The correct detection of the Berezinskii-Kosterlitz-Thouless (BKT) transition in quasi-two-dimensional superconductors still remains a controversial issue. Its main signatures, indeed, are often at odds with the theoretical expectations. In a recent work\cite{me} we have shown that the presence of spatially correlated disorder plays a key role in this sense being it the reason underlying the experimentally-observed smearing of the universal superfluid-density jump. In the present paper, we closely investigate the effects of correlated disorder on the BKT transition, addressing specifically the issue whether it changes or not the BKT universality class.
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 theor…
Occurrence of the Berezinskii-Kosterlitz-Thouless (BKT) transition is investigated by superfluid density measurements for two-dimensional (2D) disordered NbN films with disorder level very close to a superconductor-insulator transition (SIT). Our data show a robust BKT transition even near this 2D disorder-tuned quantum critical point (QCP). This observation is in direct contrast with previous data on deeply underdoped quasi-2D cuprates near the SIT. As our NbN films approach the QCP, the vortex-core energy, an important energy scale in the BKT transition, scales with the superconducting gap, …
We analyze the occurrence of the Beresinkii-Kosterlitz-Thouless transition in thin films of NbN at various film thickness, by probing the effect of vortex fluctuations on the temperature dependence of the superfluid density below $T_{BKT}$ and of the resistivity above $T_{BKT}$. By direct comparison between the experimental data and the theory we show the crucial role played by the vortex-core energy in determining the characteristic signatures of the BKT physics, and we estimate its dependence on the disorder level. Our work provides a paradigmatic example of BKT physics in a quasi-two-dimens…
We numerically investigate dynamic critical behaviors of two-dimensional (2D) Josephson-junction arrays with positional disorder in the scheme of the resistively shunted junction dynamics. Large-scale computation of the current voltage characteristics reveals an evidence supporting that a phase transition occurs at a nonzero critical temperature in the strong disorder regime, as well as in the weak disorder regime. The phase transition at weak disorder appears to belong to the Berezinskii-Kosterlitz-Thouless (BKT) type. In contrast, evidence for a non-BKT transition is found in the strong diso…
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 (B…
We explore the implications of Berezinskii-Kosterlitz-Thouless (BKT) critical behavior on the two dimensional (2D) quantum superconductor-insulator (QSI) transition driven by the tuning parameter x. Concentrating on the sheet resistance R(x) BKT behavior implies: an explicit quantum scaling function for R(x) along the superconducting branch ending at the nonuniversal critical value R_c=R(x_c); a BKT-transition line T_c(x) that is proportional to (x-x_c)^(z*nu) where z is the dynamic and nu the exponent of the zero temperature correlation length; independent estimates of z*nu, z and nu from the…
Superconductivity at the interface between the insulators LaAlO3 and SrTiO3 has been tuned with the electric field effect. The data provide evidence for a two dimensional quantum superconductor to insulator (2D-QSI) transition. Here we explore the compatibility of this phase transition line with Berezinskii-Kosterlitz-Thouless (BKT) behavior and a 2D-QSI transition. In an intermediate regime, limited by a finite size effect, we uncover remarkable consistency with BKT- criticality, weak localization in the insulating state and non-Drude behavior in the normal state. Our estimates for the critic…
In tensor network representation, the partition function of a generalized two-dimensional XY spin model with topological integer and half-integer vortex excitations is mapped to a tensor product of one-dimensional quantum transfer operator, whose eigen-equation can be solved by an algorithm of variational uniform matrix product states. Using the singularities of the entanglement entropy, we accurately determine the complete phase diagram of this model. Both the integer vortex-antivortex binding and half-integer vortex-antivortex binding phases are separated from the disordered phase by the usu…
Berezinskii-Kosterlitz-Thouless quantum transition in 2 dimensions
NiPS Laboratory, INFN and Dipartimento di Fisica e Geologia, University of Perugia（佩鲁贾大学物理与地质学系、INFN及NiPS实验室）；SwissScientific Technologies SA（瑞士科学技术有限公司）；Division of Science, New York University Abu Dhabi（阿布扎比纽约大学科学学部）
The Berezinskii-Kosterlitz-Thouless (BKT) transition in two-dimensional superconductors is usually expected to be protected against disorder. However, its typical signatures in real system, like e.g. the superfluid-density jump, are often at odd with this expectation. Here we show that the disorder-induced granularity of the superconducting state modifies the nucleation mechanism for vortex-antivortex pairs. This leads to a considerable smearing of the universal superfluid-density jump as compared to the paradigmatic clean case, in agreement with experimental observations.
