Физика низких температур, 2004, № 07-08

Superconducting and mesoscopic structures

Thu, 01 Jan 2004 00:00:00 GMT

Superconducting and mesoscopic structures Omelyanchouk, A.N.

Wigner distribution function formalism for superconductors and collisionless dynamics of the superconducting order parameter

Thu, 01 Jan 2004 00:00:00 GMT

Wigner distribution function formalism for superconductors and collisionless dynamics of the superconducting order parameter Amin, M.H.S.; Bezuglyi, E.V.; Kijko, A.S.; Omelyanchouk, A.N. A technique for studying collisionless dynamics of a homogeneous superconducting system is developed which is based on Riccati parametrization of the Wigner distribution function. The quantum evolution of the superconducting order parameter, initially deviating from the equilibrium value, is calculated using this technique. The effect of a time-dependent BCS paring interaction on the dynamics of the order parameter is also studied.

Topological solitons of the Lawrence–Doniach model as equilibrium Josephson vortices in layered superconductors

Thu, 01 Jan 2004 00:00:00 GMT

Topological solitons of the Lawrence–Doniach model as equilibrium Josephson vortices in layered superconductors Kuplevakhsky, S.V. We present a complete, exact solution of the problem of the magnetic properties of layered superconductors with an infinite number of superconducting layers in parallel fields H 0. Based on a new exact variational method, we determine the type of all stationary points of both the Gibbs and Helmholtz free-energy functionals. For the Gibbs free-energy functional, they are either points of strict, strong minima or saddle points. All stationary points of the Helmholtz free-energy functional are those of strict, strong minima. The only minimizes of both the functionals are the Meissner (0-soliton) solution and soliton solutions. The latter represent equilibrium Josephson vortices. In contrast, non-soliton configurations (interpreted in some previous publications as «isolated fluxons» and «fluxon lattices») are shown to be saddle points of the Gibbs free-energy functional: They violate the conservation law for the flux and the stationarity condition for the Helmholtz free-energy functional. For stable solutions, we give a topological classification and establish a one-to-one correspondence with Abrikosov vortices in type-II superconductors. In the limit of weak interlayer coupling, exact, closed-form expressions for all stable solutions are derived: They are nothing but the «vacuum state» and topological solitons of the coupled static sine-Gordon equations for the phase differences. The stable solutions cover the whole field range 0 < H < ∞ and their stability regions overlap. Soliton solutions exist for arbitrary small transverse dimensions of the system, provided the field H to be sufficiently high. Aside from their importance for weak superconductivity, the new soliton solutions can find applications in different fields of nonlinear physics and applied mathematics.

Topologically protected quantum states and quantum computing in Josephson junctions arrays

Thu, 01 Jan 2004 00:00:00 GMT

Topologically protected quantum states and quantum computing in Josephson junctions arrays Ioffe, L.B.; Feigel`man, M.V.; Douçot, B. We review recent results on a new class of Josephson arrays which have non-trivial topology and exhibit a novel quantum states at low temperatures. One of these states is characterized by long range order in a two Cooper pair condensate and by a discrete topological order parameter. The second state is insulating and can be considered as a result of evolution of the former state due to Bose-condensation of usual superconductive vortices with a flux quantum 0. Quantum phase transition between these two states is controlled by variation of external magnetic field. Both the superconductive and insulating states are characterized by the presence of 2K-degenerate ground states, with K being the number of topologically different cycles existing in the plane of the array. This degeneracy is «protected» from the external perturbations (and noise) by the topological order parameter and spectral gap. We show that in ideal conditions the low order effect of the external perturbations on this degeneracy is exactly zero and that deviations from ideality lead to only exponentially small effects of perturbations. We argue that this system provides a physical implementation of an ideal quantum computer with a built in error correction. A number of relatively simple «echo-like» experiments possible on small-size arrays are discussed.