We formulate the superfluid weight in unconventional superconductors with $\mathit{k}$-dependent Cooper pair potentials based on the geometric properties of Bloch electrons. We apply the formula to a model of monolayer FeSe obtained by first-principles calculation. Our numerical calculations point to a significant enhancement of the Berezinskii-Kosterlitz-Thouless transition temperature due to the geometric contribution to the superfluid weight, which is not included in the Fermi liquid theory. The $\mathit{k}$ dependence of the gap function also stabilizes the superconducting state. Our results reveal that the geometric properties of Bloch electrons play an essential role in superconducting materials and pave the way for clarifying hidden aspects of superconductivity from the viewpoint of quantum geometry.

Transport in strongly interacting Fermi gases provides a window into the nonequilibrium behavior of strongly correlated fermions. In particular, the interface between a strongly polarized normal gas and a weakly polarized superfluid at finite temperature presents a model for understanding transport at normal-superfluid and normal-superconductor interfaces. An excess of polarization in the normal phase or a deficit of polarization in the superfluid brings the system out of equilibrium, leading to transport currents across the interface. We implement a phenomenological mean-field model of the unitary Fermi gas, and investigate the transport of spin and mass under nonequilibrium conditions. We consider independently prepared normal and superfluid regions brought into contact, and calculate the instantaneous spin and mass currents across the normal-superfluid (NS) interface. For an unpolarized superfluid, we find that spin current is suppressed below a threshold value in the driving chemical potential differences, while the threshold nearly vanishes for a critically polarized superfluid. The mass current can exhibit a threshold in cases where Andreev reflection vanishes, while in general Andreev reflection prevents the occurrence of a threshold in the mass current. Our results provide guidance to future experiments aiming to characterize spin and mass transport across NS interfaces.

δ-AlOOH (δ) is a high-pressure hydrous phase that participates in the deep geological water cycle. At 0 GPa, δ has asymmetric hydrogen bonds (H bonds). Under pressure, it exhibits H-bond disordering, tunneling, and finally, H-bond symmetrization at ∼18 GPa. This study investigates these 300 K pressure-induced state changes in δ with ab initio calculations. H-bond disordering in δ was modeled using supercell multiconfiguration quasiharmonic calculations. We examine (a) energy barriers for proton jumps, (b) the pressure dependence of phonon frequencies, (c) 300 K compressibility, (d) neutron diffraction pattern anomalies, and (e) compare ab initio bond lengths with measured ones. Such thorough and systematic comparisons indicate that (a) proton “disorder” has a restricted meaning when applied to δ. Nevertheless, H bonds are disordered between 0 and 8 GPa, and a gradual change in H-bond configuration results in enhanced compressibility. (b) Several structural and vibrational anomalies at ∼8 GPa are consistent with the disappearance of a particular (HOC-12) H-bond configuration and its change into another one (HOC-11*). (c) Between 8 and 11 GPa, H-bond configuration (HOC-11*) is generally ordered, at least in short- to midrange scale. (d) Between 11.5 and 18 GPa, H-bond lengths approach a critical value that impedes compression, resulting in decreased compressibility. In this pressure range, especially approaching H-bond symmetrization at ∼18 GPa, anharmonicity and tunneling should play an essential role in the proton dynamics. Further simulations accounting for these effects are desirable to clarify the protons' state in this pressure range.

