Aharonov-Bohm Flux Research Articles

PHASE TIME FOR A TUNNELING PARTICLE

We study the nature of tunneling phase time for various quantum mechanical structures such as networks and rings having potential barriers in their arms. We find the generic presence of the Hartman effect, with superluminal velocities as a consequence, in these systems. In quantum networks, it is possible to control the "super arrival" time in one of the arms by changing the parameters on another arm which is spatially separated from it. This is yet another quantum nonlocal effect. Negative time delays (time advancement) and "ultra Hartman effect" with negative saturation times have been observed in some parameter regimes. In the presence and absence of Aharonov-Bohm (AB) flux, quantum rings show the Hartman effect. We obtain the analytical expression for the saturated phase time. In the opaque barrier regime, this is independent of even the AB flux thereby generalizing the Hartman effect. We also briefly discuss the concept of "space collapse or space destroyer" by introducing a free space in between two barriers covering the ring. Further, we show in presence of absorption that the reflection phase time exhibits the Hartman effect in contrast to the transmission phase time.

Quantum pump driven fermionic Mach-Zehnder interferometer

We have investigated the characteristics of the currents in a pump-driven fermionic Mach-Zehnder interferometer. The system is implemented in a conductor in the quantum Hall regime, with the two interferometer arms enclosing an Aharonov-Bohm flux $\Phi$. Two quantum point contacts with transparency modulated periodically in time drive the current and act as beam-splitters. The current has a flux dependent part $I^{(\Phi)}$ as well as a flux independent part $I^{(0)}$. Both current parts show oscillations as a function of frequency on the two scales determined by the lengths of the interferometer arms. In the non-adiabatic, high frequency regime $I^{(\Phi)}$ oscillates with a constant amplitude while the amplitude of the oscillations of $I^{(0)}$ increases linearly with frequency. The flux independent part $I^{(0)}$ is insensitive to temperature while the flux dependent part $I^{(\Phi)}$ is exponentially suppressed with increasing temperature. We also find that for low amplitude, adiabatic pumping rectification effects are absent for semitransparent beam-splitters. Inelastic dephasing is introduced by coupling one of the interferometer arms to a voltage probe. For a long charge relaxation time of the voltage probe, giving a constant probe potential, $I^{(\Phi)}$ and the part of $I^{(0)}$ flowing in the arm connected to the probe are suppressed with increased coupling to the probe. For a short relaxation time, with the potential of the probe adjusting instantaneously to give zero time dependent current at the probe, only $I^{(\Phi)}$ is suppressed by the coupling to the probe.

Spin-polarized transport in Rashba controlled rings

We study spin-polarized transport in a Rashba one-dimensional ring interrupted by a tunnel barrier placed in one arm and symmetrically coupled to two external leads. By means of the scattering matrix approach, we investigate the effects on the transport properties of both an applied magnetic flux (Aharonov–Bohm flux) and an effective Aharonov–Casher flux induced by the spin–orbit (SO) Rashba interaction. By varying the model parameters we show a spin-filtering effect relevant for the experimental detection of SO interaction in mesoscopic structures.

Unified description of phase lapses, population inversion, and correlation-induced resonances in double quantum dots

The two-level model for a double quantum dot coupled to two leads, which is ubiquitously used to describe charge oscillations, transmission-phase lapses and correlation-induced resonances, is considered in its general form. The model features arbitrary tunnelling matrix elements among the two levels and the leads and between the levels themselves (including the effect of Aharonov-Bohm fluxes), as well as inter-level repulsive interactions. We show that this model is exactly mapped onto a generalized Anderson model of a single impurity, where the electrons acquire a pseudo-spin degree of freedom, which is conserved by the tunnelling but not within the dot. Focusing on the local-moment regime where the dot is singly occupied, we show that the effective low-energy Hamiltonian is that of the anisotropic Kondo model in the presence of a tilted magnetic field. For moderate values of the (renormalized) field, the Bethe ansatz solution of the isotropic Kondo model allows us to derive accurate expressions for the dot occupation numbers, and henceforth its zero-temperature transmission. Our results are in excellent agreement with those obtained from the Bethe ansatz for the isotropic Anderson model, and with the functional and numerical renormalization-group calculations of Meden and Marquardt [Phys. Rev. Lett. 96, 146801 (2006)], which are valid for the general anisotropic case. In addition we present highly accurate estimates for the validity of the Schrieffer-Wolff transformation (which maps the Anderson Hamiltonian onto the low-energy Kondo model) at both the high- and low-magnetic field limits. Perhaps most importantly, we provide a single coherent picture for the host of phenomena to which this model has been applied.

