In one-dimensional wires, fluctuations destroy superconducting long-range order and stiffness at finite temperatures; in an infinite wire, quasi-long-range order and stiffness survive at zero temperature if the wire's dimensionless admittance mu is large, mu>2. We analyze the disappearance of this superconductor-insulator quantum phase transition in a finite wire and its resurrection due to the wire's coupling to its environment characterized through the dimensionless conductance K.
In one-dimensional wires, fluctuations destroy superconducting long-range order and stiffness at finite temperatures; in an infinite wire, quasi-long-range order and stiffness survive at zero temperature if the wire's dimensionless admittance mu is large, mu>2. We analyze the disappearance of this superconductor-insulator quantum phase transition in a finite wire and its resurrection due to the wire's coupling to its environment characterized through the dimensionless conductance K.
Zero-temperature or quantum phase transitions in itinerant electronic systems both with and without quenched disordered are discussed. Phase transitions considered include, the ferromagnetic transition, the antiferromagnetic transition, the superconductor-metal transition, and various metal-insulator transitions. Emphasis is placed on how to determine the universal properties that characterize these quantum phase transitions. For the first three of the phase transitions listed above, one of the main physical ideas established is that in zero-temperature systems there are soft or slow modes that exist in addition to the soft order parameter fluctuations, and that these modes can couple to the critical modes. These extra soft modes are shown to have a profound effect on the quantum critical properties. For quantum phase transitions involving zero wavenumber order parameters, i.e., the ferromagnetic and superconductor-metal transitions, these extra modes effectively lead to long-ranged effective interactions between order parameter fluctuations, which in turn lead to exactly soluble critical behaviors. For the antiferromagnetic case, we argue that while in low enough dimensions disorder fluctuation effects tend to destroy long-range order, quantum fluctuations counteract this effect and in some parameter regions manage to re-establish antiferromagnetic long-range order. For the metal-insulator transition, some recent new ideas are reviewed. In particular, it is pointed out that for interacting disordered electrons, one expects that in high dimensions the metal-insulator transition is related to the phase transition that occurs in random-field magnets in high dimensions. If the analogy also holds in three dimensions this suggests that the metal-insulator transition might have glassy characteristics.
Abstract In many two-dimensional superconducting systems1, 2, 3, 4, such as Josephson-junction arrays, granular superconducting films, and the high-temperature superconductors, it appears that the electrons bind into Cooper pairs below a pairing temperature (TP) that is well above the Kosterlitz–Thouless temperature (TKT, the temperature below which there is long-range superconducting order5, 6, 7, 8, 9, 10). The electron dynamics at temperatures between TKT and TP involve a complex interplay of thermal and quantum fluctuations, for which no quantitative theory exists. Here we report numerical results for this region, by exploiting its proximity to a T = 0 superconductor–insulator quantum phase transition11, 12. This quantum critical point need not be experimentally accessible for our results to apply. We characterize the static, thermodynamic properties by a single dimensionless parameter, γ(T). Quantitative and universal results are obtained for the frequency dependence of the conductivity, which are dependent only upon γ(T) and fundamental constants of nature.
Superconducting order in a sufficiently narrow and infinitely long wire is destroyed at zero temperature by quantum fluctuations, which induce $2\ensuremath{\pi}$ slips of the phase of the order parameter. However, in a finite-length wire, coherent quantum phase slips would manifest themselves simply as shifts of energy levels in the excitation spectrum of an electrical circuit incorporating this wire. The higher the phase slips' probability amplitude, the larger are the shifts. Phase slips occurring at different locations along the wire interfere with each other. Due to the Aharonov-Casher effect, the resulting full amplitude of a phase slip depends on the offset charges surrounding the wire. Slow temporal fluctuations of the offset charges make the phase-slip amplitudes random functions of time, and therefore turn energy level shifts into linewidths. We experimentally observed this effect on a long Josephson junction array acting as a ``slippery'' wire. The slip-induced linewidths, despite being only of order 100kHz, were resolved from the flux-dependent dephasing of the fluxonium qubit.
We investigate the superconductor-insulator phase transition in the two-dimensional boson Hubbard system with short-range interactions. Fluctuations of both the phase and the amplitude of the superfluid order parameter are included in the determination of the phase diagram at zero and finite temperatures. The mean-field phase boundary is compared to quantum Monte Carlo results. We also calculate the frequency-dependent conductivity in the vicinity of the phase transition and find it universal at the multicritical point.
Strongly disordered superconductors undergo a transition to insulation upon increasingdisorder, driven by the localization of preformed Cooper pairs. A key and implicit question in this transition is the fate of the superfluid density as the critical disorder approaches.By measuring the kinetic inductance of superconducting resonators ofamorphous indium oxide, we show that the transition to superconductivity is bosonicwith a critical temperature ruled by superconducting phase fluctuations. Upon reachingthe critical disorder terminating superconductivity, the superfluid stiffness remainssurprisingly finite at the transition to insulation. This indicates an unexpected first-ordernature of the disorder-driven quantum phase transition to insulator, opening anew paradigm for superfluid disordered systems of quantum particles.An important by-product of the interplay between localization and superconductivity is the obtention of large kinetic inductance materials, allowing the design of the sought-after superinductances which play a major role in recent quantum circuit developments.
I study the effect of Coulomb interaction on superconducting order in a d-wave lattice superconductor at T=0 by considering the superconducting saddle point in the two-dimensional $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U$ model with a repulsion U. The theory of low-energy superconducting phase fluctuations around this saddle point is derived in terms of the effective hard-core bosons (representing the density of spin-up electrons and the phase of the order parameter), interacting with the fluctuating density of spin-down electrons. Whereas the saddle-point value of the superconducting gap is found to continuously increase towards half filling, the phase stiffness at T=0 has a maximum, and then decreases with further underdoping. Right at half filling the phase stiffness vanishes for large U. This argues that the pseudogap phenomenon of the type observed in cuprates is in principle possible without a development of any competing order, purely as a result of growing correlations in the superconducting state. Implications for the finite temperature superconducting transition and the effects of static disorder are discussed qualitatively.