Superinsulator–superconductor duality in two dimensions

Abstract

For nearly a half century the dominant orthodoxy has been that the only effect of the Cooper pairing is the state with zero resistivity at finite temperatures, superconductivity. In this work we demonstrate that by the symmetry of the Heisenberg uncertainty principle relating the amplitude and phase of the superconducting order parameter, Cooper pairing can generate the dual state with zero conductivity in the finite temperature range, superinsulation. We show that this duality realizes in the planar Josephson junction arrays (JJA) via the duality between the Berezinskii-Kosterlitz-Thouless (BKT) transition in the vortex-antivortex plasma, resulting in phase-coherent superconductivity below the transition temperature, and the charge-BKT transition occurring in the insulating state of JJA and marking formation of the low-temperature charge-BKT state, superinsulation. We find that in disordered superconducting films that are on the brink of superconductor-insulator transition the Coulomb forces between the charges acquire two-dimensional character, i.e. the corresponding interaction energy depends logarithmically upon charge separation, bringing the same vortex-charge-BKT transition duality, and realization of superinsulation in disordered films as the low-temperature charge-BKT state. Finally, we discuss possible applications and utilizations of superconductivity-superinsulation duality.

Duality symmetry and its breakdown in the vicinity of the superconductor–insulator transition

“…This is in contrast to the theoretical framework of refs 11,12,17 in which the high-B insulating state, termed a superinsulator 11,12 , is taken to be a dual state of the superconducting phase. We note that in these models, and in Josephson junction arrays (ref.…”

“…This stronger insulating behaviour for B/B c > 2 violates duality symmetry already in the activated transport regime (compare R versus T in Fig. 3) and therefore cannot be explained by a low-T transition to a superinsulating state 11,12 . Near a quantum phase transition, criticality results in scaling laws 1,4 .…”

“…In the superconductor, Cooper pairs are condensed into a superfluid at low temperature (T ) values leading to a zero resistivity (ρ) state, with vortices as bosonic excitations introducing dissipation and causing finite ρ. According to the duality concept, in the insulating state, vortices are condensed in a collective mode with zero conductivity (σ ), and the Cooper pairs are the bosonic excitation contributing to a finite σ .The vortex-charge duality has also been applied to the analysis of Josephson junction arrays 15,16 , which are often used as a model system for the SIT in disordered films 11,12,17 . In these systems the insulating state is commonly ascribed to a Coulomb blockade of superconducting islands.…”

“…The vortex-charge duality has also been applied to the analysis of Josephson junction arrays 15,16 , which are often used as a model system for the SIT in disordered films 11,12,17 . In these systems the insulating state is commonly ascribed to a Coulomb blockade of superconducting islands.…”

Large magnetoresistance of insulating silicon films with superconducting nanoprecipitates

“…thin amorphous or granular metallic films on insulators, [23][24][25][26] fractal Pb films on silicon, 27 Pb-Si hetorojunctions, 28 amorphous metal-metalloid films, [29][30][31][32][33] cuprate superconductors [34][35][36][37][38] and heavily doped semiconductors. [39][40][41][42][43] There has been an academic debate about the nature of this phase transition and the origin of the large negative MR. 12,[44][45][46] Some theories consider a global quantum phase transition 21,33,47,48 or quantum corrections to the classical magnetotransport. 12,24,49,50 Here we report on large negative and positive MR in Ga-rich, p-type Si films and demonstrate that a simple phenomenological model based on local superconductivity and hopping transport can describe the complex temperature and field dependence of the resistance.…”