Entanglement between static and flying qubits in an Aharonov–Bohm double electrometer

We consider the phase-coherent transport of electrons passing through an Aharonov–Bohm ring while interacting with a tunnel charge in a double quantum dot (representing a charge qubit) which couples symmetrically to both arms of the ring. For Aharonov–Bohm flux ΦAB = h/2e we find that electrons can only be transmitted when they flip the charge qubit's pseudospin parity an odd number of times. The perfect correlations of the dynamics of the pseudospin and individual electronic transmission and reflection events can be used to entangle the charge qubit with an individual passing electron.

Ground-state properties of quantum rings with a few electrons: Magnetization, persistent current, and spin chirality

Ground-state properties of one-dimensional quantum rings with a few electrons, which interact with each other in the form of $1∕r$ Coulomb repulsion, are studied by exact diagonalization. For three electrons, the fully spin-polarized ground state is uniquely realized when the diameter of the ring is sufficiently large. In contrast, for four and five electrons, the fully polarized state never becomes the unique ground state, however large the diameter is. These results can be understood in terms of the multiple-spin exchange. When a perpendicular magnetic field is applied to the ring (i.e., the Aharonov-Bohm flux is introduced), the persistent current occurs, and the spin chirality is finite for a certain value of the flux. The difference between the quantum ring and the circularly arranged quantum dots is also discussed.

Hartman effect in a Kane-type semiconductor quantum ring

The Hartman effect for a tunnelling particle implies that group delay time is independent of the opaque barrier width. In the present study, the tunnelling delay time in the transmission mode is studied taking into account the real band structure of an InSb-type semiconductor quantum ring and compared with that of a parabolic band structure. The system considered in this study consists of a circular loop in the presence of Aharonov–Bohm flux. It is shown that while tunnelling through an opaque barrier, the group delay time for a given incident energy becomes independent of the barrier thickness as well as the magnitude of the flux.

Aharonov-Bohm oscillations in a mesoscopic ring with asymmetric arm-dependent injection

Electron transport through mesoscopic, one-dimensional rings with asymmetric injection into the arms of the ring is studied, in the presence of a Aharonov-Bohm flux, by means of an appropriate $\boldsymbol{S}$ matrix. This matrix is expressed in terms of two parameters one of which ($\lambda$) accounts phenomenologically for this asymmetric injection into the arms of the ring. In addition, the effect of a scatterer placed in one arm of the ring is considered. Explicit expressions are obtained for the transmission as a function of the incident electron energy, the magnetic field, the asymmetry parameter $\lambda$, and the strength of the scatterer. Results of the literature for symmetric rings are described by $\lambda=1$ and readily recovered. We relate our results to rings of finite width.

Fano resonance and persistent current in mesoscopic open rings: Influence of coupling and Aharonov-Bohm flux

Electronic transport and persistent current in a mesoscopic ring connected to current leads is investigated using an $S$-matrix approach. In the presence of an impurity in one arm, the transmission probability of the ring may exhibit resonances of the Fano type in addition to Breit-Wigner peaks. It is shown that the transition from the weak to the strong coupling regime leads to Fano line shapes with gradually smaller asymmetry parameters, but the positions of the transmission zeros and ones remain unaffected. This results in a modification of the resonance width. The Breit-Wigner line shape is sensitive to the coupling and disappears in the strong coupling limit. The presence of an Aharonov-Bohm flux alters the amplitudes of the Fano resonances, turning them progressively into broad oscillations. The effect of coupling on the persistent current is also investigated for various impurity strengths and positions. It is shown that increasing the coupling causes gradual suppression of the persistent current, while increasing the impurity strength may lead to negligible persistent current. Furthermore, it is shown that placing the impurity commensurately in the arm causes systematic collapse of certain Fano resonances. For those impurity positions, a divergent persistent current is obtained. The temperature smearing of the Fano resonances is also analyzed.

