Vortex motion plays a central role in determining the resistance of two-dimensional superconductors, both in the context of the Berezinskii-Kosterlitz-Thouless (BKT) transition and in the mixed state of type-II superconductors under magnetic fields. In this study, we introduce an anisotropic pinning potential to investigate vortex-induced resistance across the BKT transition and the upper critical field $H_{c2}$ transition. Our results demonstrate that the anisotropic pinning potential gives rise to distinct critical temperatures and upper critical fields along two orthogonal directions of current transport. These findings provide a general route toward the realization of multiple "critical temperatures" in two-dimensional superconductors.

When the surface states of a topological insulator becomes superconducting, topological superconductivity can be obtained, and each vortex on the surface can host one single Majorana zero-energy mode which is usually a wave packet decaying exponentially off the vortex core. Here, we predict stable Majorana zero-energy mode whose wave function is ring-shape, dubbed as annular Majorana mode, in the superconducting vortex in topological insulators respecting 3-fold or 6-fold rotational symmetry. Such topological insulators are featured with a single nonlinear Dirac cone located at or three linear Dirac cones at M̅ in the surface Brillouin zone. The annular Majorana mode originates from the effective chiral f-wave superconductivity on the nonlinear Dirac cone in the former case and the interference of the effective chiral p-wave superconductivity on the three linear Dirac cones in the latter. In both cases, the annular Majorana mode is stabilized by the rotational symmetry and the winding number 3 carried by the surface states. Candidate materials supporting the annular Majorana mode are predicted. Our work provides new insights into the topological superconductivity in superconducting topological insulators.

We comprehensively study the unconventional pairing and collective modes in the multiband kagome superconductors AV3Sb5 (A = K, Cs, Rb). By solving gap equations at zero temperature, we identify a transition from normal (s++/s +/-)-wave pairing to time-reversal symmetry-(TRS) breaking pairing with a variation of interpocket interactions or the density of states. This TRS-breaking pairing originates from the superconducting phase frustration of different Fermi pockets and can account for the experimental TRS-breaking signal in kagome superconductors. Moreover, we investigate collective modes, including the Higgs, Leggett, and Anderson-Bogoliubov modes, arising from fluctuations of the amplitude, relative phase, and overall phase of the superconducting order parameters, respectively. Remarkably, due to the presence of multibands, one branch of the Leggett modes becomes nearly massless near the TRS-breaking transition, providing a compelling smoking-gun signature of TRS-breaking superconductivity, in clear contrast to TRS-breaking charge orders. Our results elucidate the rich superconducting physics and its associated collective modes in kagome metals and suggest feasible experimental detection of TRS-breaking pairing.

Understanding the physics of doped charge transfer insulators is the most important problem in high-temperature superconductivity. In this work, we show that an in-gap bound state emerges from the localized hole of the doped charge transfer insulator. We propose an approximate ground state wavefunction based on one localized Zhang-Rice singlet and the Néel state. By calculating the excitation states with one hole added and removed from this ground state, we successfully identify the existence of bound states inside the charge transfer gap. This feature is further confirmed by a Lanczos calculation based on matrix product states (MPS) for a system of 4 × 4 CuO2 unit cells. How these bound states evolve into metallic states is further discussed. Our findings identify the key component of recent STM results on lightly doped Ca2CuO2Cl2 and provide a new understanding of hole-doped charge transfer insulators.

Boron-rich lithium borocarbides are promising candidates for phonon-mediated high-temperature superconductors due to their metallic sigma-bonding electrons. Here, we use the cluster expansion method to identify energetically stable configurations (colorings) of Li2B3C and Li3B4C2, which are characterized by a distinctive pattern of alternating B-B and B-C zigzag chains. Surprisingly, the optimal configuration of Li2B3C exhibits an extremely low superconducting transition temperature of T-c < 0.03 K, which is attributed to the suppression of deformation potentials near the Fermi level caused by the specific electron filling of B-B zigzag chains. However, the sigma-bonding electrons at the Fermi level are highly sensitive to external strain or pressure. Specifically, applying a -5% compressive uniaxial strain can significantly enhance the electron-phonon coupling and the Eliashberg spectral function, boosting up T-c to 37 K. This work not only presents a strategy for achieving high critical temperatures in LinBn+1Cn+1 compounds, but also provides valuable insights into the complex interplay between electronic structure and superconducting interaction.