Localization of plastic flow into a narrow shear band is a fundamental and ubiquitous nonequilibrium phenomenon in amorphous solids. Because of the intrinsic entangling of three types of elementary local atomic motion—shear, dilatation, and rotation—the precise physical process of shear band emergence is still an enigma. Here, to unveil this mystery, we formulate a theoretical protocol covering both affine and nonaffine components of deformation, to decode these three highly entangled local atomic-scale events. In contrast to the broad concept of the shear transformation zone, the plastic behavior can be demonstrated comprehensively as the operative manipulation of more exact shear-dominated zones, dilatation-dominated zones, and rotation-dominated zones. Their spatiotemporal evolution exhibits a transition from synchronous motion to separate distribution at the onset of the shear band. The hidden mechanism is then revealed with the help of extreme value theory and percolation analysis. Numerical evidence from extreme value theory indicates that dilatation is the dominant mode at the embryonic stage of the initial plastic units, as evidenced through the larger degree of dilatation localization compared with shear and rotation. The percolation analysis points towards the critical power-law scaling nature at the transition from stochastic activation to percolation of plastic regions. Then the comprehensive picture underlying shear banding emergence is uncovered. Firstly, dilatation triggers initial shear and rotation in soft regions, leading to the embryos of the initial flow units, which are followed by the secondary activation of rotation in neighboring hard material, thus causing an alternating distribution of rotation and shear-dilatation regions. Such rotation activation contributes to further perturbation in these regions and ultimately leads to percolation transition and shear band formation. Our findings also reinforce that the discussion of plastic behavior in disordered materials must take into account both affine and nonaffine component deformation.

Fermi-surface fluctuations and lattice instabilities in the two-dimensional metallic kagome superconductor ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ are elucidated via polarization-resolved Raman spectroscopy. The presence of a weak electronic continuum in high-quality samples marks the crossover into the charge-density-wave (CDW) ordered phase, while impurity-rich samples promote strong defect-induced electronic scattering processes that affect the coherence of the CDW phase. CDW-induced phonon anomalies appear below $T_{\mathrm{CDW}}$, with emergent $C2$ symmetry for one of the CDW amplitude modes, alluding to nematicity. In conjunction with symmetry-breaking lattice distortions, a kinklike hardening of the $A_{1g}$ phonon energy at $T_{\mathrm{CDW}}$ signifies a concerted interplay of electronic correlations and electron-phonon coupling in the exotic CDW order.

This paper focuses on topological defects, appearing in mean-field-theory treatments of physical systems such as ultracold atomic gases and gauge field theories. We begin by investigating the ambiguity and addition of topological charges using the mathematical formalism of covering spaces, which clarifies many aspects these phenomena. Subsequently, we classify topological-defect configurations consisting of several monopoles and unknotted ring defects in terms of homotopy groups and fundamental-group actions on them, thus generalizing the previous classifications of a single monopole and a single unknotted ring defect. Finally, we examine the decay of multiply charged topological monopoles under small perturbations of the physical system, and analyze the conditions under which multiply charged monopoles are inclined to split into several singly charged monopoles.

We investigate the zero-bias behavior of Josephson junctions made of encapsulated graphene boron nitride heterostructures in the long ballistic junction regime. For temperatures down to $2.7$ K, the junctions appear nonhysteretic with respect to the switching and retrapping currents $I_C$ and $I_R$. A small nonzero resistance is observed even around zero-bias current and scales with temperature as dictated by the phase diffusion mechanism. By varying the graphene carrier concentration we are able to confirm that the observed phase diffusion mechanism follows the trend for an overdamped Josephson junction. This is in contrast with the majority of graphene-based junctions which are underdamped and shorted by the environment at high frequencies.

The interplay of a potential and magnetic disorder in superconductors has remained an active field of research for decades. Within the framework of the Usadel equation, we study the local density of states (LDOS) near a solitary classical magnetic impurity in a dirty superconducting film. We find that a potential disorder results in broadening of the $\delta$-function peak in the LDOS at the Yu-Shiba-Rusinov (YSR) energy. This broadening is proportional to the square root of a normal-state spreading resistance of the film. We demonstrate that modification of multiple scattering on the magnetic impurity due to intermediate scattering on surrounding potential disorder crucially affects a profile of the LDOS in the vicinity of the YSR energy. In addition, we find that a scanning-tunneling-microscopy tip can mask a YSR feature in the LDOS. Also, we study the LDOS near a chain of magnetic impurities situated in the normal region of a dirty superconductor/normal-metal junction. We find a resonance in the LDOS near the YSR energy. The energy scale of the resonant peak is controlled by the square root of the film resistance per square in the normal state.

