Recently, a universal relation between the thermal expansion coefficient of glasses ${\alpha }_{\mathrm{g}}$, their glass-transition temperature $T_{\mathrm{g}}$, and the so-called fragility index $m$ of the corresponding supercooled liquid state was found to be valid for more than 200 glass formers, namely ${\alpha }_{\mathrm{g}}/m\propto 1/T_{\mathrm{g}}$ [Lunkenheimer et al., Nat. Phys. 19, 694 (2023)]. Here we show that this could also have far-reaching consequences for our understanding of crystal melting. Namely, when considering the empirically founded 2/3 rule, stating that the ratio of $T_{\mathrm{g}}$ and the melting temperature $T_{\mathrm{m}}$ is about 2/3 for almost all materials, for crystals a similar relation, ${\alpha }_{\mathrm{c}}/m\propto 1/T_{\mathrm{m}}$, should apply. Indeed, we find that the available experimental data are quite consistent with such a relation. This implies that the melting of a crystal into an ordinary (nonsupercooled) liquid is influenced by the fragility, a property quantifying the non-Arrhenius dynamics in the supercooled-liquid state of the material. We argue that this can be explained by a significant enhancement of the “ideal” (noncooperative) melting temperature arising from the cooperativity of the particle motion in the liquid state above $T_{\mathrm{m}}$. Therefore, a reassessment of the currently widely accepted microscopic understanding of crystal melting, still founded on the general ideas that lead to the time-honored Lindemann melting criterion, may be necessary.

This paper delves into the connection between flat and curvilinear magnetization dynamics. For this, we numerically study the evolution of the magnon spectrum of rectangular waveguides upon rolling its cross section up to a full tube. Magnon spectra are calculated over a wide range of magnetization states using a finite-element dynamic-matrix method, which allows us to trace the evolution of the magnon frequencies and several critical magnetic fields with increasing curvature. By analyzing the parity of the higher-order magnon modes, we find a curvature-induced mode heterosymmetry that originates from a chiral contribution to the exchange interaction and is related to the Berry phase of magnons in closed loops. Importantly, this curvature-induced parity loss has profound consequences for the linear coupling between different propagating magnons, allowing for hybridization between initially orthogonal modes. In this context, we demonstrate the integral role of edge modes in forming the magnon spectrum in full tubes. Our findings provide theoretical insights into curvilinear magnetization dynamics and are relevant for interpreting and designing experiments in the field.

The recent advent of artificial structures has triggered the emergence of fascinating phenomena that could not exist in natural compounds. A prime example is twisted multilayers, i.e., moiré superlattices represented by magic-angle twisted bilayer graphene (MATBG). As in the case of MATBG, unconventional band hybridization can induce a new type of superconductivity: artificial band engineering by twisting induces properties different from the original systems. Here, we apply this perspective to a monolayer superconductor ${\mathrm{NbSe}}_2$ stacked with a twist on doped graphene. We show that the superconducting states of the ${\mathrm{NbSe}}_2$ layer change dramatically by varying the twist angle. Our result shows that twist tuning, in addition to substrate effects, will provide a strategy for designing monolayer superconductors with high controllability.

In two-dimensional systems with Rashba spin-orbit coupling, it is well known that superconductivity can exhibit mixed spin-singlet and spin-triplet parity, with the $\mathit{d}$ vector of spin-triplet pairing aligning parallel to the $\mathit{g}$ vector of Rashba spin-orbit coupling. In this work, we propose a model to describe a two-dimensional system with unconventional Rashba bands and investigate its superconducting properties. We demonstrate that the $\mathit{d}$ vector of spin-triplet pairing can be either parallel or perpendicular to the $\mathit{g}$ vector of Rashba spin-orbit coupling, depending on the nature of the pairing interaction. We also propose a junction setup to identify the predominant pairing in such two similar pairing channels. Additionally, our model predicts the emergence of a subleading spin-singlet chiral $p$-wave topological superconducting state. Significantly, we find that such unconventional Rashba bands and superconducting pairings can be realized on the surface of certain superconducting topological materials, such as trigonal layered ${\mathrm{PtBi}}_2$.

We define the entanglement entropy of free fermion quantum states in an arbitrary space-time slice of a discrete set of points and particularly investigate timelike (causal) slices. For one-dimensional lattice free fermions with an energy bandwidth $E_0$, we calculate the time-direction entanglement entropy $S_A$ in a time-direction slice of a set of times $t_n=n\tau$ $(1\le n\le K)$ spanning a time length $t$ on the same site. For zero-temperature ground states, we find that $S_A$ shows volume law when $\tau \gg {\tau }_0=2\pi /E_0$; in contrast, $S_A\sim \frac{1}{3}lnt$ when $\tau ={\tau }_0$, and $S_A\sim \frac{1}{6}lnt$ when $\tau <{\tau }_0$, resembling the Calabrese-Cardy formula for one flavor of nonchiral and chiral fermion, respectively. For finite-temperature thermal states, the mutual information also saturates when $\tau <{\tau }_0$. For noneigenstates, volume law in $t$ and signatures of the Lieb-Robinson bound velocity can be observed in $S_A$. For generic space-time slices with one point per site, the zero-temperature entanglement entropy shows a clear transition from area law to volume law when the slice varies from spacelike to timelike.