We explore the implications of Berezinskii-Kosterlitz-Thouless (BKT) critical behavior and variable-range hopping on the two dimensional (2D) quantum superconductor-insulator (QSI) transition driven by tuning the gate voltage. To illustrate the potential and the implications of this scenario we analyze sheet resistance data of Parendo et al. taken on a gate voltage tuned ultrathin amorphous bismuth film. The finite size scaling analysis of the BKT-transition uncovers a limiting length preventing the correlation length to diverge and to enter the critical regime deeply. Nevertheless the attaine…
The phase transition in a model for vortex lines in high temperature superconductors with columnar defects, i.e., linearly correlated quenched random disorder, is studied with finite size scaling and Monte Carlo simulations. Previous studies of critical properties have mainly focused on the limit of strongly screened vortex line interactions. Here the opposite limit of weak screening is considered. The simulation results provide evidence for a new universality class, with new critical exponents that differ from the case of strong screening of the vortex interaction. In particular, scaling is a…
Recently superconductivity at the interface between the insulators LaAlO3 and SrTiO3 has been tuned with the electric field effect to an unprecedented range of transition temperatures. Here we perform a detailed finite size scaling analysis to explore the compatibility of the phase transition line with Berezinskii-Kosterlitz-Thouless (BKT) behavior and a 2D-quantum phase(QP)-transition. In an intermediate regime, limited by a gate voltage dependent limiting length, we uncover remarkable consistency with a BKT-critical line ending at a metallic quantum critical point, separating a weakly locali…
Superconducting nanofilms are tunable systems that can host a 3D-2D dimensional crossover, leading to the Berezinskii-Kosterlitz-Thouless (BKT) superconducting transition approaching the 2D regime. Reducing further the dimensionality, from 2D to quasi-1D, superconducting nanostructures with disorder can generate quantum and thermal phase slips (PS) of the order parameter. Both BKT and PS are complex phase fluctuation phenomena of difficult experimental detection. Here, we have characterized superconducting NbN nanofilms thinner than 15 nm, on different substrates, by temperature dependent resi…
As a part of my doctoral thesis, I studied the effect of phase fluctuations in two dimensional (2D) and three dimensional (3D) superconducting films of conventional s-wave superconductor, NbN, by measuring the electrodynamics response through magnetic penetration depth at low frequency and the complex conductivity at microwave frequencies. We show that the phase transition in 2D or quasi-2D superconductors can be reconciled with the standard Berezinskii-Kosterlitz-Thouless (BKT) transition when the small vortex core energy is taken into consideration. In 3D NbN films, we show that in presence …
The three-dimensional strongly screened vortex-glass model is studied numerically using methods from combinatorial optimization. We focus on the effect of disorder strength on the ground state and found the existence of a disorder-driven normal-to-superconducting phase transition. The transition turns out to be a geometrical phase transition with percolating vortex loops in the ground state configuration. We determine the critical exponents and provide evidence for a new universality class of correlated percolation.
Weakly disordered two-dimensional (2D) superconductors can host richer quantum phase transitions than their highly-disordered counterparts. This is due to the insertion of a metallic state in the transition between a superconductor and an insulator. Disorders were predicted to show profound influences on the boundaries surrounding this intermediate metallic phase, affecting the existence of a metallic ground state called Bose metal and the dynamic processes in a quantum Griffiths state. Here we present a study on quantum phase transitions of a clean 2D superconductor, MoS2, under a perpendicul…
We probe the presence of long-range correlations in phase fluctuations by analyzing the higher-order spectrum of resistance fluctuations in ultra-thin NbN superconducting films. The non-Gaussian component of resistance fluctuations is found to be sensitive to film thickness close to the transition, which allows us to distinguish between mean field and Berezinskii-Kosterlitz-Thouless (BKT) type superconducting transitions. The extent of non-Gaussianity was found to be bounded by the BKT and mean field transition temperatures and depend strongly on the roughness and structural inhomogeneity of t…
The interplay between quenched disorder and critical behavior in quantum phase transitions is conceptually fascinating and of fundamental importance for understanding phase transitions. However, it is still unclear whether or not the quenched disorder influences the universality class of quantum phase transitions. More crucially, the absence of superconducting-metal transitions under in-plane magnetic fields in 2D superconductors imposes constraints on the universality of quantum criticality. Here, we discover the tunable universality class of superconductor-metal transition by changing the di…
We isolated flux disorder effects on the transport at the critical point of the quantum magnetic field tuned Superconductor to Insulator transition (BSIT). The experiments employed films patterned into geometrically disordered hexagonal arrays. Spatial variations in the flux per unit cell, which grow in a perpendicular magnetic field, constitute flux disorder. The growth of flux disorder with magnetic field limited the number of BSITs exhibited by a single film due to flux matching effects. The critical metallic resistance at successive BSITs grew with flux disorder contrary to predictions of …