We investigate the spin Seebeck coefficient $S_s$ in the square lattice Hubbard model at high temperatures of relevance to cold-atom measurements. We solve the model with the finite-temperature Lanczos and with the dynamical mean-field theory methods and find they give similar results in the considered regime. $S_s$ exceeds the atomic Heikes' estimates and the Kelvin entropic estimates drastically. We analyze the behavior in terms of a mapping onto the problem of a doped attractive model and derive an approximate expression that allows relating the enhancement of $S_s$ to distinct scattering of the spin-majority and the spin-minority excitations. Our analysis reveals the limitations of entropic interpretations of Seebeck coefficient even in the high-temperature regime. Large values of $S_s$ could be observed on optical lattices. We also calculated the full diffusion matrix. We quantified the spin-thermal diffusion, that is, the extent of the mixing between the spin and the thermal diffusion and discuss the results in the context of recent measurements of the spin-diffusion constant in cold atoms.

The study of non-$s$-wave unconventional superconductivities in strongly correlated electron systems has been a central issue in condensed matter physics for more than 30 years. In such unconventional superconductivities, $d$-wave Cooper pairing with antiparallel spins has been often observed in various quasi-two-dimensional (quasi-2D) bulk systems. Interestingly, many theories predicted that the triangular lattice causes the $d$-wave pairing to be unstable and may lead to more exotic pairing such as parallel spin (spin-triplet) pairing. Here we focus on a bulk organic triangular-lattice system in which superconductivity emerges near a nonmagnetic Mott insulating phase. We demonstrate, by using low-power nuclear magnetic resonance (NMR) measurements, that the spin susceptibility of the superconducting state retains the normal state value even deep in the superconducting state. This result indicates the possibility that the material exhibits spin-triplet superconductivity. Our finding will bring insights also into understanding the 2D materials with triangular moiré superlattices that are considered also to show unconventional superconductivities near Mott-like insulating states.

We propose to realize Dirac states in an inclined two-dimensional Su-Schrieffer-Heeger model on a square lattice. We show that a pair of Dirac points protected by space-time inversion symmetry appear in the semimetal phase. The locations of these Dirac points are not pinned to any high-symmetry points of the Brillouin zone but are tunable through parameter modulations. Interestingly, the merging of two Dirac points undergoes a topological phase transition that leads to either a weak topological insulator or a nodal-line semimetal. We provide a systematic analysis of these topological phases from both bulk and boundary perspectives combined with symmetry arguments. We also discuss feasible experimental platforms to realize our model.

Two-dimensional systems with $C_2\mathcal{T}$ ($P\mathcal{T}$) symmetry exhibit the Euler class topology $E\in \mathbb{Z}$ in each two-band subspace realizing a fragile topology beyond the symmetry indicators. By systematically studying the energy levels of Euler insulating phases in the presence of an external magnetic field, we reveal the robust gaplessness of the Hofstadter butterfly spectrum in the flat-band limit, while for the dispersive bands the gapping of the Landau levels is controlled by a hidden symmetry. We also find that the Euler class $E$ of a two-band subspace gives a lower bound for the Chern numbers of the magnetic subgaps. Our study provides new fundamental insights into the fragile topology of flat-band systems going beyond the special case of $E=1$ as, e.g., in twisted bilayer graphene, thus opening the way to a very rich, still mainly unexplored, topological landscape with higher Euler classes.