We report on spin atomistic calculations used to model static and dynamic magnetic properties of inhomogeneous ultrathin iron films. Active magnetic layers in next-generation spintronic devices are becoming so thin that they exhibit some variable degree of roughness at the low scale making them magnetically inhomogeneous. We propose a multiscale approach to progressively shift from a rough atomic-scale system to an ensemble of macrospins. By studying nanoscale islands of atoms in contact with each other, we demonstrate that ultrathin rough layers can be described by a set of macrospins coupled by a Heisenberg-like exchange interaction driven by the existence and shape of nanoconstrictions linking the islands. We show that the magnetization dynamics at 0 K is strongly impacted by this surface morphology since the resonant frequency of a typical ultrathin iron layer can drop by up to an order of magnitude due to inhomogeneities. Additionally, we used Monte Carlo simulations to determine the ferromagnetic-paramagnetic and spin-reorientation transition temperatures for various morphology parameters and we show how nanoconstrictions and shapes of the atomic clusters can modify these transition temperatures. Our results demonstrate the possibility to account for the morphology of ultrathin structures with significant roughness. We believe that our approach makes it possible to model complete devices as close as possible to experimental reality.

In this work, lateral displacements of transmitted and reflected spin waves at a 360-degree domain wall (360DW), which is referred to as the spin-wave Goos-Hänchen effect (SWGHE), are systematically investigated in magnetic heterostructures with perpendicular easy/hard axis and wall-extension direction. Similar to the counterpart at heterochiral interfaces, the interfacial Dzyaloshinskii-Moriya interaction (IDMI) originated from a heavy-metal substrate is important for the emergence of SWGHE. More interestingly, the SWGHE can even survive in ferromagnets with biaxial anisotropy (either intrinsic or caused by shape anisotropy) in the absence of IDMI due to the unique 360DW-induced potentials which are distinct to the well-known Pöschl-Teller ones. Numerics shows that these lateral displacements are generally fractions of the wavelength of spin waves involved. They can be further enhanced by an array of well-separated 360DWs thus provide a large variety for spin-wave manipulation.

We investigate how strongly interacting bosons, described by the Bose-Hubbard Hamiltonian, transition from the Mott insulator to the superfluid phase and, ultimately, to a regime of vanishing interaction where the system smoothly transitions to an ensemble of free bosons undergoing Bose-Einstein condensation. Our study focuses on bosons residing on a three-dimensional simple cubic lattice, with tight-binding interactions characterized by the kinetic energy $t$ between neighboring lattice sites and on-site repulsion $U$. To achieve this, we develop a formalism based on mapping the original quantum mechanical Hamiltonian onto an effective quantum spherical model. This approach is nonperturbative in interaction energy and spans the entire range of the interaction parameter $U$. Our findings are presented through a series of multiparameter phase diagrams that include temperature, interaction energy, chemical potential, and particle density, highlighting the corresponding critical surfaces and lines. In this context, we address the issue of quantum critical points at fixed densities, which appear as endpoints in the temperature-interaction phase diagram. We also compare our theoretical results, where applicable, with other approaches, including quantum Monte Carlo simulations.

The antiferromagnetism in transition metal compounds is mostly mediated by the bridging anions through a so-called superexchange mechanism. However, in materials like normal spinels $A{B}_2{X}_4$ with local moments only at the $A$ site, such an anion-mediated superexchange needs to be modified. Here we report a new spinel compound ${\mathrm{Co}}_{1+x}{\mathrm{Ir}}_{2-x}{\mathrm{S}}_4$ ($x=0.3$). The physical property measurements strongly suggest an antiferromagnetic-like transition at 292 K in the $\mathrm{Co}\left(A\right)$ diamond sublattice. The first-principle calculations reveal that the nearest-neighbor $\mathrm{Co}\left(A\right)$ spins align antiferromagnetically with an ordered magnetic moment of $1.67{\mu }_{\mathrm{B}}$, smaller than the expected $S=3/2$ for ${\mathrm{Co}}^{2+}$. In the antiferromagnetic state, there exists an inter-cation charge-transfer gap between the nonbonding $\mathrm{Ir}\text{−}{t}_{2\mathrm{g}}$ orbitals at the valence band maximum and the Co-S antibonding molecular orbitals at the conduction band minimum. The small charge transfer energy significantly enhances the virtual hopping between these two states, facilitating a robust long-range superexchange interaction between two neighboring ${\mathrm{CoS}}_4$ complexes, which accounts for the high Néel temperature in ${\mathrm{Co}}_{1+x}{\mathrm{Ir}}_{2-x}{\mathrm{S}}_4$. This inter-cation charge transfer mediated magnetic interaction expands the traditional superexchange theory, which could be applicable in complex magnetic materials with multiple cations.