The recent discovery of superconductivity with T_c ≈ 80 K in bilayer nickelate La_3Ni_2O_7 provides a new setting in which to test the organizing principles of unconventional high-temperature superconductivity. We show that the gene principle and the collaborative Fermi-surface rule which were previously proposed to unify unconventional high temperature superconductors, extend naturally to this bilayer, multi-orbital system. We identify that there are two antiferromagnetic exchange channels that can provide the dominant pairing force: an interlayer intra-orbital nearest-neighbour exchange J_⊥ between d_z^2 orbitals mediated by the inner apical oxygen, and an intralayer inter-orbital nearest-neighbour exchange J_xz between d_z^2 and d_x^2-y^2 orbitals mediated by the in-plane oxygen. Owing to the bilayer bonding–antibonding splitting and the B_1g symmetry of the d_x^2-y^2 orbital, these two channels cooperate to produce a robust s^± superconducting state with an internal sign reversal between mirror-even and mirror-odd Fermi-surface pockets in momentum space. Both pairing channels maximize the superconducting gap on the β pocket with a form factor (cosk_x-cosk_y)^2 in momentum space. The result places La_3Ni_2O_7 within a unified framework for unconventional superconductivity while revealing a distinct electronic environment for high-T_c pairing.

The condensation of electron quartets, known as charge-4e superconductivity (SC), represents a novel quantum state of matter beyond the standard paradigm of Cooper pairing. However, concrete microscopic models realizing this phase in two dimensions remain a central challenge. Here, we introduce a non-engineered and sign-problem-free model, unambiguously demonstrating the emergence of a robust and high-temperature charge-4e SC phase using unbiased quantum Monte Carlo simulations. At zero temperature, the phase diagram reveals that charge-4e SC is the primary ground state in the strong-coupling regime. At finite temperature in the absence of charge-2e SC, we identify charge-4e SC through a Berezinskii-Kosterlitz-Thouless transition, marked by a universal jump in the superfluid stiffness consistent with a condensate of charge 4e. Remarkably, the transition temperature Tc increases nearly linearly with interaction strength, providing a robust mechanism for high-Tc quartet superconductivity. Furthermore, spectral analysis reveals a prominent pseudogap above Tc arising from strong phase fluctuations. Our results establish a canonical and numerically exact model system for charge-4e superconductivity, offering crucial guidance for its realization in experimental platforms such as moiré materials and ultracold atomic systems.

A unit cell represents the smallest repeating structure in solid-state physics and serves as the fundamental building block of a material. In iron-based superconductors, each unit cell contains two iron atoms, which form two sublattices in the two-dimensional iron layers. Under normal circumstances, these sublattices are expected to have identical physical properties due to space inversion symmetry. However, we discover that this sublattice structure can introduce a novel degree of freedom for probing unconventional pairing mechanisms in iron-based superconductors. We observe distinct dual tunneling spectra within the pairing gap energy corresponding to the two sublattices in the monolayer FeSe with atomically homogeneous (1×1) structures on SrTiO_{3}(001) substrates-a phenomenon we term sublattice dichotomy. This dichotomy can be quantitatively explained by a parity-breaking superconducting state, characterized by the coexistence of conventional pairing and interband odd-parity pairing. The interband singlet pairing arises due to the lack of inversion symmetry, which is naturally broken from the interface coupling between the FeSe and TiO_{2} layer.

