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

Abstract

The superconductor-insulator transition (SIT) is an accessible quantum phase transition 1,2 that is observed in a number of systems and can be driven by various experimental means 3-9 . A central outstanding issue regards the physical nature of the insulating phase terminating superconductivity 10 . Theoretical advances led to the proposition that this insulator is a new state of matter, termed a superinsulator 11,12 , because its properties can be inferred from the superconductor by invoking duality symmetry 13 . Here we report on the observation of duality symmetry near the magnetic-field-driven SIT in amorphous indium oxide. However, we show that the symmetry is broken by the emergence of the strong insulating state at low temperature.For the magnetic-field-driven SIT (B-SIT) in disordered films, the concept of vortex-charge duality was investigated in ref. 14, using the dirty boson model. 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. Duality is also applied to many other systems, for example, boson duality in two-dimensional electron gases 18 . Recently, evidence for the vortex-charge duality near a SIT was found in LaAlO 3 /SrTiO 3 interfaces 13 .Here, we experimentally investigate the duality symmetry across the B-SIT. We apply a duality transformation relating states within the superconductor to states in the B-driven insulator. We observe vortex-charge duality symmetry that holds up to one order of magnitude in B, T and ρ. The new aspect of this work is that we find systematic deviations from duality symmetry that originate in the B-induced magnetoresistance (ρ(B)) peak 5 . These deviations are qualitatively different at low and high T , as will be shown in detail below.In Fig. 1 we present ρ(B) isotherms obtained from sample RAM005b, which is superconducting at B = 0 with T c = 1.3 K. For all T values where reliable Ohmic data could be collected ρ increases with B until it reaches a T -dependent peak at B peak between 8.5-9.7 T. We restrict ourselves to T > 0.15 K because in the insulating phase, at T < 0.15 K, severe bi-stability of the electron T develops 19 , resulting in strongly nonlinear I -V , that prevented reliable measurements of ρ.The isotherms exhibit a weakly T -dependent crossing point close to h/(2e) 2 , where h is Planck's constant and 2e is the charge

Finite-size effects in amorphous indium oxide

“…For each device, R (B, T, E = 0) data were used to test the scaling prediction, by varying B at small increments at fixed T. In figure 5, the T-scaling of R for the film is shown. A good visual collapse of the data is obtained for zν=1.12, which is close to the previous findings 6,35 . For the wires, R flattens and become T independent on either side of B c [figure2(b)], as low-T is approached.…”

“…In the superconducting side of the Btuned SIT, the power law is consistent with the collective pinning model of transport 22,34,36 and indicate the role played by interacting bosons (vortices) in transport. The existence of the power law behavior above B c , suggest that vortex transport might be important in the insulating state 34,35 . A quantum critical point is known to separate ground states with different symmetry.…”

Zero-bias anomaly in homogeneously disordered MoGe nanowires undergoing a superconductor-insulator transition

“…In superconducting films close to the critical point, the low-bias resistance isotherms follow the finite size scaling model 4,5,16,17 , which gives strong indication that the SIT in films is also a quantum phase transition (QPT). In addition, it has been shown that in amorphous MoGe 5 and NbN 17 films, nonlinear differential resistance measured as a function of magnetic field at several finite bias voltages also scales both on the insulating and superconducting sides of the SIT.…”

Self-duality and a Hall-insulator phase near the superconductor-to-insulator transition in indium-oxide films

“…Previous studies have examined evidence for duality (18,19) from resistivity measurements, but have not examined the full conductivity tensor across the transition. In this paper we provide insights concerning the nature of the H-SIT in highly disordered films, using new measurements of the full resistivity tensor across the quantum transition.…”