CyberSec Research

This work inaugurates a series of complementary studies on Richardson-Gaudin integrable models. We begin by reviewing the foundations of classical and quantum integrability, recalling the algebraic Bethe ansatz solution of the Richardson (reduced BCS) and Gaudin (central spin) models, and presenting a proof of their integrability based on the Knizhnik-Zamolodchikov equations and their generalizations to perturbed affine conformal blocks. Building on this foundation, we then describe an alternative CFT-based formulation. In this approach, the Bethe ansatz equations for these exactly solvable models are embedded within two-dimensional Virasoro CFT via irregular, degenerate conformal blocks. To probe new formulations within the Richardson-Gaudin class, we develop a high-performance numerical solver. The Bethe roots are encoded in the Baxter polynomial, with initial estimates obtained from a secular matrix eigenproblem and subsequently refined using a deflation-assisted hybrid Newton-Raphson/Laguerre algorithm. The solver proves effective in practical applications: when applied to picket-fence, harmonic oscillator, and hydrogen-like spectra, it accurately reproduces known rapidity trajectories and reveals consistent merging and branching patterns of arcs in the complex rapidity plane. We also explain how to generalize our computational approach to finite temperatures, allowing us to calculate temperature-dependent pairing energies and other thermodynamic observables directly within the discrete Richardson model. We propose an application of the solver to Gaudin-type Bethe equations, which emerge in the classical (large central charge) limit of Virasoro conformal blocks. We conclude by outlining future directions: direct minimization of the Yang-Yang function as an alternative root-finding strategy; revisiting time-dependent extensions; and ... .

Owing to its superconducting properties, Niobium (Nb) is an excellent candidate material for superconducting electronics and applications in quantum technology. Here we perform scanning tunneling microscopy and spectroscopy experiments on Nb films covered by a thin gold (Au) film. We investigate the minigap structure of the proximitized region and provide evidence for a highly transparent interface between Nb and Au, beneficial for device applications. Imaging of Abrikosov vortices in presence of a perpendicular magnetic field is reported. The data show vortex pinning by the granular structure of the polycrystalline Au film. Our results show robust and homogeneous superconducting properties of thin Nb film in the presence of a gold capping layer. The Au film not only protects the Nb from surface oxidation but also preserves its excellent superconducting properties.

Recent observations of time-reversal breaking superconductivity at twisted cuprate interfaces motivate the development of new approaches to better characterize this emergent phenomenon. Here we study the dynamical properties of the order parameters at the twisted unconventional superconductor interfaces. We reveal the emergence of a soft collective mode (Josephson plasmon) at the time-reversal breaking transition, which can be tuned by temperature, twist angle or magnetic field. Furthermore, nonlinear dynamical responses are shown to contain direct signatures of both the transition and the broken symmetry itself. In particular, we show that second harmonic generation is a necessary and sufficient condition for the symmetry breaking. We discuss the signatures of our predictions in AC current-driven experiments and show that strong nonlinear driving allows to induce dynamical phase transitions between phases with and without spontaneous symmetry breaking.

We derive a refraction law for superconducting vortices at superconductor/normal metal interfaces. Simulations of the proximity effect under tilted geometries confirm this law and reveal vortex trapping for low effective mass. Under transport currents, we find core displacements due to differing vortex viscosities in the superconductor and normal metal. These results clarify vortex dynamics in proximity-coupled systems and offer design principles for high-current coated superconducting devices.

Overcoming the decoherence bottleneck remains a central challenge for advancing coherent superconducting quantum device and information technologies. Solitons -- non-dispersive wave packets stabilized by the collective synchronization of quantum excitations -- offer a robust pathway to mitigating dephasing, yet their realization in superconductors has remained experimentally elusive. Here, we report the observation of a driven soliton state in epitaxial thin films of an iron-based superconductor (Co-doped BaFe$_2$As$_2$), induced by intense, multi-cycle terahertz (THz) periodic driving. The dynamical transition to this soliton state is marked by the emergence of Floquet-like spectral sidebands that exhibit a strongly nonlinear dependence on THz laser field strength and a resonant enhancement with temperature. Quantum kinetic simulations corroborate these observations, allowing us to underpin the emergence of synchronized Anderson pseudo-spin oscillations -- analogous to Dicke superradiance -- mediated by persistent order parameter oscillations. In this coherently driven state, the observed sidebands result from difference-frequency mixing between the THz drive and persistent soliton dynamics. These findings establish a robust framework for coherently driving and controlling superconducting soliton time-crystal-like phases using low dissipation, time-periodic THz fields, enabling prospects for THz-speed quantum gate operations, long-lived quantum memory, and robust quantum sensing based on enhanced macroscopic pseudo-spin coherence.