Density-matrix topology, defined through the geometric property of the relevant modular Hamiltonian, can undergo transitions in the corresponding open-system dynamics. While symmetry considerations are crucial to ensure such a dynamic topological transition, we show that a hidden parity-time symmetry can further facilitate it. Considering the Lindbladian dynamics of a fermionic Gaussian state, we extract the time-evolved density-matrix topology from the single-particle correlation, whose dynamics is governed by a non-Hermitian damping matrix. We show that, for a parity-time symmetric damping matrix and a chiral symmetric correlation matrix, a dynamic transition in the density-matrix topology necessarily occurs in the parity-time unbroken regime where eigenvalues of the damping matrix are real. We illustrate our results using a concrete model, and map out the dynamic phase diagram. Remarkably, we find that the dynamic transition can also happen periodically in the parity-time symmetry broken regime.

The long-sought valley-correlated anomalous Hall effect (AHE) that is manifested in two-dimensional (2D) magnets is typically considered to occur in ferromagnetic triangular and antiferromagnetic honeycomb lattices. Here, we theoretically predict the realizability of valley-correlated AHE in 2D ferromagnetic honeycomb lattice, in which the magnetic triangular sublattices are connected by $M_{xy}T$ symmetry, developing the concept of anomalous dual valley Hall effect. Our model analysis provides a comprehensive understanding of this phenomenon, unveiling that the antiparallel arrangement of the two trigons formed by magnetic atoms is required. Through performing first-principles calculations, such mechanism for realizing anomalous dual valley Hall effect is further demonstrated in monolayer $\mathrm{Li}{\mathrm{Fe}}_4{\mathrm{O}}_6$. Additionally, the anomalous dual valley Hall effect in monolayer $\mathrm{Li}{\mathrm{Fe}}_4{\mathrm{O}}_6$ can be modulated by reversing the magnetization orientation. Our findings enrich the research on valley-correlated AHE in 2D materials.

The time evolution of topological systems is an active area of interest due to their expected applications in fault-tolerant quantum computing. Here, we analyze the dynamics of a noninteracting spinless fermion chain in its topological phase, quenched out of equilibrium by a Hamiltonian belonging to the same symmetry class. Due to particle-hole symmetry, the bulk properties of the system remain intact throughout its evolution. However, the boundary properties may be drastically altered, with the initially localized Majorana edge modes extending across the chain. Up to a timescale $t^{*}$, identified by area-law behavior of the entanglement entropy, these extended edge modes are an example of exotic effects in topological systems out of equilibrium. Further, while local disorder can be utilized to preserve localization and increase $t^{*}$, we still identify nontrivial dynamics in the Majorana polarization and Loschmidt echo.

The anomalous Hall effect (AHE), which provides a bridge between the geometry of quantum wave functions and transport measurements, has been a key focus of intensive studies. In addition to the well-studied linear AHE, governed by the electronic Berry curvature, nonlinear AHE originating from higher-order Berry-curvature multipoles has also been observed in recent studies. Inspired by the third-order AHE and its room temperature sign switching in kagome antiferromagnet FeSn, we investigate the generic sign structure of Berry-curvature-induced third-order AHE in topological magnetic material. We find that in contrast to the linear Hall coefficient, whose sign is determined by the broken time-reversal symmetry, the sign of the third-order Hall coefficient is dictated by the interplay between time-reversal symmetry breaking, magnetic order, and spin-orbit couplings. Our calculations give a picture using third-order AHE response to identify the Fermi-surface topology in the phase space spanned by the in- and out-of-plane magnetization, the spin-orbital coupling strength, and the chemical potential. We further propose realistic experiment setups to systematically reveal the sign structure in the third-order AHE response via continuously rotating the magnetic field directions.

When a two-dimensional $d$-wave altermagnet is grown on a substrate, the interplay of momentum-dependent spin splittings arising from altermagnetism and Rashba spin-orbit coupling gives rise to a nodal band structure with band degeneracies enforced by a $C_{4z}\mathcal{T}$ symmetry. If the $C_{4z}\mathcal{T}$ symmetry is broken by an exchange field, we find that the band degeneracies are immediately lifted, leading to a topological band structure characterized by nontrivial strong and weak topological indices. Remarkably, both the strong topological index and the $Z_2$-valued weak topological indices depend sensitively on the direction of the exchange field. As a consequence of the bulk-defect correspondence, we find that the unique dependence of weak topological indices on the exchange field in this system dictates that the presence or absence of topological bound states at lattice dislocations also depends sensitively on the direction of the exchange field. When the substrate is an $s$-wave superconductor, we find that a similar dependence of band topology on the exchange field gives rise to field-sensitive dislocation Majorana zero modes. As topological dislocation bound states are easily detectable by scanning tunneling microscopy, our findings unveil a promising experimental diagnosis of altermagnetic materials among an ever growing list of candidates.

