We study the superconductor-insulator quantum phase transition in disordered Josephson junction chains. To this end, we derive the field theory from the lattice model that describes a chain of superconducting islands with a capacitive coupling to the ground (C0) as well as between the islands (C1). We analyze the theory in the short-range (C1 C0) and in the long-range (C1 C0) limits. The transition to the insulating state is driven by the proliferation of quantum phase slips. The most important source of disorder originates from trapped charges in the substrate that suppress the coherence of phase slips, thus favoring superconducting correlations. Using the renormalizationgroup approach, we determine the phase diagram and evaluate the temperature dependence of the dc conductivity and system-size dependence of the resistance around the superconductor-insulator transition. These dependences have in general strongly non-monotonic character, with several distinct regimes reflecting an intricate interplay of superconductivity and disorder.
We study the damping of plasma waves in linear Josephson junction chains as well as in two capacitively coupled chains. In the parameter regime where the ground capacitance can be neglected, the theory of the antisymmetric mode in the double chain can be mapped onto the theory of a single chain. We consider two sources of relaxation: the scattering from quantum phase slips (QPS) and the interaction among plasmons related to the nonlinearity of the Josephson potential. The contribution to the relaxation rate 1/τ from the nonlinearity scales with the fourth power of frequency ω, while the phase-slip contribution behaves as a power law with a non-universal exponent. In the parameter regime where the charging energy related to the junction capacitance is much smaller than the Josephson energy, the amplitude of QPS is strongly suppressed. This makes the relaxation mechanism related to QPS efficient only at very low frequencies. As a result, for chains that are in the infrared limit on the insulating side of the superconductor-insulator transition, the quality factor ωτ shows a strongly non-monotonic dependence on frequency, as was observed in a recent experiment.
We study the localization and decay properties as well as the thermal conductance of onedimensional plasmons. Our model contains a Luttinger-liquid part with spatially random plasmon velocity and interaction parameter as well as a nonlinearity that is cubic in density. The scaling of the decay rate of plasmons is obtained in several regimes. At sufficiently high frequencies, it describes the inelastic life time of localized plasmon excitations that crosses over to the clean result with lowering frequencies. For higher frequencies, we analyze implications of many-body-localization effects that lead to a suppression of the decay rate. We find that the thermal conductance depends in a non-trivial fashion on the system size L. Specifically, it scales as L −1/2 for sufficiently short wires and crosses over to L −2/3 scaling for longer wires.
The energy dependence of the relaxation rate of hot electrons due to interaction with the Fermi sea is studied. We consider 2D and 3D systems, quasi-1D quantum wires with multiple transverse bands, as well as single-channel 1D wires. Our analysis includes both spinful and spin-polarized setups, with short-range and Coulomb interactions. We show that, quite generally, the relaxation rate is a non-monotonic function of the electron energy and decays as a power-law at high energies.In other words, ultra-hot electrons regain their coherence with increasing energy. Such a behavior was observed in a recent experiment on multi-band quantum wires, J. Reiner et al, Phys. Rev. X 7, 021016 (2017). arXiv:1802.10429v2 [cond-mat.mes-hall]
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