Recent discoveries in kagome materials have unveiled their capacity to harbor exotic quantum states, including intriguing charge density wave (CDW) and superconductivity. Notably, accumulating experimental evidence suggests time-reversal symmetry breaking within the CDW, hinting at the long-pursued loop current order (LCO). Despite extensive research efforts, achieving its model realization and understanding the mechanism through unbiased many-body simulations have remained both elusive and challenging. In this Letter, we develop a microscopic model for LCO on the spinless kagome lattice with nonlocal interactions, utilizing unbiased functional renormalization group calculations to explore ordering tendencies across all two-particle scattering channels. At the Van Hove filling, we identify sublattice interference to suppress onsite CDW order, leaving LCO, charge bond order, and nematic CDW state as the main competitors. Remarkably, a 2×2 LCO emerges as the many-body ground state over a significant parameter space with strong second nearest-neighbor repulsion, stemming from the unique interplay between sublattice characters and lattice geometry. The resulting electronic model with LCO bears similarities to the Haldane model and culminates in a quantum anomalous Hall state. We also discuss potential experimental implications for kagome metals.

Vanadium diselenide (VSe2), a layered metallic material with a three-dimensional charge density wave (CDW), has received considerable attention due to the high tunability of its CDW phase. Recently, organic tetrabutyl ammonium (TBA) cations have been intercalated into bulk VSe2, resulting in a novel metal-insulator transition with a new two-dimensional in-plane periodicity lattice modulation. In this study, we employ infrared spectroscopy and first-principles calculations to investigate the electronic structure of both pristine VSe2 and TBA+-intercalated VSe2. Our findings reveal a gradual development of a CDW energy gap in pristine VSe2 during the CDW transition, whereas TBA+-intercalated VSe2 undergoes an abrupt and intricate electronic band reconstruction at the phase transition. The study directly distinguishes between traditional CDW order, characterized by a change in band structure at low energy with the formation of an energy gap, and a first-order phase transition with abrupt band reconstruction over broad energies, as seen in (TBA+)xVSe2. Infrared spectroscopy provides a straightforward method to distinguish between these two scenarios. These findings enhance our understanding of structural phase transitions driven by Fermi surface nesting or alternative mechanisms.

Despite extensive progress in iron-based superconductors, how interlayer coupling affects superconductivity remains a key unresolved issue. Here, using angle-resolved photoemission spectroscopy, we successfully resolve the electronic structure of a surface-decoupled FeAs monolayer in KCa2Fe4As4F2, a rare example in iron pnictides. This allows for a direct, side-by-side comparison between the basic FeAs unit and its bulk bilayer counterpart within a single sample. Two distinct superconducting phases are identified: a bulk bilayer phase with Tc ∼ 34 K and a surface-decoupled monolayer phase with a smaller gap vanishing at ∼18 K. In addition to probable enhanced fluctuations in single-layer FeAs, we propose that this Tc difference may originate from either interfacial effect, such as phonon-mediated assistance from the CaF layers or electronic interlayer hopping within the bilayer unit. Our work offers a refined framework for understanding the superconductivity in multilayer iron-based superconductors.

Electronic flat bands have localized Wannier-like orbitals as zero modes. In the Lieb or the kagome models, the localized orbitals satisfy a topological condition that entails two non-contractible loop eigenstates along x/y-axis in real space, and one topological band touching point with other bands in momentum space. In these topological-flat bands, the Bloch state at the touching point is ill-defined, and so is any topological invariant for the entire band. We propose a new topological condition that the loop states in different directions be linearly dependent. Its satisfaction removes the singularity at the band touching point, and enforces nontrivial, well-defined topological invariants. Enforcing the new condition, we obtain topological-topological (top^2)-flat bands in 2D and 3D that have nontrivial invariants including the Chern numbers, the ℤ_2 invariants, and the topological-crystalline invariants. Under small, generic interactions, top^2-flat bands flow to correlated topological insulators with a symmetric mass term; and specially designed interacting models can have top^2-flat bands as exact zero modes.

