Berezinskii-Kosterlitz-Thouless Transition Temperature Research Articles

Study of the Berezinskii–Kosterlitz–Thouless transition: an unsupervised machine learning approach

The Berezinskii–Kosterlitz–Thouless (BKT) transition in magnetic systems is an intriguing phenomenon, and estimating the BKT transition temperature is a long-standing problem. In this work, we explore anisotropic classical Heisenberg XY and XXZ models with ferromagnetic exchange on a square lattice and antiferromagnetic exchange on a triangular lattice using an unsupervised machine learning approach called principal component analysis (PCA). The earlier PCA studies of the BKT transition temperature ( TBKT ) using the vorticities as input fail to give any conclusive results, whereas, in this work, we show that the proper analysis of the first principal component-temperature curve can estimate TBKT which is consistent with the existing literature. This analysis works well for the anisotropic classical Heisenberg with a ferromagnetic exchange on a square lattice and for frustrated antiferromagnetic exchange on a triangular lattice. The classical anisotropic Heisenberg antiferromagnetic model on the triangular lattice has two close transitions: the TBKT and Ising-like phase transition for chirality at Tc , and it is difficult to separate these transition points. It is also noted that using the PCA method and manipulation of their first principal component not only makes the separation of transition points possible but also determines transition temperature.

Giant amplification of Berezinskii-Kosterlitz-Thouless transition temperature in superconducting systems characterized by cooperative interplay of small-gapped valence and conduction bands

Two-dimensional superconductors and electron-hole superfluids in van der Waals heterostructures having tunable valence and conduction bands in the electronic spectrum are emerging as rich platforms to investigate novel quantum phases and topological phase transitions. In this work, by adopting a mean-field approach considering multiple-channel pairings and the Kosterlitz-Nelson criterion, we demonstrate giant amplifications of the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature and a shrinking of the pseudogap for small energy separations between the conduction and valence bands and small density of carriers in the conduction band. The presence of the holes in the valence band, generated by intra-band and pair-exchange couplings, contributes constructively to the phase stiffness of the total system, adding up to the phase stiffness of the conduction band electrons that is boosted as well, due to the presence of the valence band electrons. This strong cooperative effect avoids the suppression of the BKT transition temperature for low density of carriers, that occurs in single-band superconductors where only the conduction band is present. Thus, we predict that in this regime, multi-band superconducting and superfluid systems with valence and conduction bands can exhibit much larger BKT critical temperatures with respect to single-band and single-condensate systems.

Two-dimensional Rashba superconductivity in Ni/Bi bilayers evidenced by nonreciprocal transport

When two different materials are brought together, a plethora of quantum phenomena and functionalities can emerge. A prominent example is the superconductivity in Ni/Bi bilayers, which arises from the artificial layered structure composed of the non-superconducting ferromagnetic and heavy metals. Although this system has been shown to exhibit unconventional superconducting properties, the underlying mechanism of the superconductivity remains elusive. Here, we provide experimental evidence of the microscopic coexistence of two-dimensional (2D) superconductivity and broken space-inversion symmetry in the Ni/Bi bilayer. The evidence is obtained from nonreciprocal transport around the superconducting transition temperature, where the resistance depends on the direction of an applied current and an external magnetic field. We find that the nonreciprocal superconducting transport is most pronounced around the Berezinskii–Kosterlitz–Thouless transition temperature. These observations support the 2D Rashba superconductivity in the Ni/Bi bilayer, which will serve as a basis for advancing the understanding of unconventional superconductivity.

Superconductivity near the (2+1)-Dimensional Ferromagnetic Quantum Critical Point

We utilize both analytical and numerical methods to study the superconducting transition temperature T c near a fermionic quantum critical point (QCP) using a model constructed by Xu et al. [Phys. Rev. X 7, 031059 (2017)] as an example. In this model, the bosonic critical fluctuation plays the role of pairing glue for the Cooper pairs, and we use a Bardeen–Cooper–Schrieffer-type mean-field theory to estimate T c. We further argue that the T c computed from the BCS theory approximates a pseudogap temperature T PG, instead of the Berezinskii–Kosterlitz–Thouless transition temperature T KT, which is confirmed by our determinant quantum Monte Carlo simulation. Moreover, due to the fact that electron density of state starts to deplete at T PG, the critical scaling of the underlying QCP is also affected below T PG. Thus, when studying the critical behavior of fermionic QCPs, we need to monitor that the temperature is above T PG instead of T KT. This was often ignored in previous studies.

