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We investigate a shift in the critical temperature of rotating Bose-Einstein condensates mediated by the melting of the vortex lattice. Numerical simulations reveal that this temperature exhibits contrasting behavior depending on the system configuration: a negative shift occurs for fixed trap potentials due to the expansion of the condensate, while a positive shift is observed for fixed volumes, where vortex lattice rigidity suppresses thermal fluctuations. We introduce a vortex-energy model that captures the role of vortex interactions, the positional energy of the vortex lattice, as well as the phase transition and how the vortex lattice disappears. The findings provide insights into the thermodynamic properties of rotating condensates and the dynamics of vortex lattice melting, offering potential parallels with other quantum systems such as type-II superconductors.

The muon spin rotation ($\mu$SR) technique has been applied to determine the behavior of the in-plane magnetic penetration depth ($\lambda_{ab}$) in the vortex state of the unconventional superconductor Sr$_2$RuO$_4$ as a means of gaining insight into its still unknown superconducting order parameter. A recent $\mu$SR study of Sr$_2$RuO$_4$ reported a $T$-linear temperature dependence for $\lambda_{ab}$ at low temperatures that was not identified in an earlier $\mu$SR study. Here we show that there is no significant difference between the data in the early and recent $\mu$SR studies and both are compatible with the limiting low-temperature $\lambda_{ab} \sim T^2$ dependence expected from measurements of the change in $\lambda_{ab}(T)$ in the Meissner state by other techniques. However, we argue that at this time there is no valid theoretical model for reliably determining the absolute value of $\lambda_{ab}$ in Sr$_2$RuO$_4$ from $\mu$SR measurements. Instead, we identify the formation of an unusual square vortex lattice that introduces a new constraint on candidate superconducting order parameters for Sr$_2$RuO$_4$., Comment: 6 pages, 3 figures

This study explores the impact of in-plane magnetic fields on the superconducting state in layered Ising superconductors, resulting in the emergence of the orbital Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state coupled with Josephson vortices. Recent experiments have revealed an unexpected first-order phase transition in these superconductors under strong in-plane magnetic fields. Our theoretical analysis demonstrates that this phase transition is primarily driven by the formation and subsequent melting of a Josephson vortex lattice within the superconducting layers. As the magnetic field increases, the vortex lattice undergoes a transition from a solid to a liquid state, triggering the observed first-order phase transition. We calculate both the melting line and the in-plane critical field in the phase diagram, showing strong agreement with experimental results.

We show that the ground state of a weakly charged two-dimensional electron-hole fluid in a strong magnetic field is a broken translational symmetry state with interpenetrating lattices of localized vortices and antivortices in the electron-hole-pair field. The vortices and antivortices carry fractional charges of equal sign but unequal magnitude and have a honeycomb lattice structure that contrasts with the triangular lattices of superconducting electron-electron-pair vortex lattices. We predict that increasing charge density and weakening magnetic fields drive vortex delocalization transitions signaled experimentally by abrupt increases in counterflow transport resistance.

We investigate the impact of various impurities on rotating Bose-Einstein condensates confined within two-dimensional harmonic and optical lattice potentials. Without impurities, the rotating condensates display an organized square lattice pattern of vortices due to the influence of a square optical lattice. The introduction of impurity potentials disrupts this lattice structure, inducing a phase transition from an ordered state to a disordered state. Our analysis encompasses both static and dynamic types of impurities. The static impurities are implemented using a randomly varying potential with a spatially random amplitude. The transformation of the vortex lattice structure, in this case, relies on the strength and lattice constant of the impurity potential. For dynamical impurities, we employ a Gaussian obstacle that orbits around the condensate at a specific distance from its center. In this scenario, the vortex lattice melting occurs beyond a certain threshold radius and frequency of oscillation of the rotating obstacle. We characterize the melting of the vortex lattice due to impurities using various quantities, such as the structure factor and angular momentum. Notably, in the vortex-melted state, the angular momentum follows a power-law dependence with an exponent of approximately $1.73$, regardless of the type of impurity. Finally, we demonstrate the signature of the presence of a turbulent state within the vortex-melted state generated by both static and dynamical impurities., Comment: 19Pages, 23 figures