Strong electron correlations drive Mott insulator transitions. Yet, there exists no framework to classify Mott insulators by their degree of correlation. Cuprate superconductors, with their tunable doping and rich phase diagrams, offer a unique platform to investigate the evolution of those interactions. However, spectroscopic access to a clean half-filled Mott-insulating state is lacking in compounds with the highest superconducting onset temperature. To fill this gap, we introduce a pristine, half-filled thallium-based cuprate system, Tl$_2$Ba$_5$Cu$_4$O$_{10+x}$ (Tl2504). Using high-resolution resonant inelastic x-ray scattering (RIXS), we probe long-lived magnon excitations and uncover a pronounced kink in the magnon dispersion, marked by a simultaneous change in group velocity and lifetime broadening. Modeling the dispersion within a Hubbard-Heisenberg approach, we extract the interaction strength and compare it with other cuprate systems. Our results establish a cuprate universal relation between electron-electron interaction and magnon zone-boundary dispersion. Superconductivity seems to be optimal at intermediate correlation strength, suggesting an optimal balance between localization and itinerancy.

Grain boundaries are critical for determining the functionality of polycrystalline materials. Here we present on the structural $\&$ transport properties of grain boundaries in the unconventional superconductor CeCoIn$_5$. We provide a detailed recipe for the fabrication of isolated grain boundary devices from of as-grown polycrystalline samples of CeCoIn$_5$. Electron backscattered diffraction imaging of polycrystalline CeCoIn$_5$ samples reveals an abundance of $90^\circ$ misorientation grain boundaries suggesting a preferential nucleation of CeCoIn$_5$ grains with 90$^\circ$ misorientation over a random distribution of grain orientations. Transport measurements across grain boundary devices establish coherence of superconductivity and allows us to establish a lower bound on the critical current density for the grain boundaries. Our work opens new possibilities for fabrication of quantum devices such as Josephson-junctions out of bulk unconventional superconducting materials.

Superconductors are famously capable of supporting persistent electrical currents, that is, currents that flow without any measurable decay as long as the material is kept in the superconducting state. We introduce here a class of materials -- superconducting altermagnets -- that can both generate and carry persistent {\em spin} currents. This includes spin-polarized electrical supercurrent as well as pure spin supercurrent that facilitates spin transport in the absence of any charge transport. A key to this remarkable property is the realization that the leading superconducting instability of altermagnetic metals consists of two independent condensates formed of spin-up and spin-down electrons. In the non-relativistic limit the two condensates are decoupled and can thus naturally support persistent currents with any spin polarization, including pure spin supercurrents realized in the charge counterflow regime. We describe a novel ``spin-current dynamo effect'' that can be used to generate pure spin supercurrent in such systems by driving a charge current along certain crystallographic directions. Away from the non-relativistic limit, when spin-orbit interactions and magnetic disorder are present, we find that the spin current generically develops spatial oscillations but, importantly, no dissipation or decay. This is in stark contrast to spin currents in normal diffusive metals which tend to decay on relatively short lengthscales. We illustrate the above properties by performing model calculations relevant to two distinct classes of altermagnets and various device geometries.

Quasiparticle interference imaging (QPI) provides a route to characterize electronic structure from real space images acquired using scanning tunneling microscopy. It emerges due to scattering of electrons at defects in the material. The QPI patterns encode details of the $k$-space electronic structure and its spin and orbital texture. Recovering this information from a measurement of QPI is non-trivial, requiring modelling not only of the dominant scattering vectors, but also the overlap of the wave functions with the tip of the microscope. While, in principle, it is possible to model QPI from density functional theory (DFT) calculations, for many quantum materials it is more desirable to model the QPI from a tight-binding model, where inaccuracies of the DFT calculation can be corrected. Here, we introduce an efficient code to simulate quasiparticle interference from tight-binding models using the continuum Green's function method.