Precision Many-Body Study of the Berezinskii-Kosterlitz-Thouless Transition and Temperature-Dependent Properties in the Two-Dimensional Fermi Gas.

We perform large-scale, numerically exact calculations on the two-dimensional interacting Fermi gas with a contact attraction. Reaching much larger lattice sizes and lower temperatures than previously possible, we determine systematically the finite-temperature phase diagram of the Berezinskii-Kosterlitz-Thouless (BKT) transitions for interaction strengths ranging from BCS to crossover to BEC regimes. The evolutions of the pairing wave functions and the fermion and Cooper pair momentum distributions with temperature are accurately characterized. In the crossover regime, we find that the contact has a nonmonotonic temperature dependence, first increasing as temperature is lowered, and then showing a slight decline below the BKT transition temperature to approach the ground-state value from above.

Ultradilute Quantum Droplets in the Presence of Higher-Order Quantum Fluctuations

We investigate the effects of higher-order quantum fluctuations on the bulk properties of self-bound droplets in three-, two- and one-dimensional binary Bose mixtures using the Hartree–Fock–Bogoliubov theory. We calculate higher-order corrections to the equation of state of the droplet at both zero and finite temperatures. We show that our results for the ground-state energy are in a good agreement with recent quantum Monte Carlo simulations in any dimension. Our study extends to the finite temperature case where it is found that thermal fluctuations may destabilize the droplet state and eventually destroy it. In two dimensions, we reveal that the droplet occurs at temperatures well below the Berezinskii–Kosterlitz–Thouless transition temperature.

Sound modes in collisional superfluid Bose gases

We theoretically investigate sound modes in a weakly-interacting collisional Bose gas in D dimensions. Using the Landau’s two-fluid hydrodynamics and working within the Bogoliubov theory, we observe the hybridization of the first and second sound modes for D ⩾ 2. To model the recent measurements of the sound velocities in 2D, obtained in the weakly-interacting regime and around the Berezinskii–Kosterlitz–Thouless transition temperature, we derive a refined calculation of the superfluid density, finding a fair agreement with the experiment. In the 1D case, for which experimental results are currently unavailable, we find no hybridization, triggering the necessity of future investigations. Our analysis provides a systematic understanding of sound propagation in a collisional weakly-interacting Bose gas in D dimensions.

Superfluid weight and Berezinskii-Kosterlitz-Thouless transition temperature of strained graphene

We obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for highly unconventional superconducting states with the coexistence of chiral d-wave superconductivity, charge density waves and pair density waves in the strained graphene. Our results show that the strain-induced flat bands can promote the superconducting transition temperature approximately 50% compared to that of the original doped graphene, which suggests that the flat-band superconductivity is a potential route to get superconductivity with higher critical temperatures. In particular, we obtain the superfluid weight for the pure superconducting pair-density-wave states from which the deduced superconducting transition temperature is shown to be much lower than the gap-opening temperature of the pair density wave, which is helpful to understand the phenomenon of the pseudogap state in high-Tc cuprate superconductors. Finally, we show that the BKT transition temperature versus doping for strained graphene exhibits a dome-like shape and it depends linearly on the spin-spin interaction strength.

Temperature and doping dependent flat-band superconductivity on the Lieb-lattice* *Project supported by the National Natural Science Foundation of China (Grant No. 11804213), the Scientific Research Program Funded by Shaanxi Provincial Education Department (Grant No. 20JK0573), the Scientific Research Foundation of Shaanxi University of Technology (Grant No. SLGRCQD2006), and the Natural Science Basic Research Program of Shaanxi (Grant No. 2021JQ-748).