Increasing the number of internal components in a quantum many-body system can host collective orders inaccessible to simpler settings. Quantum Hall bilayers provide a canonical realization of interlayer exciton condensation, yet extending such coherence across three independently addressable electronic fluids has remained elusive. Here we report evidence for three-component interlayer coherent exciton condensation in triple-layer graphene system. Using Rydberg excitons in an adjacent WSe2 monolayer as a layer-sensitive optical probe, we resolve interaction-induced incompressibility at zeroth-Landau-level crossings for all three pairwise layer combinations, establishing top-middle, middle-bottom and top-bottom exciton condensate channels within the same device. Independent control of displacement field and interlayer bias continuously tunes these pairwise states towards a regime where Landau levels from all three layers approach simultaneous degeneracy. At their convergence, incompressibility persists while the exciton energy and spectral weight evolve smoothly between the pairwise limits, suggesting coherent participation of all three layers in a single three-component state. More broadly, the ability to independently control layer potentials and engineer interlayer interactions establishes multilayer graphene as a programmable synthetic dimension for exploring higher-component quantum Hall order and simulating strongly correlated quantum matter.

Spin-wave excitations provide a central probe of magnetic order and electronic correlations in strongly correlated materials. In this work, we develop an adiabatic theory of spin dynamics by combining the Niu-Kleinman formalism with Kotliar-Ruckenstein slave-boson theory (NK+KRSB). For each frozen spin configuration, the constrained slave-boson saddle point is solved self-consistently, allowing the Berry-curvature matrix and energy Hessian entering the linearized adiabatic equations of motion to be extracted directly. Applied to the half-filled single-orbital Hubbard model, the resulting spin-wave dispersion shows substantially improved agreement with determinant quantum Monte Carlo benchmarks compared with the random phase approximation and closely approaches results from the time-dependent Gutzwiller approximation. We further extend the method to a two-orbital model of La_2NiO_4, demonstrating its applicability to realistic multi-orbital correlated systems. Because the approach only requires saddle-point solutions near the magnetic ground state, it remains computationally efficient while incorporating strong-correlation effects beyond conventional weak-coupling descriptions, providing a practical framework for studying low-energy spin excitations in correlated quantum materials.

The discovery of superconductivity in Ruddlesden-Popper nickelates has established a new frontier in the study of high-temperature superconductors. However, the underlying pairing mechanism and its relationship to the material's electronic and magnetic ground states remain elusive. Since unconventional superconductivity often emerges from a complex interplay of magnetic correlations, elucidating the magnetic ground state of the nickelates at ambient pressure is crucial for understanding the emergence of superconductivity under high pressure. Here, we combine high-resolution angle-resolved photoemission spectroscopy with tight-binding model simulation to investigate the electronic structure of the representative trilayer Ruddlesden-Popper nickelate La_4Ni_3O_10. We provide the first experimental evidence of band splitting induced by interlayer coupling and further resolve the momentum-dependent density wave gap structures along all the Fermi surfaces. Our findings identify the mirror-selective Fermi surface nesting as the origin of the interlayer antiferromagnetic spin density wave and demonstrate the dominant role of Ni-3d_z^2 orbitals in the low-energy physics of La_4Ni_3O_10. These results provide a fundamental framework for understanding the magnetic interactions and high-temperature superconductivity mechanism in the Ruddlesden-Popper nickelate family.