Melting of a solid is one of the most ubiquitous phenomena observed in nature. Most solids, when heated, melt from a crystalline state to an isotropic liquid at a characteristic temperature. There are however situations where increase in temperature can induce a transition to a more ordered state. Broadly termed as "inverse melting", experimental realisations of such situations are rare. Here, we report such a phenomenon in the 2-dimensional vortex liquid that forms in a moderately pinned amorphous Re6Zr (a-ReZr) thin film, from direct imaging of the vortex lattice using a scanning tunnelling microscope. At low temperature and magnetic fields, we find that the vortices form a "pinned liquid" , that is characterised by a low mobility of the vortices and vortex density that is spatially inhomogeneous. As the temperature or magnetic field is increased the vortices become more ordered, eventually forming a nearly perfectly ordered vortex lattice. Above this temperature/magnetic field, the ordered vortex lattice melts again into a vortex liquid. This re-entrant transformation from a liquid to solid-like state and then back to a liquid also leaves distinct signature in the magnetotransport properties of the superconductor.

We study the vortex pinning effect on the vortex lattice structure of the rotating two-component Bose-Einstein condensates (BECs) in the presence of impurities or disorder by numerically solving the time-dependent coupled Gross-Pitaevskii equations. We investigate the transition of the vortex lattice structures by changing conditions such as angular frequency, the strength of the inter-component interaction and pinning potential, and also the lattice constant of the periodic pinning potential. We show that even a single impurity pinning potential can change the unpinned vortex lattice structure from triangular to square or from triangular to a structure which is the overlap of triangular and square. In the presence of periodic pinning potential or optical lattice, we observe the structural transition from the unpinned vortex lattice to the pinned vortex lattice structure of the optical lattice. In the presence of random pinning potential or disorder, the vortex lattice melts following a two-step process by creation of lattice defects, dislocations, and disclinations, with the increase of rotational frequency, similar to that observed for single component Bose-Einstein condensates. However, for the binary BECs, we show that additionally the two-step vortex lattice melting also occurs with increasing strength of the inter-component interaction.

Inspired by the stable bilayer water ice grown in the laboratory (Nature 577, 60, 2020), we propose a model representing water ice as a two-layer six-vertex model. Using the loop update Monte Carlo method, we unveil meaningful findings. While the square lattice six-vertex model exhibits an antiferromagnetic to disordered phase transition known as the Berezinskii-Kosterlitz-Thouless transition, we observe a different scenario for the bilayer six-vertex model, where the transition type transforms into an Ising transition. We discover the emergence of vortices in the disordered phase, and to stabilize them, vortex excitation is induced. This leads to the presence of distinct 1/2 filling and 2/3 filling vortex lattice phases. More importantly, we identify the phase transitions between the vortex lattice phase and the disordered phase, as well as between the 1/2 and 2/3 vortex lattices, as being of first order. We also propose an experimental scheme for realizing a two-layer six-vertex model based on the artificial ice of particles in a double well trap array. Our findings provide valuable insight into the nature of phase transitions occurring in layered water ice and artificial spin ice systems in experimental setups., Comment: 15 pages, 17 figures, accepted by Physical Review B

We report the observation of the melting of a vortex lattice in a fast rotating quasi-two dimensional Bose gas, under the influence of thermal fluctuations. We image the vortex lattice after a time-of-flight expansion, for increasing rotation frequency at constant atom number and temperature. We detect the vortex positions and study the order of the lattice using the pair correlation function and the orientational correlation function. We evidence the melting transition by an abrupt change in the decay of orientational correlations, associated to a proliferation of dislocations. Our findings are consistent with the hexatic to liquid transition in the KTHNY scenario for two-dimensional melting.

2$H$-NbS$_2$ is a classic example of an anisotropic multi-band superconductor, with significant recent work focussing on the interesting responses seen when high magnetic fields are applied precisely parallel to the hexagonal niobium planes. It is often contrasted with its sister compound 2$H$-NbSe$_2$ because they have similar onset temperatures for superconductivity, but 2$H$-NbS$_2$ has no charge density wave whereas in 2$H$-NbSe$_2$ the charge density wave order couples strongly to the superconductivity. Using small-angle neutron scattering, a bulk-sensitive probe, we have studied the vortex lattice and how it responds to the underlying superconducting anisotropy. This is done by controlling the orientation of the field with respect to the Nb planes. The superconducting anisotropy, $\Gamma_{ac} = 7.07 \pm 0.2$, is found to be field independent over the range measured (0.15 to 1.25 T), and the magnetic field distribution as a function of the applied magnetic field is found to be in excellent quantitative agreement with anisotropic London theory modified with a core-size cut-off correction, providing the first complete validation of this model. We find values of $\lambda_{ab} = 141.9 \pm 1.5 $ nm for the in-plane London penetration depth, and $\lambda_{c} \sim$ 1 \textmu m for the out-of-plane response. The field-independence indicates that we are primarily sampling the larger of the two gaps generating the superconductivity in this material., Comment: 13 pges, 8 figuers