We consider the superconducting properties of Lieb lattice, which produces a flat-band energy spectrum in the normal state under the strong electron–electron correlation. Firstly, we show the hole-doping dependent superconducting order amplitude with various electron–electron interaction strengths in the zero-temperature limit. Secondly, we obtain the superfluid weight and Berezinskii–Kosterlitz–Thouless (BKT) transition temperature with a lightly doping level. The large ratio between the gap-opening temperature and BKT transition temperature shows similar behavior to the pseudogap state in high-T c superconductors. The BKT transition temperature versus doping level exhibits a dome-like shape in resemblance to the superconducting dome observed in the high-T c superconductors. However, unlike the exponential dependence of T c on the electron–electron interaction strength in the conventional high-T c superconductors, the BKT transition temperature for a flat band system depends linearly on the electron–electron interaction strength. We also show the doping-dependent superconductivity on a lattice with the staggered hoping parameter in the end. Our predictions are amenable to verification in the ultracold atoms experiment and promote the understanding of the anomalous behavior of the superfluid weight in the high-T c superconductors.

Berezinskii-Kosterlitz-Thouless transition effects on spin current: The normal-metal–insulating-ferromagnet junction case

We investigate the temperature effects on the spin current through an interface between a normal metal and a quasi-two-dimensional ferromagnetic insulator. Conductive electrons are reflected at the interface absorbing or emitting magnons. The interaction process depends on the temperature, and we are interested in finding out how the transport of spin current is affected close to the Berezinskii-Kosterlitz-Thouless (BKT) transition. That is an important open question. While the thermodynamics of spin currents in the usual normal-metal--insulating-ferromagnet interfaces are known, the results of a BKT transition are still unknown. As it is well documented, the BKT transition is associated with the unbinding of vortex-antivortex pairs in two-dimensional models with an O(2) symmetry. In our work, the ferromagnet is a layered quasi-two-dimensional material, and in the limit of weak interplane coupling, a BKT transition is expected. Using the self-consistent harmonic approximation), we have obtained the BKT transition temperature (${T}_{\text{BKT}}$) and the spin current as a function of the temperature. The spin current behavior at low temperatures is similar to those obtained from theoretical and experimental systems. At ${T}_{\text{BKT}}$, the spin current shows a discontinuous jump associated with vortex dissociation.

Flat-band superconductivity in periodically strained graphene: mean-field and Berezinskii–Kosterlitz–Thouless transition

In the search of high-temperature superconductivity one option is to focus on increasing the density of electronic states. Here we study both the normal and s-wave superconducting state properties of periodically strained graphene, which exhibits approximate flat bands with a high density of states, with the flatness tunable by the strain profile. We generalize earlier results regarding a one-dimensional harmonic strain to arbitrary periodic strain fields, and further extend the results by calculating the superfluid weight and the Berezinskii–Kosterlitz–Thouless (BKT) transition temperature TBKT to determine the true transition point. By numerically solving the self-consistency equation, we find a strongly inhomogeneous superconducting order parameter, similarly to twisted bilayer graphene. In the flat-band regime the order parameter magnitude, critical chemical potential, critical temperature, superfluid weight, and BKT transition temperature are all approximately linear in the interaction strength, which suggests that high-temperature superconductivity might be feasible in this system. We especially show that by using realistic strain strengths TBKT can be made much larger than in twisted bilayer graphene, if using similar interaction strengths. We also calculate properties such as the local density of states that could serve as experimental fingerprints for the presented model.

Spinless Fulde–Ferrell superfluid in Haldane model with nearest-neighbor interaction

Fulde–Ferrell (FF) state is an exotic superconducting or superfluid state, characterized by Cooper pairs with a finite center-of-mass momentum, and it has been intensively investigated in spinful systems, but the spin population imbalance is usually necessary. Here we propose a model to realize and modulate the spinless FF superfluid, namely, Haldane model with nearest-neighbor interaction. The FF state appears when the space-inversion and time-reversal symmetries are broken simultaneously, and there exists the first order phase transition. A higher Berezinskii–Kosterlitz–Thouless transition temperature is obtained at larger absolute value of Peierls phase and smaller energy offset of the sublattices. Our proposal provides a feasible option for experimental researchers to detect the FF superfluid.

