The Superconductor-Superinsulator Transition: S-duality and the QCD on the Desktop

Abstract

We show that the nature of quantum phases around the superconductor-insulator transition (SIT) is controlled by charge-vortex topological interactions, and does not depend on the details of material parameters and disorder. We find three distinct phases, superconductor, superinsulator and bosonic topological insulator. The superinsulator is a state of matter with infinite resistance in a finite temperatures range, which is the S-dual of the superconductor and in which charge transport is prevented by electric strings binding charges of opposite sign. The electric strings ensuring linear confinement of charges are generated by instantons and are dual to superconducting Abrikosov vortices. Material parameters and disorder enter the London penetration depth of the superconductor, the string tension of the superinsulator and the quantum fluctuation parameter driving the transition between them. They are entirely encoded in four phenomenological parameters of a topological gauge theory of the SIT. Finally, we point out that, in the context of strong coupling gauge theories, the many-body localization phenomenon that is often referred to as an underlying mechanism for superinsulation is a mere transcription of the well-known phenomenon of confinement into solid state physics language and is entirely driven by endogenous disorder embodied by instantons with no need of exogenous disorder.The superconductor-insulator transition (SIT) [1-7] is a paradigmatic quantum phase transition found in Josephson junction arrays (JJA) [1,6] and in 2D disordered superconducting films at low temperatures T [2-5]. The tuning parameter driving the SIT is the ratio of the single junction Coulomb energy to the Josephson coupling. In 2D films this ratio is effectively controlled by varying the film thickness d which regulates the strength of disorder and hence of Coulomb screening or by applying a magnetic field that suppresses the Josephson coupling. This can cause a dramatic change in the ground state so that superconductivity is lost in favour of insulating behaviour.In 1978, G. 't Hooft [8] appealed to a solid state physics analogy in a Gedankenexperiment to explain quark confinement and demonstrated that this is realized in a phase which is in many respects similar to the superconducting phase, but is in a sense a zero particle mobility phase, the extreme opposite of a superconductor and called hence this phase a "superinsulator." In 1996, two of the present authors (mcd and cat) [9] developed a comprehensive field theory framework for the description of the SIT in JJA. They predicted that, on the insulating side of the SIT, a new ground state forms, corresponding to a novel phase with infinite resistance. This novel phase is dual to the superconductor, characterized by zero resistance, and they thus independently also called this phase a superinsulator. Independently, superinsulators where also soon proposed in [10]. Finally, the name and phenomenon of superinsulation was rediscovered and experimentally detected by one of the authors (...

Type‐III Superconductivity

“…[1], would become larger than the experimental system size for small d. Second, near the quantum transition, the electric fields induced by charges residing in the system remain in-plane over the whole sample because of the large dielectric constant. [9][10][11] Usually, such electric fields are not very relevant in standard superconductors. In our planar superconductors, however, these 2D electric fields are much stronger than the usual 3D ones, since they decay as 1/r with the increasing distance r from the charge and cannot be neglected.…”

“…[19,20] In this type of percolating superconductivity, electron pairs survive above T c , which is the case both in 2D [21] and 3D, [22] and there is a quantum transition to an insulating state, both in 2D, see refs. [9][10][11], and 3D. [23] In 2D, the fragmentation into separate condensate droplets is due to strong infrared divergences near the quantum insulating transition.…”

“…The granularity of these systems is associated with a superconductor‐to‐superinsulator quantum phase transition [ 4 , 5 , 6 ] which may occur via an intermediate Bose metal [ 4 , 7 , 8 ] phase, see refs. [ 9 , 10 , 11 ], and has been detected experimentally. [ 12 , 13 ]…”

On the Formation of Solid States Beyond Perfect Crystals: Quasicrystals, Geometrically-Frustrated Crystals and Glasses

“…In particular, in the two-dimensional N = 2 case, the O(2) quantum rotor model predicts the existence of a quantum phase transition between the superfluid and a Mott-insulator ordered state 22 that has been realized experimentally. In charged superfluids, this is the superconductor-to-superinsulator transition [33][34][35][36] .…”

Theoretical proposal for dual transformation between the Josephson effect and quantum phase slip in single junction systems and nanowires

“…A Hamiltonian with two cosine terms, competing with each other, similar to Eq. ( 25) to (28) is a new form which has not been known until now. Such a system is a system in which both JJ and QPSJ which are in a coherent state compete with each other, and the circuit in which JJ and QPSJ are connected in series is called a JJ-QPSJ competitive circuit.…”