Phase-Controlled Force and Magnetization Oscillations in Superconducting Ballistic Nanowires

The emergence of superconductivity-induced phase-controlled forces in the (0.01-0.1) nN range, and of magnetization oscillations, in nanowire junctions, is discussed. A giant magnetic response to applied weak magnetic fields, is predicted in the ballistic Josephson junction formed by a superconducting tip and a surface, bridged by a normal metal nanowire where Andreev states form.Comment: 5 pages, 3 figure

Ballistic electronic transport in Quantum Cables

We studied theoretically ballistic electronic transport in a proposed mesoscopic structure - Quantum Cable. Our results demonstrated that Qauntum Cable is a unique structure for the study of mesoscopic transport. As a function of Fermi energy, Ballistic conductance exhibits interesting stepwise features. Besides the steps of one or two quantum conductance units ($2e^2/h$), conductance plateaus of more than two quantum conductance units can also be expected due to the accidental degeneracies (crossings) of subbands. As structure parameters is varied, conductance width displays oscillatory properties arising from the inhomogeneous variation of energy difference betweeen adjoining transverse subbands. In the weak coupling limits, conductance steps of height $2e^2/h$ becomes the first and second plateaus for the Quantum Cable of two cylinder wires with the same width.Comment: 11 pages, 5 figure

Aharonov-Bohm effect and plasma oscillations in superconducting tubes and rings

Low frequency plasma oscillations in superconducting tubes are considered. The emergence of two different dimensionality regimes of plasma oscillations in tubes, exhibiting a crossover from one-dimensional to two-dimensional behavior, depending on whether $k R\ll 1$ or $k R\gg 1$, where $k$ is the plasmon wave vector and $R$ is the radius of the tube, is discussed. The Aharonov-Bohm effect pertaining to plasma oscillations in superconducting tubes and rings, resulting in an oscillatory behavior of the plasmon frequency as a function of the magnetic flux, with a flux quantum period $hc/2e$ (analog of the Little-Parks effect), is studied. The amplitude of the oscillations is proportional to $(\xi/R)^2$, where $\xi$ is the superconducting coherence length.Comment: 18 pages, 4 figure

Coherent quantum phenomena in mesoscopic metallic conductors (Review Article)

The quantum coherent phenomena in mesoscopic cylindrical metallic conductors have been considered. Pure double-and single-connected normal samples were placed in a longitudinal magnetic field, which generated interference phenomena depending on the magnetic flux through the cross-section of the conductor. The period of the induced oscillations is equal to the flux quantum hc/e of the normal metal. The quantum states are formed in the structures by collisions of the electrons with the dielectric boundary of the sample. The magnetic flux is included in the expression for the spectrum of quasiparticles. The proximity effect and its influence on the modification of the spectrum of quantum coherent phenomena have been investigated. The behavior of cylindrical samples consisting of a superconducting (S) metal with a deposited thin pure normal (N) metal layer has been analyzed. In this structure the electrons are localized in a well bounded by a dielectric on one side and by a superconductor on the other. The specific feature of the generated quantized Andreev levels is that in the varying field H (or temperature T) each of the levels in the well can coincide periodically with the chemical potential of the metal. As a result, the state of the system experiences strong degeneracy and the density of states exhibits resonance spikes of the energy of the NS sample. This makes a significant contribution to the magnetic moment. A theory of the reentrant effect for NS structures has been developed, which interprets the anomalous behavior of the magnetic susceptibility of such structures as a function of the magnetic field and temperatures

Persistent currents, flux quantization, and magnetomotive forces in normal metals and superconductors (Review Article)

The notion of persistent current comes back to orbital currents in normal metals, semiconductors and even insulators displaying diamagnetic behavior in weak magnetic fields, but came to focus at the discovery of current persistence and magnetic flux quantization at large fields in atomically big but macroscopically small (mesoscopic) objects. The phenomenon bears much similarity with supercurrents in superconductive metals. We will review progress in developing of our understanding of the physical and technological aspects of this phenomenon. The exact solution for currents, magnetic moments and magnetomotive forces (torques) in crossed magnetic fields are presented. Time-dependent phenomena in crossed magnetic and electric fields, and in possibility of spontaneous persistent currents and of work extraction from static and dynamic quantum states are discussed