Strong pairing in two dimensions: pseudogaps, domes, and other implications

This paper addresses the transition from the normal to the superfluid state in strongly correlated two dimensional fermionic superconductors and Fermi gases. We arrive at the Berezinskii–Kosterlitz–Thouless (BKT) temperature TBKT as a function of attractive pairing strength by associating it with the onset of ‘quasi-condensation’ in the normal phase. Our approach builds on a criterion for determining the BKT transition temperature for atomic gases which is based on a well established quantum Monte Carlo analysis of the phase space density. This latter quantity, when derived from BCS–BEC crossover theory for fermions, leads to non-monotonic behavior for TBKT as a function of the attractive interaction or inverse scattering length. In Fermi gases, this implies a robust superconducting dome followed by a long tail from the flat BEC asymptote, rather similar to what is observed experimentally. For lattice systems we find that TBKT has an absolute maximum of the order of 0.1EF. We discuss how our results compare with those derived from the Nelson–Kosterlitz criterion based on the mean field superfluid density and the approach to the transition from below. While there is agreement in the strict mean-field BCS regime at weak coupling, we find that at moderate pairing strength bosonic excitations cause a substantial increase in TBKT followed by an often dramatic decrease before the system enters the BEC regime.

Berezinskii–Kosterlitz–Thouless Transition of Spin-1 Spinor Bose Gases in the Presence of the Quadratic Zeeman Effect

We numerically study the Berezinskii-Kosterlitz-Thouless (BKT) transition of a spin-1 spinor Bose gas under the quadratic Zeeman effect. A calculation of the mass and spin superfluid densities shows that (i) the BKT transition occurs only when vortices are classified by the integer group $\mathbb{Z}$, and $\mathbb{Z}_2$ vortices do not contribute to the BKT transition, (ii) the two BKT transition temperatures for mass and spin superfluid densities are different for a positive quadratic Zeeman effect and equal for a negative quadratic Zeeman effect, and (iii) the universal relation of the superfluid densities at the BKT transition temperature is changed when multiple kinds of vortices contribute to the transition. We have further found that (iv) spin-singlet pairs in non-magnetic states show the quasi-off-diagonal-long-range order at the different temperature lower than the BKT transition temperature, giving the new universal relation of the superfluid density.

High-temperature tunable superfluidity of polaritons in Xene monolayers in an optical microcavity

We study tunable polaritons in monolayers of silicene, germanene, and stanene (Xenes) via an external electric field in an open optical microcavity whose length can be adjusted. An external electric field applied perpendicular to the plane of the Xene monolayer simultaneously changes the band gap and the exciton binding energy, while the variable length of the open microcavity allows one to keep the exciton and cavity photon modes in resonance. First, the Schr\"{o}dinger equation for an electron and hole in an Xene monolayer is solved, yielding the eigenergies and eigenfunctions of the exciton as a function of the external electric field. The dependence of the polaritonic properties, such as the Rabi splitting and cavity photon damping, on the external electric field and on the cavity length, is analyzed. The Berezinskii-Kosterlitz-Thouless (BKT) transition temperature of polaritons is calculated as a function of the external electric field. We analyze and present the conditions for a room-temperature superfluid of lower polaritons by simultaneously maximizing the Rabi splitting and BKT transition temperature.

Pseudogap Regime of a Two-dimensional Uniform Fermi Gas

We investigate pseudogap phenomena in a two-dimensional Fermi gas. Including pairing fluctuations within a self-consistent $T$-matrix approximation, we determine the pseudogap temperature $T^*$ below which a dip appears in the density of states $\rho(\omega)$ around the Fermi level. Evaluating $T^*$, we identify the pseudogap region in the phase diagram of this system. We find that, while the observed BKT (Berezinskii-Kosterlitz-Thouless) transition temperature $T^{\rm exp}_{\rm BKT}$ in a $^6$Li Fermi gas is in the pseudogap regime, the detailed pseudogap structure in $\rho(\omega)$ at $T^{\rm exp}_{\rm BKT}$ still differs from a fully-gapped one, indicating the importance of amplitude fluctuations in the Cooper channel there. Since the observed $T^{\rm exp}_{\rm BKT}$ in the weak-coupling regime cannot be explained by the recent BKT theory which only includes phase fluctuations, our results may provide a hint about how to improve this BKT theory. Although $\rho(\omega)$ has not been measured in this system, we show that the assessment of our results is still possible by using the observable Tan's contact.