Renormalization group methods are well-established tools for the (numerical) investigation of the low-energy properties of correlated quantum many-body systems, allowing us to capture their scale-dependent nature. The functional renormalization group (FRG) allows us to continuously evolve a microscopic model action to an effective low-energy action as a function of decreasing energy scales via an exact functional flow equation, which is then approximated by some truncation scheme to facilitate computation. Here, we report on our implementation of multiloop FRG, an extended truncation scheme recently developed for electronic FRG calculations, within the pseudofermion functional renormalization group (pf-FRG) framework for interacting quantum spin systems. We discuss in detail the conceptual intricacies of the flow equations generated by the multiloop truncation, as well as essential refinements to the integration scheme for the resulting integrodifferential equations. To benchmark our approach, we analyze antiferromagnetic Heisenberg models on the pyrochlore, simple cubic, and face-centered cubic lattice, discussing the convergence of physical observables for higher-loop calculations and comparing with existing results where available. Combined, these methodological refinements systematically improve the pf-FRG approach to one of the numerical tools of choice when exploring frustrated quantum magnetism in higher spatial dimensions.

Materials realizing the $XY$ model in two dimensions are sparse. Here we use neutron triple-axis spectroscopy to investigate the critical static and dynamical magnetic fluctuations in the square-lattice antiferromagnets ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$ and ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$. We probe the temperature dependence of the antiferromagnetic Bragg intensity, the $Q$ width, the amplitude, and the energy width of the magnetic diffuse scattering in the vicinity of the Néel temperature $T_{\mathrm{N}}$ to determine the critical behavior of the magnetic order parameter $M$, correlation length $\xi$, susceptibility $\chi$, and the characteristic energy $\mathrm{\Gamma }$ with the corresponding critical exponents $\beta , \nu , \gamma$, and $z$, respectively. We find that the critical behaviors of the single-layer compound ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$ follow universal scaling laws that are compatible with predictions of the two-dimensional (2D) $XY$ model. The bilayer compound ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ is only partly consistent with the 2D $XY$ theory and best described by the three-dimensional (3D) Ising model, which is likely a consequence of the intrabilayer exchange interactions in combination with an orthorhombic single-ion anisotropy. Hence, our results suggest that layered ruthenates are promising solid-state platforms for research on the 2D $XY$ model and the effects of 3D interactions and additional spin-space anisotropies on the magnetic fluctuations.

This study demonstrates that the zeros of the diagonal components of Green functions are key quantities that can detect noninteracting topological insulators. We show that zeros of the Green functions traverse the band gap in the topological phases. The traverses induce the crosses of zeros, and the zeros' surface in the band gap, analogous to the Fermi surface of metals. By calculating the zeros of the microscopic models, we show the traverses of the zeros universally appear in all six classes of conventional noninteracting topological insulators. By utilizing the eigenvector-eigenvalue identity, which is a recently rediscovered relation in linear algebra, we prove that the traverses of the zeros in the bulk Green functions are guaranteed by the band inversions, which occur in the topological phases. The relevance of the zeros to detecting the exotic topological insulators such as the higher-order topological insulators is also discussed. For the Hamiltonians with the nearest-neighbor hoppings, we also show that the gapless edge state guarantees the zeros' surfaces in the band gap. The analysis demonstrates that the zeros can be used to detect a wide range of topological insulators and thus useful for searching new topological materials.

In this paper we identify a previously unexplored type of topological defect in spiral spin liquids—the momentum vortex—and reveal its dominant role in shaping the low-energy physics of such systems. Spiral spin liquids are a class of classical spin liquids featuring subextensively degenerate ground states. They are distinct from spin liquids on geometrically frustrated lattices, in which the ground-state degeneracy is extensive and connected by local spin flips. Despite a handful of experimental realizations and many theoretical studies, a concrete physical picture of their spin liquidity has not been established so far. In this paper, we study a 2D spiral spin liquid model to answer this question. We find that the local momentum vector field can carry topological defects in the form of vortices, which, however, have very different properties from the commonly known spin vortices. The fluctuations of such vortices lead the system into a liquid phase at intermediate temperatures. Furthermore, the effective low-energy theory of such vortices indicates their equivalence to quadrupoles of fractons in a rank-2 U(1) gauge theory or, alternatively, to quadrupoles of disclinations in elasticity theory. At very low temperatures, the system freezes into a glassy state in which these vortices form a rigid network with straight-line domain walls. Our paper sheds light on the nature of spiral spin liquids and also paves the way toward understanding their quantum limit.