Electronic Mach-Zehnder interferometer as a tool to probe fractional statistics

We study transport through an electronic Mach-Zehnder interferometer recently devised at the Weizmann Institute. We show that this device can be used to probe statistics of quasiparticles in the fractional quantum Hall regime. We calculate the tunneling current through the interferometer as the function of the Aharonov-Bohm flux, temperature and voltage bias, and demonstrate that its flux-dependent component is strongly sensitive to the statistics of tunneling quasiparticles. More specifically, the flux-dependent and flux-independent contributions to the current are related by a power law, the exponent being a function of the quasiparticle statistics.

Signatures of a Noise-Induced Quantum Phase Transition in a Mesoscopic Metal Ring

We study a mesoscopic ring with an inline quantum dot threaded by an Aharonov-Bohm flux. Zero-point fluctuations of the electromagnetic environment capacitively coupled to the ring, with omega(s) spectral density, can suppress tunneling through the dot, resulting in a quantum phase transition from an unpolarized to a polarized phase. We show that robust signatures of such a transition can be found in the response of the persistent current in the ring to the external flux as well as to the bias between the dot and the arm. Particular attention is paid to the experimentally relevant cases of Ohmic (s = 1) and sub-Ohmic (s = 1/2) noise.

Pumping in a mesoscopic ring with Aharonov-Casher effect

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 the AC effect, and time-reversal symmetry breaking, intrinsic in the parametric pumping procedure. We analyze the conditions for operating the AB-AC ring as a pure spin pump useful in spintronics and discuss the generalization of our results to Rashba-gate-controlled rings.

Effects of electron-electron interaction and electron spin correlations on the exchange coupling in mesoscopic rings

Using the formalism of Lobo, Singwi, and Tosi (LST), we study the effect of electron-electron interaction and electron spin correlations on the indirect exchange interaction between two nuclear spins embedded in a mesoscopic metallic ring, threaded by an Aharonov-Bohm magnetic flux. We first calculate the spin local field correction and the spin-density response function of the ring in a self-consistent manner. Then, we employ the Ruderman-Kittel-Kasuga-Yosida (RKKY) theory to determine the variation of the exchange coupling as a function of the magnetic flux and the angular distance between the two nuclear spins. The LST approach predicts a reach behavior for the exchange coupling as a function of the magnetic flux. Our numerical results show that due to the electron-electron interaction and the electron spin-correlations the exchange coupling can change sign as a function of the magnetic flux, contrary to the prediction of the random phase approximation. Furthermore, the exchange coupling beside its usual oscillatory behavior acquires an oscillatory envelope which brings about strong RKKY interaction between the two nuclear spins even at far distances on the ring.

Cyclic hydrocarbons: nanoscopic (π)-SQUIDs?

A nonperturbative method for calculating persistent currents in molecules and nanoscopic quantum rings is presented. Starting from the extended Hubbard model on a ring threaded by an Aharonov-Bohm flux, a feedback term through which the current can generate magnetic flux is added. Another extension of the Hamiltonian describes the energy stored in the internally generated field. This model is evaluated using exact diagonalization and an iterative scheme to find the minima of the free energy with respect to the current. The magnetic properties due to electron delocalization of conjugated hydrocarbons like benzene [magnetic anisotropy, magnetic susceptibility exaltation, nucleus-independent chemical shift (NICS)] — that have become important criteria for aromaticity — can be examined using this model. A possible novel mechanism for a permanent orbital magnetic moment in quantum rings analogous to the one in π-SQUIDs is found in the framework of the proposed model. The quantum rings must satisfy two conditions to exhibit this kind of permanent orbital magnetic moment: a negative Drude weight and an inductivity above the critical level.

Aharonov–Bohm Oscillations and Fano Resonance of a CoupledDot-Ring System

We derive an exact expression for the transmission coefficient throughan Aharonov–Bohm ring with a side-coupled quantum dot using thescattering-matrix approach. We show a sudden AB phase change by π asthe quantum dot is tuned across the resonance. The Aharonov–Bohmoscillation amplitude can be modulated effectively by tuning the quantumdot level. The transmission coefficient has an expression of thegeneralized Fano form with a complex Fano parameter q in the presenceof the Aharonov–Bohm flux.

