Quantum Phase Slips in Superconducting Wires with Weak Inhomogeneities

Quantum phase slips are traditionally considered in diffusive superconducting wires which are assumed homogeneous. We present a definite estimate for the amplitude of phase slips that occur at a weak inhomogeneity in the wire where local resistivity is slightly increased. We model such a weak link as a general coherent conductor and show that the amplitude is dominated by the topological part of the action. We argue that such weak links occur naturally in apparently homogeneous wires and adjust the estimate to that case. The fabrication of an artificial weak link would localize phase slips and facilitate a better control of the phase-slip amplitude.

Figure 1

(a) Superconducting diffusive wire with a weak link (dashed rectangle) connecting bulk superconducting electrodes. (b) Embedding the wire into a superconducting loop makes a phase-slip flux qubit [11]. (c) We model the weak link as a general coherent conductor characterized by a set of transmission eigenvalues $\{T_p\}$.

Figure 2

The phase-slip regimes (see text) in parameter space $(G_c{Z}_w,{\tau }_w\Delta )$, where $Z_w$ is the wave impedance of the wire and ${\tau }_w$ is the characteristic time of charge propagation through the wire. We concentrate on the regions $I$ and $II$, where $E_S$ does not depend on the wire parameters.

Figure 3

Phase-slip amplitude $E_S$ for tunnel contact, double-barrier junction, and short diffusive bridge estimated using topological action ${\mathcal{S}}_{c1}$ (solid curves). The true $E_S$ with a nontopological contribution taken into account is shown in the tunnel limit (dash-dotted curve).

Figure 4

Estimation of phase-slip amplitude for a long diffusive superconducting wire. Squares (□), circles (○), and triangles (△) give the estimated values of $R^{\prime }\xi$ for superconducting nanowire samples as reported in 8, 6, 10, respectively.