Berezinskii–Kosterlitz–Thouless transition of ultracold atoms in optical lattice

We study the behavior of interacting ultracold bosons in a two-dimensional optical lattice described by the Bose–Hubbard (BH) model. We apply the quantum rotor approach to reduce the BH model to a (semiclassical) effective Hamiltonian in which the phases of local order parameters play the role of dynamical variables. This leads to the effective quantum XY model, which is used to calculate the Berezinskii–Kosterlitz–Thouless transition temperature as a function of model parameters. We find that is monotonically dependent on the kinetic energy of atoms and the value of the chemical potential.

Critical behavior of the site diluted quantum anisotropic Heisenberg model in two dimensions

In this work we use the Self Consistent Harmonic Approximation and Quantum Monte Carlo technique to study the Quantum XY on a two dimensional square lattice in the presence of nonmagnetic impurities. In particular we discuss how site disorder changes the Berezinskii–Kosterlitz–Thouless transition temperature, TBKT. This temperature is determined as a function of the nonmagnetic density. Our results are consistent with an anomalous behavior of TBKT at a concentration close to the site percolation threshold. We interpret the results as due to a competition between the confining of vortices and quantum fluctuations, or due to finite size effects.

Berezinskii-Kosterlitz-Thouless phase transition in 2D spin-orbit-coupled Fulde-Ferrell superfluids.

The experimental observation of traditional Zeeman-field induced Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids has been hindered by various challenges, in particular, the requirement of low dimensional systems. In 2D, finite temperature phase fluctuations lead to an extremely small Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for FFLO superfluids, raising serious concerns regarding their experimental observability. Recently, it was shown that FFLO superfluids can be realized using a Rashba spin-orbit coupled Fermi gas subject to Zeeman fields, which may also support topological excitations such as Majorana fermions in 2D. Here we address the finite temperature BKT transition issue in this system, which may exhibit gapped, gapless, topological, and gapless topological FF phases. We find a large BKT transition temperature due to large effective superfluid densities, making it possible to observe 2D FF superfluids at finite temperature. In addition, we show that gapless FF superfluids can be stable due to their positive superfluid densities. These findings pave the way for the experimental observation of 2D gapped and gapless FF superfluids and their associated topological excitations at finite temperature.

Effects of spin-orbit coupling on the Berezinskii-Kosterlitz-Thouless transition and the vortex-antivortex structure in two-dimensional Fermi gases.

We investigate the Berezinskii-Kosterlitz-Thouless (BKT) transition in a 2D Fermi gas with spin-orbit coupling (SOC), as a function of the two-body binding energy and a perpendicular Zeeman field. By including a generic form of the SOC, as a function of Rashba and Dresselhaus terms, we study the evolution between the experimentally relevant equal Rashba-Dresselhaus (ERD) case and the Rashba-only (RO) case. We show that in the ERD case, at a fixed nonzero Zeeman field, the BKT transition temperature T(BKT) is increased by the presence of SOC for all values of the binding energy. We also find a significant increase in the value of the Clogston limit compared to the case without SOC. Furthermore, we demonstrate that the superfluid density tensor becomes anisotropic (except in the RO case), leading to an anisotropic phase-fluctuation action that describes elliptic vortices and antivortices, which become circular in the RO limit. This deformation constitutes an important experimental signature for superfluidity in a 2D Fermi gas with ERD SOC. Finally, we show that the anisotropic sound velocities exhibit anomalies at low temperatures, in the vicinity of quantum phase transitions between topologically distinct uniform superfluid phases.