Field-induced superconductor-to-insulator transition in Josephson-junction ladders

Abstract

The superconductor-to-insulator transition is studied in a self-charging model for a ladder of Josephson junctions in the presence of an external magnetic field. Path integral Monte Carlo simulations of the equivalent ͑1+1͒-dimensional classical model are used to study the phase diagram and critical behavior. In addition to a superconducting ͑vortex-free͒ phase, a vortex phase can also occur for an increasing magnetic field and small charging energy. It is found that an intervening insulating phase separates the superconducting from the vortex phases. Surprisingly, a finite-size scaling analysis shows that the field-induced superconducting-to-insulator transition is in the KT universality class, even though the external field breaks time-reversal symmetry. DOI: 10.1103/PhysRevB.72.104521 PACS number͑s͒: 74.40.ϩk, 74.81.Fa, 73.43.Nq, 74.25.Qt Superconductor-to-insulator transitions in Josephson junction arrays have attracted considerable interest. 1-5 Such arrays can currently be fabricated in any desired geometry both in one and two dimensions 4,5 with well-controlled parameters. When charging effects due to the small capacitance of the grains or junctions dominate, strong quantum fluctuations of the phase of the superconducting order parameter may drive the system into an insulating phase at zero temperature, leading to a superconductor-to-insulator transition as a function of charging energy or an external magnetic field. In two dimensions, the universality class of these transitions have already been investigated in detail numerically, 6 both in relation to experiments 3,4 and theoretical predictions. 7-9 Nevertheless, there are also remarkable quantum phase transition scenarios 10 that can take place in a Josephson-junction ladder in a magnetic field as in Fig. 1 which have not been investigated experimentally or numerically. Interestingly, a Josephson-junction ladder provides the simplest onedimensional version of the array allowing the study of commensurability effects due to the flux lattice 10-13 or charge frustration, 14 in the presence of quantum fluctuations.An important aspect of the Josephson-junction ladder in Fig. 1 is the approximate relation to the quantum sineGordon model, 15 as first shown by Kardar. 10 For an increasing magnetic field, there is a transition from a ͑vortex-free͒ superconducting phase to a vortex phase, where flux penetrates the ladder, in the absence of quantum fluctuations. This transition is the analog of the commensurateincommensurate transition 16 described by the sine-Gordon model. For small fields, the phases in different branches of the ladder are locked to each other while in the vortex state exponentially interacting kinks ͑vortices͒ appear that unlock the phases leading to a one-dimensional vortex lattice. The inclusion of quantum fluctuations due to charging effects leads to the interesting prediction that an insulating phase should occur in the vicinity of this transition and therefore a direct transition from the ͑vortex-free͒ superconducting phase to the vort...

Two peaks in the momentum distribution of bosons in a weakly frustrated two-leg optical ladder

“…2 at f = 3/10. Therefore we can estimate f c 0.3, nearly consistent with the value obtained in the Josephson-junction ladder at commensurate filling [23]. However, it is inappropriate to make a direct comparison of our results to the case at commensurate filling where the coupling to the periodic lattice potential leads to a Kosterlitz-Thouless (KT)-like transition.…”

“…They will, then, serve as useful markers in identifying the vortex state by measuring n α (k). Between the Meissner and the vortex states, a transition occurs at f = f c [22,23]. In a finite-size system, however, the transition is smeared and, near f c , the central peak and the 055602-2 peaks at finite momenta coexist as shown in Fig.…”

“…How the ground-state properties will be changed due to the phase frustration is a fundamental question on the behavior of frustrated conducting bosons [22,23]. Innovative approaches to create phase frustration [1][2][3][4][5] for neutral atoms in an optical lattice are proposed and some of them are implemented by using a spatially dependent optical coupling, freed from the limitations of rotating systems.…”

Laughlin-like States in Bosonic and Fermionic Atomic Synthetic Ladders

“…The singular behavior of the current, as in Eqs. (14) and (15), thus emerges when the Fermi energy touches the top (or bottom) of a parabolic band, and is related to the socalled van Hove singularities and signals the occurrence of a Lifshitz transition with dynamical exponent z ¼ 2.…”

Nonequilibrium relaxation analysis of a quasi-one-dimensional frustratedXYmodel for charge-density waves in ring-shaped crystals

“…The vortex lattice order in the quasi two dimensional system is considered to be of quasi long range [12]. It is also reported that the two layer system (this is purely two dimensional) has two types of KT phases [14,15], the vortex phase and the Meissner phase. It is, however, not clear whether the inter layer coupling in three dimensional system could be irrelevant or not for small but finite γ.…”