Superconductivity and the quantum Hall effect are conventionally viewed as mutually exclusive: the former is suppressed by magnetic fields, while the latter relies on them. Here, we report the surprising coexistence of these two phenomena in rhombohedral hexalayer graphene. In this system, a superconducting phase is not destroyed -- but instead stabilized -- by an out-of-plane magnetic field. Strikingly, this superconducting state coexists and competes with a sequence of quantum Hall states that appear at both integer and half-integer Landau level fillings. Both the superconducting and quantum Hall states exhibit sharply defined thermal transitions or crossovers, with nearly identical onset temperatures -- pointing to a shared underlying mechanism. Taken together, our observations uncover an unprecedented interplay between superconducting and topological phases, challenging conventional paradigms and opening a new frontier in condensed matter physics.

The task of finding a consistent relationship between a quantum Hamiltonian and a classical Lagrangian is of utmost importance for basic, but ubiquitous techniques like canonical quantization and path integrals. Nonconvex kinetic energies (which appear, e.g., in Wilczek and Shapere's classical time crystal, or nonlinear capacitors) pose a fundamental problem: the Legendre transformation is ill-defined, and the more general Legendre-Fenchel transformation removes nonconvexity essentially by definition. Arguing that such anomalous theories follow from suitable low-energy approximations of well-defined, harmonic theories, we show that seemingly inconsistent Hamiltonian and Lagrangian descriptions can both be valid, depending on the coupling strength to a dissipative environment. Essentially there occurs a dissipative phase transition from a non-convex Hamiltonian to a convex Lagrangian regime, involving exceptional points in imaginary time. This resolves apparent inconsistencies and provide computationally efficient methods to treat anomalous, nonconvex kinetic energies.

We study a dirty two-dimensional superconductor with Rashba spin-orbit coupling and in-plane Zeeman fields described by the nonlinear sigma model that includes short-range electron-electron interactions from the Coulomb and Cooper channels. The renormalized Ginzburg-Landau theory, which includes the weak localization effects at the one-loop level, is constructed by using the Keldysh functional formalism. It is shown that the tricritical point appears in the phase diagram. The superconducting diode quality factor increases divergently as the system approaches the tricritical point. Near the superconducting phase transition lines, the absolute value of the diode quality factor decreases due to the cooperation of localization and interactions. The normal conductivity of the resistive state, in which the superconducting state is destroyed by the critical current, is calculated, and localization behaviors are demonstrated.

Mercury chalcogenides are a class of materials that exhibit diverse structural phases under pressure, leading to a range of exotic physical properties, including topological phases and chiral phonons. In particular, the phase diagram of mercury sulfide (HgS) remains difficult to characterize, with significant uncertainty surrounding the transition pressure between phases. Based on recent experimental results, we employ Density Functional Theory and Superconducting Density Functional Theory to investigate the pressure-induced structural phase transition in HgS and its interplay with the emergence of superconductivity as the crystal transitions from the cinnabar phase (space group P3$_1$21) to the rock salt phase (space group Fm$\bar{3}$m). Remarkably, the rocksalt phase hosts a multigap superconducting state driven by distinct Fermi surface sheets, with two dominant gaps; the unusually high critical temperature of $\sim$11 K emerges naturally within this multiband scenario, highlighting the role of interband coupling beyond isotropic models. These results place HgS among the few systems where multiband superconducting gap structures emerge under pressure.

Magnetic adatom chains on superconductors provide a platform to explore correlated spin states and emergent quantum phases. Using low-temperature scanning tunneling spectroscopy, we study the distance-dependent interaction between Fe atoms on 2H-NbSe$_2$. While single atoms exhibit four Yu-Shiba-Rusinov states and partially occupied $d$ levels consistent with a $S=2$ spin state, the spin is quenched when two Fe atoms reside in nearest neighbor lattice sites, where the $d$ levels of the atoms hybridize. The non-magnetic dimer configuration is stable in that dimerization persists in chains with weak interactions among the dimers. Thus, the spin-state quenching has important implications also for Fe chains. While even-numbered chains are stable and non-magnetic, odd-numbered chains host a single magnetic atom at one of the chain's ends, with its position being switchable by voltage pulses. Our findings emphasize the role of interatomic coupling in shaping quantum ground states and suggest that engineering alternating hopping amplitudes analogous to the Su-Schrieffer-Heeger model may offer a pathway to realizing topological systems.

