e/3 Laughlin quasiparticle primary-filling nu=1/3 interferometer

We report experimental realization of a quasiparticle interferometer where the entire system is in 1/3 primary fractional quantum Hall state. The interferometer consists of chiral edge channels coupled by quantum-coherent tunneling in two constrictions, thus enclosing an Aharonov-Bohm area. We observe magnetic flux and charge periods h/e and e/3, equivalent to the creation of one quasielectron in the island. Quantum theory predicts a 3h/e flux period for charge e/3, integer statistics particles. Thus, the observed periods demonstrate the anyonic braiding statistics of Laughlin quasiparticles.     

Telegraph noise and fractional statistics in the quantum Hall effect

We study theoretically nonequilibrium noise in the fractional quantum Hall regime for an Aharonov-Bohm ring with a third contact in the middle of the ring. Because of their fractional statistics the tunneling of Laughlin quasiparticles between the inner and outer edges of the ring changes the effective Aharonov-Bohm flux experienced by quasiparticles going around the ring, leading to a change in the conductance across the ring. A small current in the middle contact, therefore, gives rise to fluctuations in the current flowing across the ring which resemble random telegraph noise. We analyze this noise using the chiral Luttinger liquid model. At low frequencies the telegraph noise varies inversely with the tunneling current and can be much larger than the shot noise. We propose that combining the Aharonov-Bohm effect with a noise measurement provides a direct method for observing fractional statistics.     

Magnetically tunable Kondo-Aharonov-Bohm effect in a triangular quantum dot

The role of discrete orbital symmetry in mesoscopic physics is manifested in a system consisting of three identical quantum dots forming an equilateral triangle. Under a perpendicular magnetic field, this system demonstrates a unique combination of Kondo and Aharonov-Bohm features due to an interplay between continuous [spin-rotation SU(2)] and discrete (permutation C3v) symmetries, as well as U(1) gauge invariance. The conductance as a function of magnetic flux displays sharp enhancement or complete suppression depending on contact setups.     

Optical properties in a two-dimensional quantum ring: Confinement potential and Aharonov-Bohm effect

Optical properties of a two-dimensional quantum ring with pseudopotential in the presence of an external magnetic field and magnetic flux have been theoretically investigated. Our results show that both of the pseudopotential and magnetic field can affect the third non-linear susceptibility and oscillator strength. In addition, we found that the oscillator strength and the absolute value of the resonant peak of the linear, non-linear and total absorption coefficient demonstrates the Aharonov-Bohm oscillation with magnetic flux, moreover, changes in confinement potential can influence the Aharonov-Bohm oscillation in peak while the resonant peak value of the linear, non-linear and total refractive index changes decreases as magnetic flux increases.     

Detecting non-Abelian statistics with an electronic Mach-Zehnder interferometer

Fractionally charged quasiparticles in the quantum Hall state with a filling factor nu=5/2 are expected to obey non-Abelian statistics. We demonstrate that their statistics can be probed by transport measurements in an electronic Mach-Zehnder interferometer. The tunneling current through the interferometer exhibits a characteristic dependence on the magnetic flux and a nonanalytic dependence on the tunneling amplitudes which can be controlled by gate voltages.     

Direkte Beobachtung einzelner magnetischer Flußquanten in supraleitenden Hohlzylindern. III

By use of electron interferometry the trapped magnetic flux was investigated in superconducting microcylinders (inner diameter < 1 μm). Even in thin walled cylinders (wall thickness < penetration depth) at temperatures near the superconducting transition the flux was found to be quantized in integer multipleshc/2e. In the appendix an interpretation of the magnetic Aharonov-Bohm effect as a local interaction between the excluded field and the electromagnetic field of the electron is discussed.     

Locality and topology in the molecular Aharonov-Bohm effect

It is shown that the molecular Aharonov-Bohm effect is neither nonlocal nor topological in the sense of the standard magnetic Aharonov-Bohm effect. It is further argued that there is a close relationship between the molecular Aharonov-Bohm effect and the Aharonov-Casher effect for an electrically neutral spin -1 / 2 particle encircling a line of charge.     

Magnetic Manipulation of Massless Dirac Fermions in Graphene Quantum Dot

We have theoretically analyzed the quasibound states in a graphene quantum dot (GQD) with a magnetic flux Φ in the centre. It is shown that the two-fold time reversal degeneracy is broken and the quasibound states of GQD with positive/negative angular momentum shifted upwards /downwards with increasing the magnetic flux. The variation of the quasibound energy depends linearly on the magnetic flux, which is quite different from theparabolic relationship for Schrödinger electrons. The GQD's quasibound states spectrum shows an obvious Aharonov-Bohm (AB) oscillations with the magnetic flux. It is also shown that the quasibound state with energy equal to the barrier height becomes a bound state completely confined in GQD.     

Scattering of spin-polarized electron in an Aharonov-Bohm potential

The scattering of spin-polarized electrons in an Aharonov-Bohm vector potential is considered. We solve the Pauli equation in 3 + 1 dimensions taking into account explicitly the interaction between the three-dimensional spin magnetic moment of electron and magnetic field. Expressions for the scattering amplitude and the cross section are obtained for spin-polarized electron scattered off a flux tube of small radius. It is also shown that bound electron states cannot occur in this quantum system. The scattering problem for the model of a flux tube of zero radius in the Born approximation is briefly discussed.     

Non-Abelian braiding of lattice bosons

We report on a numerical experiment in which we use time-dependent potentials to braid non-Abelian quasiparticles. We consider lattice bosons in a uniform magnetic field within the fractional quantum Hall regime, where ν, the ratio of particles to flux quanta, is near 1/2, 1, or 3/2. We introduce time-dependent potentials which move quasiparticle excitations around one another, explicitly simulating a braiding operation which could implement part of a gate in a quantum computation. We find that different braids do not commute for ν near 1 and 3/2, with Berry matrices, respectively, consistent with Ising and Fibonacci anyons. Near ν=1/2, the braids commute.     

