Nonequilibrium restoration of duality symmetry in the vicinity of the superconductor-to-insulator transition

Abstract

The magnetic field driven superconductor to insulator transition in thin films is theoretically understood in terms of the notion of vortex-charge duality symmetry. The manifestation of such symmetry is the exchange of roles of current and voltage between the superconductor and the insulator. While experimental evidence obtained from amorphous Indium Oxide films supported such duality symmetry it is shown to be broken, counterintuitively, at low temperatures where the insulating phase exhibits discontinuous current-voltage characteristics. Here, we demonstrate that it is possible to effectively restore duality symmetry by driving the system beyond the discontinuity into its high current, far from equilibrium, state.The superconductor to insulator transition [1, 2] (SIT) is an experimentally accessible quantum phase transition [3]. By varying an externally controlled parameter in the Hamiltonian, a disordered superconducting thin film can be driven between its superconducting and insulating ground states [4][5][6][7][8][9][10][11]. Two decades ago Fisher theoretically studied [12] a specific case in which an applied magnetic field (B) drives the SIT. At low B, the induced Abrikosov vortices are localized by the disorder and a superconducting state prevails. Upon increasing B, Fisher found that the proliferation of vortices can result in a Bose-Einstein condensation of the vortex state that, in turn, leads to insulating behavior where the Cooperpairs are now localized [13][14][15][16][17][18][19][20][21][22]. The exchange of roles between the Cooper-pairs and vortices across the transition is analyzed via a duality transformation applied to the Hamiltonian [23].Experimentally, vortex-charge duality will manifest itself via the exchange of roles of current (I) and voltage (V ) between the superconductor and the insulator [24][25][26]. Duality symmetry implies that, for a given resistance (R ≡ V /I) measured at a given B = B SC in the superconductor, there exists a dual B = B Ins in the insulator where the conductivity (G ≡ I/V ) obeys the condition G(B Ins ) = R(B SC ). In previous publications [27,28] we found that our data follow a phenomenological, powerlaw, form across the SIT:where P (T ) ∼ Counterintuitively, duality symmetry breaks down at low temperatures (T 's) [28]. This is most conveniently illustrated through the deviations from the power-law dependence, graphically shown in Figure 1. Interestingly, these deviations appear only in the insulating side of the SIT. In the superconducting side, the data continue to follow the power-law dependence down to our lowest T 's [30].Together with the appearance of deviations from duality symmetry, our insulator develops strongly non-linear I − V characteristics (I − V 's) [31]. At T 0.2 K, applying a bias V above a well-defined V = V th (which is a function of both B and T ), results in a discontinuous increase, of several orders of magnitude, in I. Upon reducing V , a discontinuous decrease in I is observed recovering previous I values (see, for example, the 0.05 ...

Excessive noise as a test for many-body localization

“…In this scenario, which is dual to the vortex-BKT transition in superconducting thin-films [24][25][26], charge anti-charge unbinding above a critical T (T c-BKT ) constitutes the main contribution of the measured conductivity thus explaining its rapid decay as T approaches T c-BKT . It is interesting to note that in a:InO thin-films, the fasterthan-activated R(T ) insulating behavior severely violates duality-symmetry at low T 's [27,28].…”