We present a study of the Berezinskii-Kosterlitz-Thouless (BKT) transition in mildly disordered NbN nanoporous (NP) films. The measured superfluid stiffness, Js, is found to be much lower than that predicted considering a reduced geometric area. For a 5 nm thick NP film, a distinct BKT transition is observed. By fitting the experimental data via the BKT renormalization-group equations, we show how both Js and the vortex-core energy, μ, decrease in the presence of nanopores. The variation of Js and μ is also reproduced theoretically via Monte Carlo numerical simulations on a 2D diluted XY model. Our results show that nanopore geometries effectively enhance the 2D nature of the superconducting films, increasing the parameter space to explore the BKT physics while offering a pathway to systematically control the two energy scales, Js and μ, that govern the vortex physics in these systems.

Materials that break multiple symmetries allow the formation of four-fermion condensates above the superconducting critical temperature (T c). Such states can be stabilized by phase fluctuations. Recently, a fermionic quadrupling condensate that breaks the Z 2 time-reversal symmetry was reported in Ba1−xKxFe2As2. A phase transition to the new state of matter should be accompanied by a specific heat anomaly at the critical temperature where Z 2 time-reversal symmetry is broken (TcZ2>Tc). Here, we report on detecting two anomalies in the specific heat of Ba1−xKxFe2As2 at zero magnetic field. The anomaly at the higher temperature is accompanied by the appearance of a spontaneous Nernst effect, indicating the breakdown of Z 2 symmetry. The second anomaly at the lower temperature coincides with the transition to a zero-resistance state, indicating the onset of superconductivity. Our data provide the first example of the appearance of a specific heat anomaly above the superconducting phase transition associated with the broken time-reversal symmetry due to the formation of the novel fermion order.

Two-dimensional superconductors with disorder at the nanoscale can host a variety of intriguing phenomena. The superconducting transition is marked by a broad percolative transition with a long tail of the resistivity as function of the temperature. The fragile filamentary superconducting clusters, forming at low temperature, can be strengthened further by proximity effect with the surrounding metallic background, leading to an enhancement of the superfluid stiffness well below the percolative transition. Finite-frequency dissipation effects, e.g., related to the appearance of thermally excited vortices, can also significantly contribute to the resulting physics. Here, we propose a random impedance model to investigate the role of dissipation effects in the formation and strengthening of fragile superconducting clusters, discussing the solution within the effective medium theory.

The most well-known example of an ordered quantum state—superconductivity—is caused by the formation and condensation of pairs of electrons. Fundamentally, what distinguishes a superconducting state from a normal state is a spontaneously broken symmetry corresponding to the long-range coherence of pairs of electrons, leading to zero resistivity and diamagnetism. Here we report a set of experimental observations in hole-doped Ba1−xKxFe2As2. Our specific-heat measurements indicate the formation of fermionic bound states when the temperature is lowered from the normal state. However, when the doping level is x ≈ 0.8, instead of the characteristic onset of diamagnetic screening and zero resistance expected below the superconducting phase transition, we observe the opposite effect: the generation of self-induced magnetic fields in the resistive state, measured by spontaneous Nernst effect and muon spin rotation experiments. This combined evidence indicates the existence of a bosonic metal state in which Cooper pairs of electrons lack coherence, but the system spontaneously breaks time-reversal symmetry. The observations are consistent with the theory of a state with fermionic quadrupling, in which long-range order exists not between Cooper pairs but only between pairs of pairs.

The Berezinskii-Kosterlitz-Thouless (BKT) mechanism describes universal vortex unbinding in many two-dimensional systems, including the paradigmatic XY model. However, most of these systems present a complex interplay between excitations at different length scales that complicates theoretical calculations of nonuniversal thermodynamic quantities. These difficulties may be overcome by suitably modifying the initial conditions of the BKT flow equations to account for noncritical fluctuations at small length scales. In this work, we perform a systematic study of the validity and limits of this two-step approach by constructing optimised initial conditions for the BKT flow. We find that the two-step approach can accurately reproduce the results of Monte Carlo simulations of the traditional XY model. To systematically study the interplay between vortices and spin-wave excitations, we introduce a modified XY model with increased vortex fugacity. We present large-scale Monte Carlo simulations of the spin stiffness and vortex density for this modified XY model and show that even at large vortex fugacity, vortex unbinding is accurately described by the nonperturbative functional renormalization group.

Some two-dimensional superconductors like, e.g., LaAlO3/SrTiO3 heterostructures or thin films of transition metal dichalcogenides, display peculiar properties that can be understood in terms of electron inhomogeneity at the nanoscale. In this framework, unusual features of the metal-superconductor transition have been interpreted as due to percolative effects within a network of superconducting regions embedded in a metallic matrix. In this work we use a mean-field-like effective medium approach to investigate the superconducting phase below the critical temperatureTcat which the resistivity vanishes. Specifically, we consider the finite frequency impedance of the system to extract the dissipative part of the conductance and the superfluid stiffness in the superconducting state. Intriguing effects arise from the metallic character of the embedding matrix: upon decreasing the temperature below T-c proximity effects may rapidly increase the superfluid stiffness. Then, a rather fragile superconducting state, living on a filamentary network just below T-c, can be substantially consolidated by additional superconducting regions induced by proximity effect in the interstitial metallic regions. This mean-field prediction should call for further theoretical analyses and trigger experimental investigations of the superconducting properties of the above systems.

We present a study of the Berezinskii-Kosterlitz-Thouless (BKT) transition in mildly disordered NbN nanoporous (NP) films. The measured superfluid stiffness, Js, is found to be much lower than that predicted by considering the reduction in the geometric area. This effect is also reproduced theoretically via Monte Carlo simulations on a 2D XY model with different nanopore geometries. For a 5 nm thick NP film, a distinct BKT transition is observed. BKT renormalization group flow equations, incorporating the broadening in Js due to the presence of inhomogeneities, are used to fit the experimental data. From this analysis we see that both Js and the vortex core energy, mu, decrease in the presence of nanopores. Our results show that nanopore geometries effectively enhance the 2D nature of the films, thereby increasing the parameter space to explore BKT physics in superconducting films.