Aharonov-Bohm Period Research Articles

Enhanced 2π-periodic Aharonov–Bohm Effect as a Signature of Majorana Zero Modes Probed by Nonlocal Measurements

We propose the $2\pi$-periodic Aharonov-Bohm (AB) effect as a nonlocal probe of Majorana zero modes (MZMs) without the restriction of fermion parity. We demonstrate the enhancement of the AB effect, where the topological protection of MZMs yields amplified and robust Andreev reflection mediated by MZMs at multiple superconductor-normal metal junctions. We investigate the influence of trivial bound states and show that a nonlocal index enables a more explicit distinction between the trivial and topological bound states than local probes.

Fingerprint of Majorana Zero Modes through Nonlocal Measurements

The enhancement and robustness of the 2π periodic Aharonov-Bohm effect can serve as a nonlocal probe of Majorana zero modes in topological superconductors that are not restricted by fermion parity.

Geometry tailored magneto-optical absorption spectra of elliptically deformed double quantum rings

ABSTRACT We theoretically investigated the effect of the geometry change on the electronic and magneto-optical absorption spectra of GaAs/Ga0.7Al0.3As double quantum rings. The inner ring shape was changed continuously from circular to elliptic. Our numerical results revealed the decrement of the levels energies with the augments of the eccentricity of the internal/external ellipses that limit the inner ring, leading to a blue shift of the maxima in the absorption spectra in the magnetic field absence. Analysing separately the electronic spectra of the inner/outer single rings and of the double quantum rings structure in the magnetic field, we have found that, in the electronic spectra of the double ring, only the energies and the Aharonov–Bohm periodicity of the outer ring are altered by interference, while the Aharonov–Bohm oscillations of the inner ring levels propagate unchanged in the spectra. The magneto-optical spectra of elliptically deformed double quantum rings cover a wider range of energies than those of circular double ring and, at higher magnetic fields, present new peaks corresponding to transitions to higher states. Also, they show superposed peaks of increased absorption for a particular elliptic geometry and a red-shift of low energy maxima at the augment of the magnetic field which is the more pronounced the eccentricity increases. Moreover, the influence of the temperature is stronger than for the symmetrical structure.

Fano–Kondo shot noise in a quantum dot embedded interferometer irradiated with microwave fields

Abstract The shot noise of a quantum dot embedded Aharonov–Bohm (AB) interferometer under the perturbation of microwave fields is investigated by employing equation of motion method. The frequency-dependent shot noise formula is derived, and the photon-assisted Fano–Kondo resonance, the suppression of Kondo peak are presented with increasing the direct tunneling strength. The interference and correlation of electrons induce the asymmetric resonant peak–valley behavior of shot noise. The enhancement and suppression of shot noise are resulting from the competition of incoherent correlation and destructive interference effects, and super-Poissonian and sub-Poissonian noise can be adjusted by the applied photon irradiation, gate bias, and direct tunneling strength. The periodic oscillation versus AB phase with period 2 π appears to show plateaus and flat valleys.

Electric field geometries dominate quantum transport coupling in silicon nanoring

Investigations on the relation between the geometries of silicon nanodevices and the quantum phenomenon they exhibit, such as the Aharonov–Bohm (AB) effect and the Coulomb blockade, were conducted. An arsenic doped silicon nanoring coupled with a nanowire by electron beam lithography was fabricated. At 1.47 K, Coulomb blockade oscillations were observed under modulation from the top gate voltage, and a periodic AB oscillation of ΔB = 0.178 T was estimated for a ring radius of 86 nm under a high sweeping magnetic field. Modulating the flat top gate and the pointed side gate was performed to cluster and separate the many electron quantum dots, which demonstrated that quantum confinement and interference effects coexisted in the doped silicon nanoring.

Localized End States in Density Modulated Quantum Wires and Rings

We study finite quantum wires and rings in the presence of a charge-density wave gap induced by a periodic modulation of the chemical potential. We show that the Tamm-Shockley bound states emerging at the ends of the wire are stable against weak disorder and interactions, for discrete open chains and for continuum systems. The low-energy physics can be mapped onto the Jackiw-Rebbi equations describing massive Dirac fermions and bound end states. We treat interactions via the continuum model and show that they increase the charge gap and further localize the end states. The electrons placed in the two localized states on the opposite ends of the wire can interact via exchange interactions and this setup can be used as a double quantum dot hosting spin qubits. The existence of these states could be experimentally detected through the presence of an unusual 4π Aharonov-Bohm periodicity in the spectrum and persistent current as a function of the external flux.