We investigate a fractional Chern insulator (FCI) candidate arising from moiré bands with higher Chern number $C=2$ on a magic-angle twisted bilayer checkerboard lattice (MATBCB). There are two nearly flat low lying bands in the single-particle energy spectrum under the first magic angle $\varphi \approx 1.{608}^{\circ }$ and chiral limit. We find that MATBCB hosts a nearly uniform Berry curvature distribution and exhibits tiny violation of quantum geometric trace condition in the first moiré Brillouin zone (mBZ), indicating that there is a nearly ideal quantum geometry in MATBCB in single-particle level. Turning on projected Coulomb interactions, we perform exact diagonalization and find a 10-fold ground-state quasidegeneracy in many-body energy spectrum with filling fraction $\nu =1/5$. The 10-fold quasidegenerate ground states further show spectra flow under flux pumping. By diagnosing the particle entanglement spectrum (PES) of the ground states, we obtain a clear PES gap and quasihole state counting consistent with Halperin spin singlet generalized Pauli principle, suggesting that a $C=2$ Abelian fractional Chern insulator is realized in this system.

Termination of the fractional quantum Hall states (FQHSs) and the emergence of Wigner crystal phases at very small Landau-level filling factors ($\nu$) have been of continued interest for decades. Recently, in ultra-high-quality, dilute GaAs two-dimensional electron systems (2DESs), strong evidence was reported for FQHSs at $\nu =1/7,2/13$, and 2/11, which fall in the $\nu =p/(6p\pm 1)$ Jain series of FQHSs, interpreted as integer ($p=1$, 2) QHSs of six-flux composite fermions (${}^6\mathrm{CFs}$). These states are surrounded by strongly insulating phases which are generally believed to be Wigner crystals. Here, we study an ultra-high-quality 2DES confined to an AlAs quantum well where the 2D electrons have a much larger effective mass ($m^{*}\simeq 0.45m_e$) and a smaller dielectric constant ($\epsilon \simeq 10{\epsilon }_0$) compared to GaAs 2D electrons ($m^{*}\simeq 0.067m_e$ and $\epsilon \simeq 13{\epsilon }_0$). This combination of $m^{*}$ and $\epsilon$ renders the Landau-level mixing parameter $\kappa$, defined as the ratio of the Coulomb and cyclotron energies, $\simeq 9$ times larger in AlAs 2DESs ($\kappa \propto m^{*}/\epsilon$). Qualitatively similar to the GaAs 2DESs, we observe an insulating behavior reentrant around a strong $\nu =1/5$ FQHS, and extending to $\nu <1/5$. Additionally, we observe a clear minimum in magnetoresistance at $\nu =2/11$, and an inflection point at $\nu =1/7$ which is very reminiscent of the first report of an emerging FQHS at $\nu =1/7$ in GaAs 2DESs. The data provide evidence for developing QHSs of ${}^6\mathrm{CFs}$ at very small fillings. This is very surprising because $\kappa$ near $\nu \simeq 1/6$ in our sample is very large ($\simeq 4$), and larger $\kappa$ has the tendency to favor Wigner crystal states over FQHSs at small fillings. Our data should inspire calculations that accurately incorporate the role of Landau-level mixing in competing many-body phases of ${}^6\mathrm{CFs}$ at extremely small fillings near $\nu =1/6$.

The electronic properties of one- and two-dimensional biphenylene-based systems, such as nanoribbons and bilayers, are studied within a unified approach. Besides the bilayer with direct (AA) stacking, we found two additional symmetric stackings for bilayer biphenylene that we denote by AB, in analogy with bilayer graphene, and AX, which can be derived by a small translation (slip) from the AA bilayer, with distinct electronic band structures. We combine first-principles calculations with a long-range tight-binding model to provide a realistic effective description of these biphenylene materials. Our approach provides a global framework to analyze realistically the robustness of the characteristic type-II Dirac cones present in all the bilayers studied and of the nanoribbons. In particular, we capture the opening in the Dirac cone for certain nanoribbons, which we relate to the symmetries of the system, as well as the variations caused by different stackings. We expect that these structures will constitute an avenue to explore novel physics, as they occur with bilayer graphene and the one-dimensional derivatives of graphene, such as nanoribbons and nanotubes.