A Magnetic-Field-Effect Transistor and Spin Transport

A magnetic-field-effect transistor is proposed that generates a spin-polarized current and exhibits a giant negative magnetoresitance. The device consists of a nonmagnetic conducting channel (wire or strip) wrapped, or sandwiched, by a grounded magnetic shell. The process underlying the operation of the device is the withdrawal of one of the spin components from the channel, and its dissipation through the grounded boundaries of the magnetic shell, resulting in a spin-polarized current in the nonmagnetic channel. The device may generate an almost fully spin-polarized current, and a giant negative magnetoresistance effect is predicted.Comment: 4 pages, 3 figure

The theory of the reentrant effect in susceptibility of cylindrical mesoscopic samples

A theory has been developed to explain the anomalous behavior of the magnetic susceptibility of a normal metal-superconductor ($NS$) structure in weak magnetic fields at millikelvin temperatures. The effect was discovered experimentally by A.C. Mota et al \cite{10}. In cylindrical superconducting samples covered with a thin normal pure metal layer, the susceptibility exhibited a reentrant effect: it started to increase unexpectedly when the temperature lowered below 100 mK. The effect was observed in mesoscopic $NS$ structures when the $N$ and $S$ metals were in good electric contact. The theory proposed is essentially based on the properties of the Andreev levels in the normal metal. When the magnetic field (or temperature) changes, each of the Andreev levels coincides from time to time with the chemical potential of the metal. As a result, the state of the $NS$ structure experiences strong degeneracy, and the quasiparticle density of states exhibits resonance spikes. This generates a large paramagnetic contribution to the susceptibility, which adds up to the diamagnetic contribution thus leading to the reentrant effect. The explanation proposed was obtained within the model of free electrons. The theory provides a good description for experimental results [10]

Edge effects in graphene nanostructures: I. From multiple reflection expansion to density of states

We study the influence of different edge types on the electronic density of states of graphene nanostructures. To this end we develop an exact expansion for the single particle Green's function of ballistic graphene structures in terms of multiple reflections from the system boundary, that allows for a natural treatment of edge effects. We first apply this formalism to calculate the average density of states of graphene billiards. While the leading term in the corresponding Weyl expansion is proportional to the billiard area, we find that the contribution that usually scales with the total length of the system boundary differs significantly from what one finds in semiconductor-based, Schr\"odinger type billiards: The latter term vanishes for armchair and infinite mass edges and is proportional to the zigzag edge length, highlighting the prominent role of zigzag edges in graphene. We then compute analytical expressions for the density of states oscillations and energy levels within a trajectory based semiclassical approach. We derive a Dirac version of Gutzwiller's trace formula for classically chaotic graphene billiards and further obtain semiclassical trace formulae for the density of states oscillations in regular graphene cavities. We find that edge dependent interference of pseudospins in graphene crucially affects the quantum spectrum.Comment: to be published in Phys. Rev.

Berry's Phases of Ground States of Interacting Spin-One Bosons: Chains of Monopoles and Monosegments

We study Berry's connection potentials of many-body ground states of spin-one bosons with antiferromagnetic interactions in adiabatically varying magnetic fields. We find that Berry's connection potentials are generally determined by, instead of usual singular monopoles, linearly positioned monosegments each of which carries one unit of topological charge; in the absence of a magnetic field gradient this distribution of monosegments becomes a linear chain of monopoles. Consequently, Berry's phases consist of a series of step functions of magnetic fields; a magnetic field gradient causes rounding of these step-functions. We also calculate Berry's connection fields, profiles of monosegments and show that the total topological charge is conserved in a parameter space

Quantum interference of surface states in bismuth nanowires probed by the Aharonov-Bohm oscillatory behavior of the magnetoresistance

We report the observation of a dependence of the low temperature resistance of individual single-crystal bismuth nanowires on the Aharonov-Bohm phase of the magnetic flux threading the wire. 55 and 75-nm wires were investigated in magnetic fields of up to 14 T. For 55 nm nanowires, longitudinal magnetoresistance periods of 0.8 and 1.6 T that were observed at magnetic fields over 4 T are assigned to h/2e to h/e magnetic flux modulation. The same modes of oscillation were observed in 75-nm wires. The observed effects are consistent with models of the Bi surface where surface states give rise to a significant population of charge carriers of high effective mass that form a highly conducting tube around the nanowire. In the 55-nm nanowires, the Fermi energy of the surface band is estimated to be 15 meV. An interpretation of the magnetoresistance oscillations in terms of a subband structure in the surface states band due to quantum interference in the tube is presented.Comment: 30 pages, 9 figure