In this article we study microwave absorption in superconductors in the presence of a vortex lattice. We show that in addition to the conventional absorption mechanism associated with the vortex core motion, there is another mechanism of microwave absorption, which is caused by the time-dependence of the quasiparticle density of states outside the vortex cores. This mechanism exists even in the absence of vortex motion and provides the dominant contribution to microwave absorption in a broad interval of physical parameters. At low frequencies, the dissipative part of the microwave conductivity $\sigma(\omega)$ is proportional to the inelastic relaxation time, $\tau_{\mathrm{in}}$, which is typically much larger than the elastic relaxation time, $\tau_{\mathrm{el}}$. At high frequencies $\sigma(\omega)$ is proportional to the quasiparticle diffusion time across the inter-vortex distance, $\tau_{\mathrm D}$, which is still larger than $\tau_{\mathrm{el}}$., Comment: 8 pages, 1 figure

We show that a three-dimensional (3D) fully gapped type-II superconductor can feature emergent in-gap Fermi surfaces of Caroli-de Gennes Matricon (CdGM) quasiparticles in the presence of an Abrikosov vortex lattice. In particular, these CdGM Fermi surfaces manifest in the emergent 3D band structure enabled by the intervortex tunneling physics, and their stability is guaranteed by a $\mathbb{Z}_2$ topological index. By developing an effective analytical theory, we find that each vortex line carrying a 1D nodal dispersion is a sufficient condition for the vortex lattice to form CdGM Fermi surfaces. Following this prediction, in-gap CdGM Fermi surfaces are numerically confirmed in a microscopic vortex-lattice simulation of a superconducting Dirac semimetal with an $s$-wave spin-singlet pairing, which is directly applicable to a large class of type-II superconductors such as LiFeAs. Remarkably, the CdGM Fermi surfaces persist even when the normal state is deformed to a doped insulator of trivial band topology. Our work establishes the vortex lattice as a new experimentally feasible control knob for emergent topological phenomena in conventional superconductors., Comment: 6 + 9 pages, 3 + 6 figures

We study an effective field theory of a vortex lattice in a two-dimensional neutral rotating superfluid. Utilizing particle-vortex dualities, we explore its formulation in terms of a $U(1)$ gauge theory coupled to elasticity, that at low energies reduces to a compact Lifshitz theory augmented with a Berry phase term encoding the vortex dynamics in the presence of a superflow. Utilizing elasticity- and Lifshitz-gauge theory dualities, we derive dual formulations of the vortex lattice in terms of a traceless symmetric scalar-charge theory and demonstrate low-energy equivalence of our dual gauge theory to its elasticity-gauge theory dual. We further discuss a multipole symmetry of the vortex lattice and its dual gauge theory's multipole one-form symmetries. We also study its topological crystalline defects, where the multipole one-form symmetry plays a prominent role. It classifies the defects, explains their restricted mobility, and characterizes descendant vortex phases, which includes a novel vortex supersolid phase. Using the dual gauge theory, we also develop a mean-field theory for the quantum melting transition from a vortex crystal to a vortex supersolid., Comment: 19 pages, 1 figure. v2: published version

A rapidly rotating Bose gas in the quantum Hall limit is usually associated with a melted vortex lattice. In this work, we report a self-bound and visible triangular vortex lattice without melting for a two-dimensional Bose-Bose droplet rotating in the quantum Hall limit, i.e., with rotation frequency $\Omega$ approaching the trapping frequency $\omega$. Increasing $\Omega$ with respect to interaction strength $U$, we find a smooth crossover of the vortex lattice droplet from a needling regime, as featured by small vortex cores and an equilibrium flat-top surface, to the lowest-Landau-level regime with Gaussian-extended cores spreading over the whole surface. The surface density of such a rotating droplet is higher than that of a static one, and their ratio is found to be a universal function of $\Omega/U$. We have demonstrated these results by both numerical and variational methods. The results pave the way for future experimental exploration of rapidly rotating ultracold droplets into the quantum Hall limit., Comment: 7 pages, 6 figures

