Fluctuation persistent current in small superconducting rings

We extend previous theoretical studies of the contribution of fluctuating Cooper pairs to the persistent current in superconducting rings subjected to a magnetic field. For sufficiently small rings, in which the coherence length $\xi$ exceeds the radius $R$, mean field theory predicts the emergence of a flux-tuned quantum critical point separating metallic and superconducting phases near half-integer flux through the ring. For larger rings with $R\gtrsim \xi$, the transition temperature is periodically reduced, but superconductivity prevails at very low temperatures. We calculate the fluctuation persistent current in different regions of the metallic phase for both types of rings. Particular attention is devoted to the interplay of the angular momentum modes of the fluctuating order parameter field. We discuss the possibility of using a combination of different pair-breaking mechanisms to simplify the observation of the flux-tuned transition in rings with $\xi>R$.Comment: 16 pages, 8 figure

Topological Superconducting Phases of Weakly Coupled Quantum Wires

An array of quantum wires is a natural starting point in realizing two-dimensional topological phases. We study a system of weakly coupled quantum wires with Rashba spin-orbit coupling, proximity coupled to a conventional s-wave superconductor. A variety of topological phases are found in this model. These phases are characterized by "Strong" and "Weak" topological invariants, that capture the appearance of mid-gap Majorana modes (either chiral or non-chiral) on edges along and perpendicular to the wires. In particular, a phase with a single chiral Majorana edge mode (analogous to a $p+ip$ superconductor) can be realized. At special values of the magnetic field and chemical potential, this edge mode is almost completely localized at the outmost wires. In addition, a phase with two co-propagating chiral edge modes is observed. We also consider ways to distinguish experimentally between the different phases in tunneling experiments

Adiabatic Pumping in Interacting Systems

A dc current can be pumped through an interacting system by periodically varying two independent parameters such as magnetic field and a gate potential. We present a formula for the adiabatic pumping current in general interacting systems, in terms of instantaneous properties of the system, and find the limits for its applicability. This formula generalizes the scattering approach for noninteracting pumps. We study the pumped spin in a system that exhibits the two-channel Kondo effect as an application of the adiabatic pumping formula. We find that a quantized spin of $\hbar$ is transferred between the two channels as the temperature approaches zero, and discuss the non-Fermi liquid features of this system at finite temperatures.Comment: 4 pages and 1 figur