Path integrals with topological constraints: Aharonov-Bohm effect and polymer entanglements

For Wiener- and Feynman integrals over paths with certain topological properties we compare various methods for explicit calculation. This leads to a one-to-one correspondence between the Aharonov-Bohm effect and a certain polymer entanglement problem. We briefly comment on two generalizations of the Aharonov-Bohm effect. First, we consider this effect due to a closed magnetic flux loop of arbitrary shape; next, we consider the combined effect due to a gas of microscopic magnetic flux loops.     

Low-energy subgap states and the magnetic flux periodicity in d-wave superconducting rings

Wave functions of low-energy quasiparticle subgap states in d-wave superconducting rings, threaded by an Aharonov-Bohm magnetic flux, are found analytically. The respective energies are closest to the midgap position at small magnetic fluxes and deviate from the Fermi surface due to the Doppler shift, produced by the supercurrent. The Doppler-shifted zero-energy states result in a paramagnetic response of the ring at small fluxes. The states exist only for even angular momenta of the center of mass of Cooper pairs, in agreement with recent numerical studies of the problem. This macroscopic quantum effect in d-wave rings results in broken h/2e periodicity, retaining only the h/e periodic behavior of the supercurrent with varying magnetic flux.     

Conductance in an Aharonov-Bohm Interferometer with Parallel-Coupled Double Dots

We present a theoretical study of the conductance in an Aharonov-Bohm interferometer containing two coupled quantum dots. The interdot tunneling divides the interferometer into two coupled subrings, where opposite magnetic fluxes are threaded separately while the net flux is kept zero. Using the Green function technique we derive the expression of the linear conductance. It is found that the Aharonov-Bohm effect still exists, and when the level of each dot is aligned, the exchange of the Fano and Breit-Wigner resonances in the conductance can be achieved by tuning the magnetic flux. When the two levels are mismatched the exchange may not happen. Further, for some specific asymmetric systems where the coupling strengths between the two dots and the leads are not equal, the flux can change the Fano resonance into an antiresonance, which is absent in symmetric systems.     

Direkte Beobachtung einzelner magnetischer Flußquanten in supraleitenden Hohlzylindern. I

By use of electron interferometry in connection with the Aharonov-Bohm effect it was possible to observe directly single magnetic flux quanta, trapped in superconducting tubes with an inner diameter ranging from 0.5 μm to 1 μm. The flux coincided with the fluxoid quantumhc/2e within the experimental error of 4% for thick walled cylinders. The flux distribution along the cylinders was found to be not constant in time and space. Flux quanta down to 8 μm length have been observed. The method permits the observation of flux creep of single flux quanta.     

Aharonov-Bohm effect in spherical billiard

Using Gutzwiller's periodic orbit theory, we study the quantum level density of a spherical billiard in the presence of a magnetic flux line added at its center, especially discuss the influence of the magnetic flux strength on the quantum level density. The Fourier transformed quantum level density of this system has allowed direct comparison between peaks in the level density and the length of the periodic orbits. For particular magnetic flux strength, the amplitude of the peaks in the level density decreased and some of the peaks disappeared. This result suggests that Aharonov-Bohm effect manifests itself through the cancellation of periodic orbits. This phenomenon will provide a new experimental testing ground for exploring Aharonov-Bohm effect.     

Effects of external fields on a two-dimensional Klein-Gordon particle under pseudo-harmonic oscillator interaction

We study the effects of the perpendicular magnetic and Aharonov-Bohm(AB) flux fields on the energy levels of a two-dimensional(2D) Klein-Gordon(KG) particle subjected to an equal scalar and vector pseudo-harmonic oscillator(PHO).We calculate the exact energy eigenvalues and normalized wave functions in terms of chemical potential parameter,magnetic field strength,AB flux field,and magnetic quantum number by means of the Nikiforov-Uvarov(NU) method.The non-relativistic limit,PHO,and harmonic oscillator solutions in the existence and absence of external fields are also obtained.     

Aharonov-Bohm oscillations in disordered topological insulator nanowires

A direct signature of electron transport at the metallic surface of a topological insulator is the Aharonov-Bohm oscillation observed in a recent study of Bi2Se3 nanowires [Peng, Nature Mater. 9, 225 (2010)] where conductance was found to oscillate as a function of magnetic flux ? through the wire, with a period of one flux quantum ?0=h/e and maximum conductance at zero flux. This seemingly agrees neither with diffusive theory, which would predict a period of half a flux quantum, nor with ballistic theory, which in the simplest form predicts a period of ?0 but a minimum at zero flux due to a nontrivial Berry phase in topological insulators. We show how h/e and h/2e flux oscillations of the conductance depend on doping and disorder strength, provide a possible explanation for the experiments, and discuss further experiments that could verify the theory.     

Exhibition of surface steps by high resolution electron microscopy of monoclinic rare earth sesquioxides

On high resolution structure images, the existence of a superperiod has been observed, linked with the apparition of extraspots in the diffraction diagram. The specimen (B-Sm₂O₃) can be described as composed of layers of thickness 6 Å, nearly perpendicular to the incident electron beam. These layers are of 3 different kinds. We have shown that the apparition of the superperiod can be linked with steps of height 6 or 12 Å (i.e. 1 or 2 layers): computed images, using this hypothesis exhibit the observed superperiod, even for thicknesses around 230 Å. This allows atomic steps to be imaged with a high resolution structure image.