Two-dimensional Josephson junction arrays frustrated by a perpendicular magnetic field are predicted to form a cascade of distinct vortex lattice states. Here, we show that the resistivity tensor provides both structural and dynamical information on the vortex-lattice states and intervening phase transitions, which allows for experimental identification of these symmetry-breaking ground states. We illustrate our general approach by a microscopic theory of the resistivity tensor for a range of magnetic fields exhibiting a rich set of vortex lattices as well as transitions to liquid-crystalline vortex states., Comment: 5+3 pages, 5 figures

Recently, we presented a new numerical scheme for vortex lattice formation in a rotating Bose-Einstein condensate (BEC) using smoothed particle hydrodynamics (SPH) with an explicit time-integrating scheme; our SPH scheme could reproduce the vortex lattices and their formation processes in rotating quasi-two-dimensional (2D) BECs trapped in a 2D harmonic potential. In this study, we have successfully demonstrated a simulation of rotating 3D BECs trapped in a 3D harmonic potential forming "cigar-shaped" condensates. We have found that our scheme can reproduce the following typical behaviors of rotating 3D BECs observed in the literature: (i) the characteristic shape of the lattice formed in the cross-section at the origin and its formation process, (ii) the stable existence of vortex lines along the vertical axis after reaching the steady state, (iii) a "cookie-cutter" shape, with a similar lattice shape observed wherever we cut the condensate in a certain range in the vertical direction, (iv) the bending of vortex lines when approaching the inner edges of the condensate, and (v) the formation of vortex lattices by vortices entering from outside the condensate. Therefore, we further validated our scheme by simulating rotating 3D BECs.

We study the vortex formation in coupled atomic and molecular condensates in a rotating double well trap by numerically solving the coupled Gross-Pitaevskii like equations. Starting with the atomic condensate in the double well potential we considered two-photon Raman photoassociation for coherent conversion of atoms to molecules. It is shown that the competition between atom-molecule coupling strength and repulsive atom-molecule interaction controls the spacings between atomic and molecular vortices and the rotation frequency of the trap is the key player for controlling the number of visible atomic and molecular vortices. Whereas the Raman detuning controls the spacing between atomic and molecular vortices as well as the number of atomic and molecular vortices in the trap. We have shown by considering the molecular lattices the distance between two molecular vortices can be controlled by varying the Raman detuning. In addition we have found that the Feynman rule relating the total number of vortices and average angular momentum both for atoms and molecules can be satisfied by considering the atomic and molecular vortices those are hidden in density distribution and seen as singularities in phase distribution of the coupled system except for the lattice structure where molecular vortices are overlapped with each other. It is found that although the number of visible/core vortices in atomic and molecular vortex lattices depends significantly on the system parameters the number of atomic and molecular hidden vortices remains constant in most of the cases.

Numerical simulations are used to examine the transition dynamics between metastable and ground state vortex lattice phases in a system with combined sixfold and twelvefold contributions to the vortex-vortex interactions. The system is initially annealed using a twelvefold anisotropy, yielding domains of two different orientations and separated by grain boundaries. The vortex-vortex interaction is then suddenly changed to a sixfold anisotropy, rendering the twelvefold state metastable. Applying a drive that mimics an oscillating magnetic field causes the metastable state to decay, indicated by the structure factor that evolves from twelve to six peaks. The results fit the behavior seen in recent small-angle neutron scattering studies of the vortex lattice in MgB2. At higher drive amplitudes, the decay exhibits a two step process in which the initial fast decrease is followed by a slower regime where avalanches or bursts are correlated with dislocation annihilation events. The results are compared to other types of metastable systems with quenched disorder that decay under a periodic external drive., Comment: Accepted for publication, New J. Phys

The noncentrosymmetric superconductor Ru$_7$B$_3$ has in previous studies demonstrated remarkably unusual behaviour in its vortex lattice, where the nearest neighbour directions of the vortices dissociate from the crystal lattice and instead show a complex field-history dependence, and the vortex lattice rotates as the field is changed. In this study, we look at the vortex lattice form factor of Ru$_7$B$_3$ during this field-history dependence, to check for deviations from established models, such as the London model. We find that the data is well described by the anisotropic London model, which is in accordance with theoretical predictions that the alterations to the structure of the vortices due to broken inversion symmetry should be small. From this, we also extract values for the penetration depth and coherence length.

