Effective Carrier Mean-Free Path in Confined Geometries

The concept of exchange length is used to determine the effects of boundary scattering on transport in samples of circular and rectangular cross section. Analytical expressions are presented for an effective mean-free path for transport in the axial direction. The relationship to the phonon thermal conductivity is discussed. (This letter outlines the results presented in detail in the longer version, available as cond-mat/9402081)Comment: 12 pages, Late

Magnetic flux pinning in superconductors with hyperbolic-tesselation arrays of pinning sites

We study magnetic flux interacting with arrays of pinning sites (APS) placed on vertices of hyperbolic tesselations (HT). We show that, due to the gradient in the density of pinning sites, HT APS are capable of trapping vortices for a broad range of applied magnetic fluxes. Thus, the penetration of magnetic field in HT APS is essentially different from the usual scenario predicted by the Bean model. We demonstrate that, due to the enhanced asymmetry of the surface barrier for vortex entry and exit, this HT APS could be used as a "capacitor" to store magnetic flux.Comment: 7 pages, 5 figure

Optomechanical-like coupling between superconducting resonators

We propose and analyze a circuit that implements a nonlinear coupling between two superconducting microwave resonators. The resonators are coupled through a superconducting quantum interference device (SQUID) that terminates one of the resonators. This produces a nonlinear interaction on the standard optomechanical form, where the quadrature of one resonator couples to the photon number of the other resonator. The circuit therefore allows for all-electrical realizations of analogs to optomechanical systems, with coupling that can be both strong and tunable. We estimate the coupling strengths that should be attainable with the proposed device, and we find that the device is a promising candidate for realizing the single-photon strong-coupling regime. As a potential application, we discuss implementations of networks of nonlinearly-coupled microwave resonators, which could be used in microwave-photon based quantum simulation.Comment: 10 pages, 7 figure

Critical currents in superconductors with quasiperiodic pinning arrays: One-dimensional chains and two-dimensional Penrose lattices

We study the critical depinning current J_c, as a function of the applied magnetic flux Phi, for quasiperiodic (QP) pinning arrays, including one-dimensional (1D) chains and two-dimensional (2D) arrays of pinning centers placed on the nodes of a five-fold Penrose lattice. In 1D QP chains of pinning sites, the peaks in J_c(Phi) are shown to be determined by a sequence of harmonics of long and short periods of the chain. This sequence includes as a subset the sequence of successive Fibonacci numbers. We also analyze the evolution of J_c(Phi) while a continuous transition occurs from a periodic lattice of pinning centers to a QP one; the continuous transition is achieved by varying the ratio gamma = a_S/a_L of lengths of the short a_S and the long a_L segments, starting from gamma = 1 for a periodic sequence. We find that the peaks related to the Fibonacci sequence are most pronounced when gamma is equal to the "golden mean". The critical current J_c(Phi) in QP lattice has a remarkable self-similarity. This effect is demonstrated both in real space and in reciprocal k-space. In 2D QP pinning arrays (e.g., Penrose lattices), the pinning of vortices is related to matching conditions between the vortex lattice and the QP lattice of pinning centers. Although more subtle to analyze than in 1D pinning chains, the structure in J_c(Phi) is determined by the presence of two different kinds of elements forming the 2D QP lattice. Indeed, we predict analytically and numerically the main features of J_c(Phi) for Penrose lattices. Comparing the J_c's for QP (Penrose), periodic (triangular) and random arrays of pinning sites, we have found that the QP lattice provides an unusually broad critical current J_c(Phi), that could be useful for practical applications demanding high J_c's over a wide range of fields.Comment: 18 pages, 15 figures (figures 7, 9, 10, 13, 15 in separate "png" files

Position, spin and orbital angular momentum of a relativistic electron

Motivated by recent interest in relativistic electron vortex states, we revisit the spin and orbital angular momentum properties of Dirac electrons. These are uniquely determined by the choice of the position operator for a relativistic electron. We overview two main approaches discussed in the literature: (i) the projection of operators onto the positive-energy subspace, which removes the zitterbewegung effects and correctly describes spin-orbit interaction effects, and (ii) the use of Newton-Wigner-Foldy-Wouthuysen operators based on the inverse Foldy-Wouthuysen transformation. We argue that the first approach [previously described in application to Dirac vortex beams in K.Y. Bliokh et al., Phys. Rev. Lett. 107, 174802 (2011)] has a more natural physical interpretation, including spin-orbit interactions and a nonsingular zero-mass limit, than the second one [S.M. Barnett, Phys. Rev. Lett. 118, 114802 (2017)].Comment: 10 pages, 1 table, to appear in Phys. Rev.

Quantum interference from sums over closed paths for electrons on a three-dimensional lattice in a magnetic field: total energy, magnetic moment, and orbital susceptibility

We study quantum interference effects due to electron motion on a three-dimensional cubic lattice in a continuously-tunable magnetic field of arbitrary orientation and magnitude. These effects arise from the interference between magnetic phase factors associated with different electron closed paths. The sums of these phase factors, called lattice path-integrals, are ``many-loop" generalizations of the standard ``one-loop" Aharonov-Bohm-type argument. Our lattice path integral calculation enables us to obtain various important physical quantities through several different methods. The spirit of our approach follows Feynman's programme: to derive physical quantities in terms of ``sums over paths". From these lattice path-integrals we compute analytically, for several lengths of the electron path, the half-filled Fermi-sea ground-state energy of noninteracting spinless electrons in a cubic lattice. Our results are valid for any strength of the applied magnetic field in any direction. We also study in detail two experimentally important quantities: the magnetic moment and orbital susceptibility at half-filling, as well as the zero-field susceptibility as a function of the Fermi energy.Comment: 14 pages, RevTe