Superconductor-insulator transition in disordered Josephson-junction chains

Abstract

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.

Decay of plasmonic waves in Josephson junction chains

“…1a, the field theory was constructed previously in Ref. 17. We briefly recall this derivation below and extend the theory by including the terms accounting for gradient nonlinearities.…”

“…Besides the Josephson energy E J that quantifies the hopping strength of Cooper pairs, there are the two charging energy scales E 0 = (2e) 2 /C 0 and E 1 = (2e) 2 /C 1 , where e denotes the elementary charge. The charging energy E 1 quantifies the strength of the Coulomb interaction at short scales, while the energy E 0 controls the Coulomb-interaction strength in the infrared and, in particular, determines the position of the SIT 12,17 . The lattice Hamiltonian for this system has the form…”

“…More recently, the impact of various types of disorder on the SIT was studied in Ref. 17. Remarkably, the most common type of disorder, random off-set charges, works to enhance superconducting correlations.…”

Weak- versus strong-disorder superfluid—Bose glass transition in one dimension

“…In the presence of disorder, such a SF ground state is generally expected to be unstable towards localization, thus forming the so-called Bose glass (BG) phase [7][8][9]: an inhomogeneous gapless compressible fluid with exponentially suppressed correlations. Disordered interacting chains can be experimentally realized using spin ladders [10,11], ultra-cold atoms [12][13][14] and arrays of disordered Josephson junctions [15][16][17]. Broadly speaking, Luttinger liquid physics is expected to occur in various contexts [18], e.g.…”

Superconductor-insulator transition in Josephson junction chains by quantum Monte Carlo calculations

“…Surprisingly, a quantitative theoretical prediction for the phase diagram is still lacking. Mappings between the quantum JJ chain, the classical two-dimensional (2D) XY model, the 2D Coulomb gas, and the sine-Gordon model [15,16,[26][27][28][29][30][31][32][33] yielding an effective description of the system at long distances and low energies, established that the transition belongs to the Kosterlitz-Thouless universality class [34,35]. However, to precisely relate the parameters * Present address: Physics Department, Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, 80333 München, Germany † Deceased 15 May 2017…”