The wealth of complex polar topologies recently found in nanoscale ferroelectrics result from a delicate balance between the materials intrinsic tendency to develop a homogeneous polarization and the electric and mechanic boundary conditions imposed upon them. Ferroelectric dielectric interfaces are model systems where polarization curling originates from open circuit like electric boundary conditions, to avoid the build-up of polarization charges through the formation of flux closure domains that evolve into vortex like structures at the nanoscale. Interestingly, while ferroelectricity is known to couple strongly to strain (both homogeneous and inhomogeneous), the effect of mechanical constraints on thin film nanoscale ferroelectrics has been comparatively less explored because of the relative paucity of strain patterns that can be implemented experimentally. Here we show that the stacking of freestanding ferroelectric perovskite layers with controlled twist angles opens an unprecedented opportunity to tailor these topological nanostructures in a way determined by the lateral strain modulation associated to the twisting. Interestingly, we find that a peculiar pattern of polarization vortices and antivortices emerges from the flexoelectric coupling of polarization to strain gradients. This finding opens exciting opportunities to create two-dimensional high density vortex crystals that would allow us to explore novel physical effects and functionalities.

We present small angle neutron scattering studies of the magnetic vortex lattice (VL) in Ca$_{0.04}$Y$_{0.96}$Ba$_{2}$Cu$_{3}$O$_{7}$ up to a field of 16.7 T, and Ca$_{0.15}$Y$_{0.85}$Ba$_{2}$Cu$_{3}$O$_{7}$ up to 25 T. We find that the series of vortex lattice structure transitions have shifted down in field relative to those reported for the undoped compound. We attribute this mainly to the weakening of the 1-D superconductivity in the Cu-O chains by the disorder introduced by doping. The hole doping by calcium is also expected to alter the Fermi velocity and it reduces the upper critical field of the system. The high-field structure of the vortex lattice is similar to recent measurements on the parent compound in fields of 25~T, which indicates that the fundamental \textit{d}-wave nature of the superconducting gap is unchanged by calcium doping. This is corroborated by the temperature dependence of the VL form factor which also shows the same \textit{d}-wave behaviour as observed in other cuprates. We also find evidence of Pauli paramagnetic effects in the field dependence of the VL form factor., Comment: 9 pages, 6 figures

Recent experiments on the Iron-based superconductor FeSe in a high magnetic field have suggested the presence of both the fluctuation-induced vortex liquid regime and a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) vortex lattice. To get a general picture on the magnetic phase diagram in type II superconductors with strong superconducting (SC) fluctuation and strong paramagnetic pair-breaking (PPB) such as FeSe, the vortex lattice melting curve Hm(T) is theoretically investigated in the situations where a FFLO state is expected to occur. In general, the PPB tends to narrow the vortex liquid regime intervening between Hc2(T) and Hm(T). In particular, the vortex liquid regime is found to rapidly shrink upon entering, by cooling, the temperature range in which the FFLO state with a periodic modulation parallel to the magnetic field is stable in the mean field theory. Based on the present results, the high field SC phase diagrams of FeSe in the parallel and perpendicular field configurations are discussed., Comment: Submitted version

Vortices are topologically distinctive objects appearing as phase twists in coherent fields of optical beams and Bose-Einstein condensates. Structured networks and artificial lattices of coupled vortices could offer a powerful platform to study and simulate interaction mechanisms between constituents of condensed matter systems, such as antiferromagnetic interactions, by replacement of spin angular momentum with orbital angular momentum. Here, we realize such a platform using a macroscopic quantum fluid of light based on exciton-polariton condensates. We imprint all-optical hexagonal lattice that results into a triangular vortex lattice, with each cell having a vortex of charge l = +-1. We reveal that pairs of coupled condensates spontaneously arrange their orbital angular momentum antiparallel, implying a form of artificial orbital "antiferromagnetism". We discover that correlation exists between the emergent vortex patterns in triangular condensate lattices and the low-energy solutions of the corresponding antiferromagnetic Ising system. Our study offers a path toward spontaneously ordered vortex arrays with nearly arbitrary configurations and controlled couplings.