Probing crossover from analogous weak antilocalization to localization by an Aharonov-Bohm interferometer on topological insulator surface

We propose a scanning tunneling microscopy Aharonov-Bohm (AB) interferometer on the surface of a topological insulator (TI) to probe the crossover from analogous weak antilocalization to weak localization phenomenon via the AB oscillations in spin-resolved local density of states (LDOS). Based on our analytical and numerical results, we show that with increasing the energy gap of TI surface states, the Φ0/2=hc/2e periodic AB oscillations in spin-resolved LDOS gradually transit into the Φ0 periodic oscillations.

Multisubband transport and magnetic deflection of Fermi electron trajectories in three terminal junctions and rings

We study the electron transport in three terminal junctions and quantum rings looking for the classical deflection of electron trajectories in the presence of intersubband scattering. We indicate that although the Aharonov–Bohm oscillations and the Lorentz force effects co-exist in the low subband transport, for higher Fermi energies a simultaneous observation of both effects is difficult and calls for carefully formed structures. In particular, in quantum rings with channels wider than the input lead the Lorentz force is well resolved but the Aharonov–Bohm periodicity is lost in chaotic scattering events. In quantum rings with equal lengths of the channels and T-shaped junctions the Aharonov–Bohm oscillations are distinctly periodic but the Lorentz force effects are not well pronounced. We find that systems with wedge-shaped junctions allow for observation of both the periodic Aharonov–Bohm oscillations and the magnetic deflection.

Aharonov-Bohm oscillations in the local density of topological surface states

We study Aharonov-Bohm (AB) oscillations in the local density of states (LDOS) for topological insulator (TI) and conventional metal Au(111) surfaces with spin-orbit interaction, which can be probed by spin-polarized scanning tunneling microscopy. We show that the spacial AB oscillatory period in the total LDOS is a flux quantum Φ0 = hc/e (weak localization) in both systems. Remarkably, an analogous weak antilocalization with Φ0/2 periodic spacial AB oscillations in spin components of LDOS for TI surface is observed, while it is absent in Au(111).

Aharanov-Bohm Interference and Fractional Statistics in a Quantum Hall Interferometer

We compute the temperature, voltage, and magnetic field dependences of the conductance oscillations of a model interferometer designed to measure the fractional statistics of the quasiparticles in the fractional quantum Hall effect. The geometry is the same as that used in recent experiments. With appropriate assumptions concerning the relative areas of the inner and outer rings of the interferometer, we find the theoretical results, including the existence of super periodic Aharonov-Bohm oscillations, to be in remarkably good agreement with experiment. We then make additional experimental predictions with no adjustable parameters which, if verified, would confirm the proposed interpretation of the experiment as a measurement of fractional statistics.

Flux-period scaling in the Laughlin quasiparticle interferometer

We report experiments on electron interferometer devices in the quantum Hall regime, where edge channels circle a two-dimensional (2D) electron island. The main confinement is produced by etch trenches, into which front-gate metal is deposited. We find a linear dependence of the Aharonov-Bohm period on gate voltage for electrons (integer filling $f=1$) and for Laughlin quasiparticles (fractional 2/5 embedded in 1/3). The capacitance of a large 2D electron island with respect to the front gates is approximately proportional to the island radius. Comparing the experimental data for the integer and the fractional fillings and for two samples, we find the magnetic field period and its slope scale with the radius of the Aharonov-Bohm orbit. Analysis of the directly measured integer and fractional slope data allows us to determine the interferometer area in the fractional regime, and thus the Laughlin quasiparticle flux period of $5h∕e$, within the experimental accuracy.

Motion of a charged particle in a periodic Aharonov-Bohm potential

In this paper we introduce a periodic Aharonov-Bohm potential, produced by two parallel infinite thin layers. The motion of a quantum charged particle without spin, under the action of this Aharonov-Bohm potential is examined. Finally we introduce a periodic Aharonov-Bohm potential, produced by a system of parallel solenoids and the motion of the charged particle in this field is also examined.

Few-electron eigenstates of concentric double quantum rings

Few-electron eigenstates confined in coupled concentric double quantum rings are studied by the exact diagonalization technique. We show that the magnetic field suppresses the tunnel coupling between the rings localizing the single-electron states in the internal ring, and the few-electron states in the external ring. The magnetic fields inducing the ground-state angular momentum transitions are determined by the distribution of the electron charge between the rings. The charge redistribution is translated into modifications of the fractional Aharonov-Bohm period. We demonstrate that the electron distribution can be deduced from the cusp pattern of the chemical potentials governing the single-electron charging properties of the system. The evolution of the electron-electron correlations to the high field limit of a classical Wigner molecule is discussed.

