Magnetic field enhancement of superconductivity in ultra-narrow wires

We study the effect of an applied magnetic field on sub-10nm wide MoGe and Nb superconducting wires. We find that magnetic fields can enhance the critical supercurrent at low temperatures, and does so more strongly for narrower wires. We conjecture that magnetic moments are present, but their pair-breaking effect, active at lower magnetic fields, is suppressed by higher fields. The corresponding microscopic theory, which we have developed, quantitatively explains all experimental observations, and suggests that magnetic moments have formed on the wire surfaces.Comment: 4 pages, 3 figures, 1 tabl

Geometrical entanglement of highly symmetric multipartite states and the Schmidt decomposition

In a previous paper we examined a geometric measure of entanglement based on the minimum distance between the entangled target state of interest and the space of unnormalized product states. Here we present a detailed study of this entanglement measure for target states with a large degree of symmetry. We obtain analytic solutions for the extrema of the distance function and solve for the Hessian to show that, up to the action of trivial symmetries, the solutions correspond to local minima of the distance function. In addition, we show that the conditions that determine the extremal solutions for general target states can be obtained directly by parametrizing the product states via their Schmidt decomposition.Comment: 16 pages, references added and discussion expande

High Temperature Macroscopic Entanglement

In this paper I intend to show that macroscopic entanglement is possible at high temperatures. I analyze multipartite entanglement produced by the $\eta$ pairing mechanism which features strongly in the fermionic lattice models of high $T_c$ superconductivity. This problem is shown to be equivalent to calculating multipartite entanglement in totally symmetric states of qubits. I demonstrate that we can conclusively calculate the relative entropy of entanglement within any subset of qubits in an overall symmetric state. Three main results then follow. First, I show that the condition for superconductivity, namely the existence of the off diagonal long range order (ODLRO), is not dependent on two-site entanglement, but on just classical correlations as the sites become more and more distant. Secondly, the entanglement that does survive in the thermodynamical limit is the entanglement of the total lattice and, at half filling, it scales with the log of the number of sites. It is this entanglement that will exist at temperatures below the superconducting critical temperature, which can currently be as high as 160 Kelvin. Thirdly, I prove that a complete mixture of symmetric states does not contain any entanglement in the macroscopic limit. On the other hand, the same mixture of symmetric states possesses the same two qubit entanglement features as the pure states involved, in the sense that the mixing does not destroy entanglement for finite number of qubits, albeit it does decrease it. Maximal mixing of symmetric states also does not destroy ODLRO and classical correlations. I discuss various other inequalities between different entanglements as well as generalizations to the subsystems of any dimensionality (i.e. higher than spin half).Comment: 14 pages, no figure

Enhancing superconductivity: Magnetic impurities and their quenching by magnetic fields

Magnetic fields and magnetic impurities are each known to suppress superconductivity. However, as the field quenches (i.e. polarizes) the impurities, rich consequences, including field-enhanced superconductivity, can emerge when both effects are present. For the case of superconducting wires and thin films, this field-spin interplay is investigated via the Eilenberger-Usadel scheme. Non-monotonic dependence of the critical current on the field (and therefore field-enhanced superconductivity) is found to be possible, even in parameter regimes in which the critical temperature decreases monotonically with increasing field. The present work complements that of Kharitonov and Feigel'man, which predicts non-monotonic behavior of the critical temperature.Comment: 8 pages, 2 figures, EPL forma

Evolution of entanglement entropy in one-dimensional systems

We study the unitary time evolution of the entropy of entanglement of a one-dimensional system between the degrees of freedom in an interval of length l and its complement, starting from a pure state which is not an eigenstate of the Hamiltonian. We use path integral methods of quantum field theory as well as explicit computations for the transverse Ising spin chain. In both cases, there is a maximum speed v of propagation of signals. In general the entanglement entropy increases linearly with time t up to t = l/2v, after which it saturates at a value proportional to l, the coefficient depending on the initial state. This behaviour may be understood as a consequence of causality