Effects of Valley Mixing and Exchange on Excitons in Carbon Nanotubes with Aharonov–Bohm Flux

Because of the presence of two valleys and the electron spin, the exciton states have a degeneracy of 16 in the lowest order k · p approximation. Due to a weak short-range part of the Coulomb interaction, they are split into several levels, leaving only a single optically-active bright level and making all others optically-inactive or dark. Their ordering and energy splitting are shown to be determined by two parameters characterizing the short-range interaction, sensitive to detailed form of the potential and wave function. The presence of a magnetic flux through the cross section, accessible experimentally, modifies these energy levels strongly and causes the appearance of two bright excitons.

Spontaneous and persistent currents in mesoscopic Aharonov-Bohm loops: Static properties and coherent dynamic behavior in crossed electric and magnetic fields

Mesoscopic or macromolecular conducting rings with a fixed number of electrons are shown to support persistent currents due to the Aharonov-Bohm flux, and the “spontaneous” persistent currents without the flux when structural transformation in the ring is blocked by strong coupling to the externally azimuthal-symmetric environment. In the free-standing macromolecular ring, symmetry breaking removes the azimuthal periodicity, which is further restored at the increasing field, however. The dynamics of the Aharonov-Bohm loop in crossed electric and magnetic fields is investigated within the tight-binding approximation; we show that transitions between discrete quantum states occur when static voltage pulses of prescribed duration are applied to the loop. In particular, the three-site ring with one or three electrons is an interesting quantum system that can serve as a qubit (quantum bit of information) and a qugate (quantum logical gate) because in the presence of an externally applied static electric field perpendicular to a magnetic field, the macromolecular ring switches between degenerate ground states mimicking the NOT and Hadamard gates of quantum computers.

Quantum Interference of Electrons in a Ring: Tuning of the Geometrical Phase

We calculate the oscillations of the dc conductance across a mesoscopic ring, simultaneously tuned by applied magnetic and electric fields orthogonal to the ring. The oscillations depend on the Aharonov-Bohm flux and of the spin-orbit coupling. They result from mixing of the dynamical phase, including the Zeeman spin splitting, and of geometric phases. By changing the applied fields, the geometric phase contribution to the conductance oscillations can be tuned from the adiabatic (Berry) to the nonadiabatic (Ahronov-Anandan) regime. To model a realistic device, we also include nonzero backscattering at the connection between ring and contacts, and a random phase for electron wave function, accounting for dephasing effects.

Conductivity in Carbon Nanotubes with Aharonov–Bohm Flux

The Boltzmann conductivity is calculated for carbon nanotubes in the presence of an Aharonov–Bohm magnetic flux. Effects of impurity scattering are considered at low temperatures and those of elect...

Visibility of current and shot noise in electrical Mach-Zehnder and Hanbury Brown Twiss interferometers

We investigate the visibility of the current and shot-noise correlations of electrical analogs of the optical Mach-Zehnder interferometer and the Hanbury Brown Twiss interferometer. The electrical analogs are discussed in conductors subject to high magnetic fields where electron motion is along edge states. The transport quantities are modulated with the help of an Aharonov-Bohm flux. We discuss the conductance (current) visibility and shot noise visibility as a function of temperature and applied voltage. Dephasing is introduced with the help of fictitious voltage probes. Comparison of these two interferometers is of interest since the Mach-Zehnder interferometer is an amplitude (single-particle) interferometer whereas the Hanbury Brown Twiss interferometer is an intensity (two-particle) interferometer. A direct comparison is only possible for the shot noise of the two interferometers. We find that the visibility of shot noise correlations of the Hanbury Brown Twiss interferometer as function of temperature, voltage or dephasing, is qualitatively similar to the visibility of the first harmonic of the shot noise correlation of the Mach-Zehnder interferometer. In contrast, the second harmonic of the shot noise visibility of the Mach-Zehnder interferometer decreases much more rapidly with increasing temperature, voltage or dephasing rate.