Disordered Berezinskii-Kosterlitz-Thouless transition and superinsulation

Abstract

Strongly disordered superconducting films have been observed to undergo finite temperature transitions to a superinsulating state, of apparently infinite resistance, mirroring superconductivity. Approaching the transition, some of the films reportedly exhibit Berezinskii-Kosterlitz-Thouless (BKT) criticality implying that superinsulation is associated with an ordered charge BKT phase. An even more singular Vogel-Fulcher-Tammann (VFT) criticality has also been seen, positing the question of the existence of fundamentally different states of finite temperature insulators. Here we develop a theory of the criticality of a disordered lateral Josephson junction array with weak Josephson coupling. We show that it is equivalent to a two-dimensional Coulomb gas subject to a random potential with logarithmic correlations. We show that strong disorder results in a regime exhibiting VFT criticality instead of the usual BKT one, and find that it corresponds to transition to a nonergodic insulator phase.More than 40 years ago, celebrated works by Berezinskii, Kosterlitz, and Thouless (BKT) introduced the idea of topological phase transitions where pairs of bound topological vortex-like excitations unbind at the critical temperature [1][2][3][4]. Once it was recognized that BKT theory applies to two-dimensional (2D) superconductors and planar Josephson junction arrays (JJA), the realization came that in 2D systems true superconductivity is a manifestly low-temperature BKT phase, where vortices are bound in vortex dipoles, see A. M. Goldman in [5] and also [6]. Above the BKT transition temperature T BKT , the proliferation of low-energy vortices breaks down the global phase coherence, and the 2D superconducting system enters a resistive state. Studying the JJA, Fazio and Schön demonstrated that depending on the ratio of the Josephson coupling, E J to the Coulomb energy of a single junction, E C , the JJA would host either superconductivity, if E J /E C ≫ 1, or an insulator in the opposite limit, where physics is dominated by the charge degrees of freedom [7]. They showed that if the junction capacitance C ≫ C 0 , where C 0 is the capacitance to the ground, the electrostatic screening is suppressed and charges interact logarithmically over large distances. Then the vortex-charge duality transformation v i ↔ q i , πE J ↔ 2E C /π retains the form of the action describing the JJA, with q i being the charge of the junction i and v i being the vorticity of the corresponding plaquette in JJA. The zero-temperature superconductor-to-insulator transition (SIT) occurs at the self-dual point E J /E C = 2/π 2 and the charge binding-unbinding BKT transition at the insulating side takes place at T BKT = E C /2 (throughout the text we use the energy units for temperature taking Boltzmann constant k B = 1).The next important step came with Diamantini and co-workers [8] who constructed a gauge theory of JJA at zero temperature having revealed striking consequences of the charge -vortex symmetry. They established that due to logarithmic confineme...

Charge Berezinskii-Kosterlitz-Thouless transition in superconducting NbTiN films

“…One can thus ask if the observed critical behavior of the NbTiN films should instead be considered in the context of MBL. A detailed comparison of BKT and MBL physics is given in 63 , but we briefly note that our data and analysis unambiguously evidences the primary role of the long range two dimensional logarithmic Coulomb interactions between charges which are a platform for BKT physics. By contrast, the original MBL model 64 , 65 was constructed for one dimensional systems in the strict absence of the long range interactions.…”

“…The temperature dependence of the conductance in InO was found to follow the so-called Vogel-Fulcher-Tamman dependence, σ ∝ exp[−const/(T * −T )] [36][37][38]. This, however, can be viewed as a manifestation of the same BKT physics but in a more disordered system [39].…”

Keldysh field theory of a driven dissipative Mott insulator: Nonequilibrium response and phase transitions

“…direction, especially after taking into account long-range Coulomb interactions, would shed more light to understand the sudden jumbs observed in the I-V characteristics of disordered superconductors that are in the insulating side and in the proximity of superconductor to insulator transition [56][57][58][59].…”

Large current-induced broadening of the superconducting transition in Mo/Au transition edge sensors

“…Contrary to the prediction, there is no abrupt jump in n but, instead, it continuously decreases from values much larger than 3 at low temperatures, down to values near to 1 for higher temperatures closer to T'o. However, as already discussed, this abrupt jump is strictly expected to take place in the small current limit and can be smeared out in the presence of finite currents, inhomogeneities or disorder [14,15,[25][26][27][28], which may be our case. Therefore, although these data do not unambiguously proof the existence of a BKT transition, they are compatible with this scenario in the case of a smearing or broadening of the transition.…”

“…Nevertheless, some authors have argued [15,25] that at finite currents the BKT transition is expected to smear out, and most of its features could vanish so that its manifestation may be quite inaccessible from the experimental point of view or even unobservable. This can be even more so in the presence of flux pinning centers [14] or strong disorder, which is analysed in several recent theoretical works [26][27][28].…”