Theory of quantum phase slips in disordered one-dimensional superconductors

In this thesis quantum phase slips in one-dimensional superconductors are studied. One-dimensional superconductors can be represented by two physical systems: a superconducting wire and a Josephson junction chain. A superconducting wire can be considered one-dimensional, if its transverse dimensions are smaller than the superconducting coherence length. In one-dimensional systems fluctuations strongly influence the system properties. The quantum phase slips correspond to quantum tunneling between different phase configurations along the superconductor. They can be of two types. Coherent quantum phase slips do not involve dissipation and only shift energy levels of the system. Incoherent quantum phase slips lead to a dissipative relaxation in the system.We start with studying an incoherent phase-slip process in a single underdamped current-biased Josephson junction. This process corresponds to dissipative tunneling between weakly broadened levels in neighboring minima of the tilted washboard potential. We derive an expression for the voltage peaks near the resonant values of the external current, which correspond to matching energies of the lowest level in one minimum and an excited level in the lower neighboring minimum. This process is analogous to resonant Zener breakdown known for electrons in a superlattice subject to a strong electric field.We continue with studying coherent quantum phase slips in a Josephson junction chain. First, we determine the amplitude of a coherent quantum phase slip in a homogeneous chain. It has already been shown that the amplitude is determined by the imaginary-time instanton action, which can be divided into the local (corresponding to phase winding by 2π on one junction) and environmental (corresponding to phase readjustment in the rest of the chain, which is determined by gapless Mooij-Schon modes) parts. We derive a numerical correction to the environmental part of the action, going beyond logarithmic precision. Second, we study the effect of spatial periodic modulations of the chain parameters on the coherent quantum phase slip process. We calculate the corrections both to the local and environmental part of the coherent quantum phase slip action and show that both of them can be significant, depending on the chain and modulations parameters. Then, we study the effect of two types of quenched disorder: random spatial modulation of the junction areas and random induced background charges. The main result is that the dominant contribution to the coherent quantum phase slip action is local. We also study the statistics of the mesoscopic fluctuations of the quantum phase slips amplitude and show that it can be non-Gaussian for chains which are not sufficiently long.Finally, we consider one-dimensional superconducting wires. There is no microscopic theory available for the fast phase winding in the phase-slip core, where the order parameter is suppressed. However, the slow phase readjustment process, determined by the Mooij-Schon modes with frequencies lower than 2Δ, is analogous to that in Josephson junction chains, so the resulting environmental part of the coherent quantum phase slip action takes the same form. Therefore, we discuss how our results, obtained for Josephson junction chains, can be applied to inhomogeneous superconducting wires.