Aharonov-Bohm electron interferometer in the integer quantum Hall regime

We report experiments on a quantum electron interferometer fabricated from high mobility, low density $\mathrm{Al}\mathrm{Ga}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ heterostructure material. In this device, a nearly circular electron island is defined by four front gates deposited in etched trenches. The island is separated from the two-dimensional (2D) electron bulk by two nearly open constrictions. In the quantum Hall regime, two counterpropagating edge channels are coupled by tunneling in the constrictions, thus forming a closed electron interference path. For several fixed front gate voltages, we observe periodic Aharonov-Bohm interference oscillations in four-terminal resistance as a function of the enclosed flux. The oscillation period $\ensuremath{\Delta}B$ gives the area of the interference path $S$ via the quantization condition $S=h∕e\ensuremath{\Delta}B$. We experimentally determine the dependence of $S$ on the front gate voltage, and find that the Aharonov-Bohm quantization condition does not require significant corrections due to the confining potential. These results can be interpreted as a constant integrated compressibility of the island with respect to the front gates. We also analyze experimental results using two classical electrostatics models: one modeling the 2D electron density due to depletion from an etch trench, and another modeling the gate voltage dependence of the electron density profile in the island.

Fractional statistics of Laughlin quasiparticles in quantum antidots

In two dimensions, fractionally charged particles must possess fractional exchange statistics. In experiments on quantum antidots in the quantum Hall regime the charge of the tunneling particles can be determined directly as a measure of the gate voltage needed to attract one particle. In the same experiments, when the magnetic field is varied, it is observed that the fundamental Aharonov-Bohm period is $h∕e$ even for fractionally charged Laughlin quasiparticles. In this paper we analyze these experiments, explicitly taking into account the fractional statistical Berry's phase contribution.

Kondo Effect in a Many-Electron Quantum Ring

The Kondo effect is investigated in a many-electron quantum ring as a function of the magnetic field. For fields applied perpendicular to the plane of the ring a modulation of the Kondo effect with the Aharonov-Bohm period is observed. This effect is discussed in terms of the energy spectrum of the ring and the parametrically changing tunnel coupling. In addition, we use gate voltages to modify the ground-state spin of the ring. The observed splitting of the Kondo-related zero-bias anomaly in this configuration is tuned with an in-plane magnetic field.

Aharonov–Bohm effect of a quantum ring in the Kondo regime

AbstractWe investigate a small tuneable quantum ring fabricated by direct local oxidation using an atomic force microscope. The device contains very few electrons and is tuned into the Kondo regime. We study this Kondo effect by temperature dependent measurements. At finite bias voltages we observe additional peaks. These vanish with increasing temperature indicating Kondo correlations for these excited states. Additionally, the geometry of our device allows to study Aharonov–Bohm oscillations in the Kondo regime for a device containing less than ten electrons. We observe a modulation of the Kondo effect with a reduced Aharonov–Bohm period explained by electron–electron interaction in our small quantum ring.

Electronic structures of chiral carbon toroids

The π-electronic states of chiral carbon toroids are calculated from the tight-binding model. The electronic structures, the energy gap, the energy spacing and the degeneracy of discrete states, are studied. They are mainly determined by the geometric structures (height, chiral angle and radius) the curvature effect and the magnetic flux (gf). Carbon toroids have four (three) types of energy gaps, while the curvature effect is important (negligible). The relations between energy gaps and geometric structures are complex (simple) in the presence (absence) of the curvature effect. The gf-dependent electronic structures exhibit the periodic Aharonov-Bohm oscillations. The magnetic flux could also effectively affect the state degeneracy of zigzag carbon toroids.

Bethe-Ansatz Analysis of the Extended AB Period in the One-Dimensional Hubbard Model

The extended spectral flow at the normal-superconducting transition is investigated for the one-dimensional Hubbard model. Recombination of spectral flow lines at U =±0, which causes halving of the extended Aharonov-Bohm period for U <0 found in a recent paper [K. Kusakabe and H. Aoki: J. Phys. Soc. Jpn. 65 (1996) 2772], is exactly analyzed using the Bethe ansatz solution. Adiabatic motion of charge rapidities which are real for U >0 (normal Luttinger liquid) or complex for U <0 (superconducting Luther-Emery liquid) dominates sudden response of the spectral flow at the transition point. The extended period is obtained not only against the charge flux but also against the spin flux for both U >0 and U <0.

Extended AB Period Study of the Electron Pairing Transition int-J Ladders

The extended Aharonov-Bohm period test, recently proposed by the present authors, is used to study the electron pairing transition in the t-J ladders. The critical point is detected as a gap opening in the extended spectral flow. The result suggests a pairing prior to the onset of a phase separation, which is consistent with a recent Tomonaga-Luttinger analysis.