arranged in coaxial annular arrays.
Electronic topological phases are typified by the conducting surface states that exist on the boundary of an insulating three-dimensional bulk. While the transport response of the two-dimensional surface states has been studied, the quantum response of the one-dimensional hinge modes has not been demonstrated. Here we provide evidence for quantum transport in gapless topological hinge states existing within the insulating bulk and surface energy gaps in the intrinsic topological insulator α-Bi 4 Br 4 . Our magnetoresistance measurements reveal pronounced Aharonov–Bohm oscillations that are periodic in h/e (where h denotes Planck’s constant and e is the electron charge). The observed periodicity evinces quantum interference of electrons circumnavigating around the hinges. We also demonstrate that the h/e oscillations evolve as a function of magnetic field orientation, following the interference paths along the hinge modes that are allowed by topology and symmetry. Furthermore, our findings reveal the quantum transport response of topological hinge modes with both topological nature and quantum coherence, which can eventually be applied to the development of efficient topological electronic devices.
We demonstrate a quantum Hall edge-channel interferometer in a high-quality graphene pn junction under a high magnetic field. The co-propagating p and n quantum Hall edge channels traveling along the pn interface functions as a built-in Aharonov-Bohm-type interferometer, the interferences in which are sensitive to both the external magnetic field and the carrier concentration. The trajectories of peak and dip in the observed resistance oscillation are well reproduced by our numerical calculation that assumes magnetic flux quantization in the area enclosed by the co-propagating edge channels. Coherent nature of the co-propagating edge channels is confirmed by the checkerboard-like pattern in the dc-bias and magnetic-field dependences of the resistance oscillations.
We propose a scheme to observe the Majorana-zero-mode-induced crossed Andreev reflection by measuring tunneling current directly. In this scheme a metallic ring structure is utilized to separate electron and hole signals. Since tunneling electrons and holes have different propagating wave vectors, the conditions for them to be constructively coherent in the ring differ. We find that when the magnetic flux threading the ring varies, it is possible to observe adjacent positive and negative tunneling current peaks of about equal amplitudes.
We outline a range of proposals on using quantum rings and nanohelices for terahertz device implementations. We show that an Aharonov-Bohm quantum ring system and a double-gated quantum ring system both permit control over the polarization properties of the associated terahertz radiation. In addition, we review the superlattice properties of a mathematically similar system, that of a nanohelix in external electric fields, which reveals negative differential conductance.
Veselago lens focusing in graphene p-n junction is promising for realizations of new generation electron optics devices. However, the effect of the strain-induced Aharonov-Bohm interference in a p-n junction has not been discussed before. We provide an experimentally feasible setup based on the Veselago lens in which the presence of strain can result in both the valley-dependent Lorentz force and Aharonov-Bohm interference. Inparticular, by employing the Green’s function and tight-binding methods, we study the strain induced by dislocations and line defects in a p-n junction and show how the resulting Aharonov-Bohm phase and interference can be detected. Furthermore, for a different strain configuration, e.g., corresponding to corrugated graphene, we find strong signatures of valley splitting induced by the fictitious magnetic field. Our proposal can be useful for mapping elastic deformations and defects, and for studying valley-dependent effects in graphene.
Long ago Weinberg showed, from first principles, that the amplitude for a single photon exchange between an electric current and a magnetic current violates Lorentz invariance. The obvious conclusion at the time was that monopoles were not allowed in quantum field theory. Since the discovery of topological monopoles there has thus been a paradox. On the one hand, topological monopoles are constructed in Lorentz invariant quantum field theories, while on the other hand, the low-energy effective theory for such monopoles will reproduce Weinberg’s result. We examine a toy model where both electric and magnetic charges are perturbatively coupled and show how soft-photon resummation for hard scattering exponentiates the Lorentz violating pieces to a phase that is the covariant form of the Aharonov-Bohm phase due to the Dirac string. The modulus of the scattering amplitudes (and hence observables) are Lorentz invariant, and when Dirac charge quantization is imposed the amplitude itself is also Lorentz invariant. For closed paths there is a topological component of the phase that relates to aspects of 4D topological quantum field theory.
Electronic interferometers using the chiral, one-dimensional (1D) edge channels of the quantum Hall effect (QHE) can demonstrate a wealth of fundamental phenomena. The recent observation of phase jumps in a Fabry-Pérot (FP) interferometer revealed anyonic quasiparticle exchange statistics in the fractional QHE. When multiple integer edge channels are involved, FP interferometers have exhibited anomalous Aharonov-Bohm (AB) interference frequency doubling, suggesting putative pairing of electrons into 2e quasiparticles. Here, we use a highly tunable graphene-based QHE FP interferometer to observe the connection between interference phase jumps and AB frequency doubling, unveiling how strong repulsive interaction between edge channels leads to the apparent pairing phenomena. By tuning electron density in-situ from filling factor v < 2 to v > 7, we tune the interaction strength and observe periodic interference phase jumps leading to AB frequency doubling. Our observations demonstrate that the combination of repulsive interaction between the spin-split v = 2 edge channels and charge quantization is sufficient to explain the frequency doubling, through a near-perfect charge screening between the localized and extended edge channels. Our results show that interferometers are sensitive probes of microscopic interactions and enable future experiments studying correlated electrons in 1D channels using density-tunable graphene.