The recent discovery of superconductivity in La_5Ni_3O_11 extends the family of superconducting Ruddlesden–Popper nickelates beyond La_3Ni_2O_7. Unlike conventional members of a single Ruddlesden–Popper series, La_5Ni_3O_11 contains an intercalated La_2NiO_4 layer between La_3Ni_2O_7 blocks, raising the question of whether this additional layer participates in the low-energy electronic structure. Here, we combine density functional theory, Wannier-based tight-binding modeling, and rotationally invariant slave-boson calculations to investigate the electronic role of the intercalated layer. We find that realistic electronic parameters place the La_2NiO_4 layer in gapped insulating regimes rather than a paramagnetic metallic state. Furthermore, realistic interlayer hybridization fails to generate any appreciable La_2NiO_4-derived spectral weight at the Fermi level. Our results demonstrate that the low-energy electronic structure of La_5Ni_3O_11 is governed primarily by the La_3Ni_2O_7 block, with the intercalated La_2NiO_4 layer remaining electronically inactive. This establishes a minimal low-energy description of La_5Ni_3O_11 and provides a unified framework for understanding superconductivity in intercalated Ruddlesden–Popper nickelates.

Orderings in charge and spin have been extensively studied to unravel their correlation to emergent superconductivity over the past decades. Bragg-Williams order (BWO), a classical structural order parameter describing site occupancy in alloys, has long been speculated to influence superconducting behavior. Yet, its role still remains ambiguous, largely due to the difficulty of isolating BWO from concomitant charge doping or competing electronic instabilities. Here, we establish In2/3PSe3 as a platform wherein indium vacancies are reversibly configurable between ordered and disordered states via thermal treatment. We show that the disordered phase undergoes a pressure-induced superconducting transition with a Tc of 11 K, significantly higher than the 7 K observed in its ordered counterpart. This constitutes a rare instance in which pure BWO variation drives a substantial shift in Tc. By combining a Ginzburg-Landau phenomenological analysis with a BCS-McMillan microscopic description, we demonstrate that BWO naturally suppresses superconductivity through electron-phonon interactions, a mechanism supported by ultra-low-wavenumber Raman measurements. Our findings support BWO as an independent order parameter that competes directly with superconductivity, extending the concept of competing orders beyond conventional electronic and magnetic degrees of freedom.

The recent discovery of high-temperature superconductivity in both bulk and thin-film bilayer nickelates La 3 Ni 2 O 7 has garnered significant attention. However, the corresponding pairing symmetry remains debated in both experiments and theoretical studies due to conflicting experimental evidence from bulk and thin-film materials. In this work, we examine the electronic Raman response across different channels for various pairing symmetries within a two-orbital bilayer model. By comparing Raman susceptibilities obtained from multiorbital and band-additive approaches, we demonstrate that Raman response can distinguish between different pairing symmetries and identify pocket-dependent gap amplitudes for both fully gapped and nodal superconducting states. Specifically, the nodal d x 2 - y 2 / d xy -wave pairing exhibits robust low-energy power-law behavior, distinct from a fully gapped pairing. Additionally, for the s ± -wave pairing, the detailed gap anisotropy on the β pocket can be determined. Possible experimental implications are also discussed. Our results highlight the crucial role of multiorbital effects in shaping the Raman spectra and establish electronic Raman scattering as a powerful and symmetry-resolved probe for determining the superconducting gap in unconventional superconductors.

The quantum Pontus-Mpemba effect (QPME) is a counterintuitive phenomenon wherein a quantum system relaxes more rapidly through a two-step evolution protocol than through direct evolution under a symmetric Hamiltonian alone. In this protocol, the system first evolves under a symmetry-breaking Hamiltonian and then switches to a symmetric one. We demonstrate that QPME occurs under both real-time and imaginary-time dynamics with respect to U (1) symmetry. Using tilted ferromagnetic initial states, we demonstrate that a transient asymmetric evolution significantly accelerates thermalization or convergence to the ground state for both real-time and imaginary-time evolutions, respectively. The effect is pronounced for small tilt angles, while larger tilts or antiferromagnetic initial states suppress it. Further numerical evidence confirms the consistency of QPME across different system sizes studied. Finally, by implementing a variational optimization procedure, we identify an optimized dynamical path, demonstrating that the relaxation rate can be further enhanced through tailored symmetry-breaking protocols. This work extends the framework of nonequilibrium quantum phenomena to incorporate active state preparation, with direct implications for the implementation of quantum simulation.