Searching for new superconductors, especially unconventional superconductors, has been studied extensively for decades but remains one of the major outstanding challenges in condensed matter physics. Medium/high-entropy alloys (MEAs-HEAs) are new fertile soils of unconventional superconductors and generate widespread interest and questions on the existence of superconductivity in highly disordered materials. Here, we report on the effect of Ni-doped on the crystal structure and superconductivity properties of strongly coupled TiHfNbTa MEA. XRD results indicate that the maximum solid solution of (Ti1/4Hf1/4Nb1/4Ta1/4)1-xNix is about 7.7%. Resistivity, magnetic susceptibility, and specific heat measurements demonstrated that (Ti1/4Hf1/4Nb1/4Ta1/4)1-xNix HEAs are all bulk type-II superconductors and follow the trend of the increase of Tc with the increase of Ni-doped contents. The specific heat jump of all (Ti1/4Hf1/4Nb1/4Ta1/4)1-xNix are much larger than the BCS value of 1.43, suggesting all these HEAs are strongly coupled superconductors. Additionally, large Kadawaki-Woods ratio values suggest that there is a strong electron correlation effect in this system. The (Ti1/4Hf1/4Nb1/4Ta1/4)1-xNix HEA system is a new ideal material platform for the study of strong correlation behavior and strongly coupled superconductivity, which provides an insight into the physics of high-temperature superconductors or other unconventional superconductors.

We introduce a class of dynamical field theories for $N$-component "Borromean" ($N\geq 3$) super-counterfluid order, naturally formulated in terms of inter-species bosonic fields $\psi_{\alpha\beta}$. Their condensation breaks the normal-state [U(1)]$^N$ symmetry down to its diagonal U(1) subgroup, thereby encoding the arrest of the net superflow. This approach broadens our understanding of dynamical properties of super-counterfluids, at low energies capturing its universal properties, phase transition, counterflow vortices, and many of its other properties. Such super-counterfluid strikingly exhibits $N$ distinct flavors of energetically stable elementary vortex solutions, despite $\mathbb{Z}^{N-1}$ homotopy group of its $N\! -\! 1$ independent Goldstone modes, with $N\! -\! 1$ topologically distinct elementary vortex types, obeying modular arithmetic. The model leads to Borromean hydrodynamics as a low-energy theory, reveals counteflow AC Josephson effect, and generically predicts a first-order character of the phase transitions into Borromean super-counterfluid state in dimensions greater than two.

The negative thermal expansion (NTE) effect has been found generally combined with structural phase transitions. However, the charge and orbital freedoms of the NTE has not been well studied. This study employs angle-resolved photoemission spectroscopy and first-principles calculations to elucidate the charge and orbital kinetics of the anomalous two-step negative thermal expansion structural phase transitions in PbTa2Se4. As the temperature decreases, each transition undergoes a similar block-layer sliding, although the charge transfer behaviors differ significantly. During the first transition, charge is mainly transferred from the Pb 6pz orbital to an M-shaped band below the Fermi level, barely altering the Fermi surface. In contrast, the second transition involves modifications to both the Fermi surface and charge-transfer orbitals, with charge selectively transferred from Pb 6px/py orbitals to Ta 5dz2 orbitals and a decrease of the Fermi pockets formed by Pb 6px/py orbitals. Furthermore, a small pressure can easily tune the base structure phase among the three phases and the corresponding superconductivity. Therefore, our findings reveal that the orbital-selective charge transfer drives the unusual structure transition in PbTa2Se4, offering new insights into the NTE mechanisms and providing a unique window to study the pressure-tuned superconductivity in this metal-intercalated transition chalcogenides.

The superconducting diode effect (SDE), characterized by a directional asymmetry in the critical supercurrents, typically requires external magnetic fields to break time-reversal symmetry -- posing challenges for scalability and device integration. Here, we demonstrate a field-free realization of the SDE in a helical Shiba chain proximitized by a d-wave altermagnet. Using a self-consistent Bogoliubov-de Gennes approach, we uncover a topological Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state that hosts tunable Majorana zero modes at the chain ends. This state is stabilized by the interplay between the exchange coupling of magnetic adatoms and the induced altermagnetic spin splitting. Crucially, the same FFLO phase supports strong nonreciprocal supercurrents, achieving diode efficiencies exceeding 45% without applied magnetic fields. The d-wave altermagnet plays a dual role: it intrinsically breaks time-reversal symmetry, enabling topological superconductivity, and introduces inversion symmetry breaking via momentum-dependent spin-splitting, driving the field-free SDE in a junction-free setting. The supercurrent-controlled finite Cooper pair momentum of the FFLO state modulates both the topological gap and the diode response. Our results establish the Shiba chain-altermagnet heterostructure as a promising platform for realizing topological superconducting devices with efficient, intrinsic superconducting diode functionality -- offering a scalable pathway towards dissipationless quantum technologies.