Using small-angle neutron scattering we have studied the vortex lattice in superconducting MgB$_2$ with the magnetic field applied along the $c$-axis, doped with either manganese or carbon to achieve a similar suppression of the critical temperature. For Mn-doping, the vortex lattice phase diagram remains qualitatively similar to that of pure MgB$_2$, undergoing a field-and temperature-driven $30^{\circ}$ rotation transition, indicating only a modest effect on the vortex-vortex interaction. In contrast, the vortex lattice rotation transition is completely suppressed in the C-doped case, likely due to a change in the electronic structure which affects the two-band/two-gap nature of superconductivity in MgB2. The vortex lattice longitudinal correlation length shows the opposite behavior, remaining roughly unchanged between pure and C-doped MgB$_2$ while it is significantly reduced in the Mn-doped case. However, the extensive vortex lattice metastability and related activated behavior, observed in conjunction with the vortex lattice transition in pure MgB$_2$, is also seen in the Mn doped sample. This shows that the vortex lattice disordering is not associated with a substantially increased vortex pinning., Comment: To appear in the Journal of Applied Crystallography for the special issue "Magnetic Small-Angle Neutron Scattering - from nanoscale magnetism to long-range magnetic structures"

We have used small-angle neutron scattering to determine the vortex lattice phase diagram in the topological superconductor UPt3 for the applied magnetic field along the crystalline c-axis. A triangular vortex lattice is observed throughout the superconducting state, but with an orientation relative to the hexagonal basal place that changes with field and temperature. At low temperature, in the chiral B phase, the vortex lattice undergoes a non-monotonic rotation with increasing magnetic field. The rotation amplitude decreases with increasing temperature and vanishes before reaching the A phase. Within the A phase an abrupt +/-15 degree vortex lattice rotation was previously reported by Huxley et al., Nature 406, 160-164 (2000). The complex phase diagram may be understood from competing effects of the superconducting order parameter, the symmetry breaking field, and the Fermi surface anisotropy. The low-temperature rotated phase, centered around 0.8 T, reported by Avers et al., Nature Physics 16, 531-535 (2020), can be attributed directly to the symmetry breaking field., Comment: To appear in Frontiers of Electronic Materials, Research topic on "New Heavy Fermion Superconductors"

We investigate the thermodynamics of two-flavor quark matter in presence of nonzero isospin chemical potential and external magnetic field. It is known that at sufficiently high isospin chemical potential, charged pions undergo Bose-Einstein condensation (BEC). The condensate behaves as a superconductor, exhibiting Meissner effect in weak external magnetic fields. Stronger fields stress the superconducting state, turning it first into an Abrikosov lattice of vortices, and eventually destroying the condensate altogether. On the other hand, for sufficiently strong magnetic fields and low-to-moderate isospin chemical potential, the ground state of quantum chromodynamics (QCD) is expected to be a spatially modulated condensate of neutral pions, induced by the chiral anomaly: the chiral soliton lattice (CSL). We map the phase diagram of QCD as a function of isospin chemical potential and magnetic field in the part of the parameter space accessible to a low-energy effective field theory description of QCD. Our main result is an explicit account of the competition between the CSL and the Abrikosov vortex lattice. This is accomplished by adopting a fast numerical algorithm for finding the vortex lattice solution of the equation of motion and the corresponding Gibbs energy. We find that the Abrikosov vortex lattice phase persists in the phase diagram, separating the uniform charged pion BEC phase from the CSL phase. The precise layout of the phase diagram depends sensitively on the choice of the vacuum pion mass., Comment: 13 pages, 5 figures

The system of Bose-Fermi superfluid mixture offers a playground to explore rich macroscopic quantum phenomena. In a recent experiment of Yao {\it et al.} [Phys. Rev. Lett. {\bf 117}, 145301 (2016)], $^{41}$K-$^{6}$Li superfluid mixture is implemented. Coupled quantized vortices are generated via rotating the superfluid mixture, and a few unconventional behaviors on the formations of vortex numbers are observed, which can be traced to boson-fermion interactions. Here we provide a theoretical insight into the unconventional behaviors observed in the experiment. To this end, the orbital-free density functional theory is hired, and its utility is validated by making comparison of the numerical results and a microscopic theory for vortex lattices in strongly interacting Fermi superfluids alone. We also predict interesting phenomena which can be readily explored experimentally, including the novel structures of bosonic-fermionic vortices, and attractive interactions between the bosonic and fermionic vortices., Comment: Journal-ref: Physics Letters A 481 129017 (2023)

Using sound velocity and attenuation measurements in high magnetic fields, we identify a new transition in the vortex lattice state of La$_{2-x}$Sr$_{x}$CuO$_4$ (LSCO). The transition, observed in magnetic fields exceeding 35 T and temperatures far below zero field $T_c$, is detected in the compression modulus of the vortex lattice, at a doping level $x=p=0.17$. Our theoretical analysis based on Eilenberger theory of vortex lattice shows that the transition corresponds to the long-sought 45 degrees rotation of the square vortex lattice, predicted to occur in $d$-wave superconductors near a van Hove singularity., Comment: Main text 5 pages, 3 figures, total 9 pages supplementary material included

In superconducting films, the role of intrinsic disorder is typically to compete with superconductivity by fragmenting the global phase coherence and lowering the superfluid density. Nonetheless, when a transverse magnetic field is applied to the system and an Abrikosov vortex lattice forms, the presence of disorder can actually strengthen the superconducting state against thermal fluctuations. By means of Monte Carlo simulations on the uniformly frustrated XY model in two dimensions, we show that while for weak pinning the superconducting critical temperature $T_c$ increases with the applied field $H$, for strong enough pinning the experimental decreasing dependence between $T_c$ and $H$ is recovered with a resulting more robust vortex lattice.

We estimate the conjectured interaction between the Earth gravitational field and a superconductor immersed in external, static electric and magnetic field. The latter is close to the sample upper critical field and generates the presence of a vortex lattice. The proposed interaction could lead to multiple, measurable effects. First of all, a local affection of the gravitational field inside the superconductor could take place. Second, a new component of a generalized electric field parallel to the superconductor surface is generated inside the sample. The analysis is performed by using the time-dependent Ginzburg-Landau theory combined with the gravito-Maxwell formalism. This approach leads us to analytic solutions of the problem, also providing the average values of the generated fields and corrections inside the sample. We will also study which are the physical parameters to optimize and, in turn, the most suitable materials to maximize the effect., Comment: 17 pages, 2 figures, 1 table (corrected figure scales)

We investigate the properties of a spin-imbalanced and rotating unitary Fermi gas. Using a density functional theory (DFT), we provide insight into states that emerge as a result of a competition between Abrikosov lattice formation, spatial phase separation and the emergence of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. A confrontation of the experimental data [M. Zwierlein et al., Science 311, 492 (2006)] with theoretical predictions provides a remarkable qualitative agreement. In case of gas confined in a harmonic trap, the phase separation into a superfluid core populated by the Abrikosov lattice and a spin-polarized corona is the dominant process. Changing confinement to a box-like trap, reverts the spatial location of the component: gas being in the normal state is surrounded by superfluid threaded by quantum vortices. The vortex lattice no longer exhibits the triangular symmetry, and emergence of exotic geometries may be an indirect signature of the FFLO-like state formation in the system., Comment: 10 pages, 7 figures

In two-dimensional (2D) systems, the melting from a solid to an isotropic liquid can occur via an intermediate phase that retains orientational order. However, in 2D superconducting vortex lattices, the effect of orientational correlations on transport, and their interplay with disorder remain open questions. Here we study a 2D weakly pinned vortex system in amorphous MoGe films over an extensive range of temperatures ($\bm{T}$) and perpendicular magnetic fields ($\bm{H}$) using linear and nonlinear transport measurements. We find that, at low fields, the resistivity obeys the Vogel-Fulcher-Tamman (VFT) form, $\bm{\rho(T)\propto\exp[-{W}(H)/(T-T_0(H))]}$, characteristic of fragile glasses. As $\bm{H}$ increases, $\bm{T_0(H)}$ is suppressed to zero, and a standard vortex liquid behavior consistent with a $\bm{T=0}$ superconducting transition is observed. Our findings, supported also by simulations, suggest that the presence of orientational correlations gives rise to a heterogeneous dynamics responsible for the VFT behavior. The effects of quenched disorder become dominant at high $\bm{H}$, where a crossover to a strong-glass behavior is observed. This is a new insight into the dynamics of melting in 2D systems with competing orders., Comment: 16 pages, 12 figures