We study the higher-order topological insulators at finite temperature based on a generalized real-space quadrupole moment, which extends the ground-state expectations to ensemble averages. Our study reveals that chiral symmetry alone dictates that the quadrupole moment must be quantized to two values of 0 and $1/2$, even at finite temperature. It is found that finite temperature can induce a topological phase transition from nontrivial to trivial. Furthermore, we found that the anisotropic intracell hopping can lead to a reentrant topological phase transition, in which the system becomes topological again with rising temperature. This reentrant behavior is in stark contrast to the results at zero temperature. We also investigate the effects of the quasiperiodic disordered hopping on the topology. It is found that the initially trivial system can be driven into a topological phase with strong enough disorder strength, which closely resembles the topological Anderson transition. Our work provides an example for studying the finite-temperature topology of higher-order topological insulators.

We investigate heterostructures composed of hexagonal Ge quantum wells embedded within hexagonal ${\mathrm{Si}}_{0.25}{\mathrm{Ge}}_{0.75}$ alloy layers, systematically considering variations in crystallographic orientation, well thickness, and external biaxial strain. This study employs density functional theory together with accurate functionals for calculations of the quasiparticle electronic structure. Overall, the heterostructures exhibit type-I band alignment, with the localization of electron and hole wave functions predominantly within the hexagonal Ge regions. The quantum confinement of both charge carrier types is determined by the orientation and thickness of the Ge layer for three different external strains. The results obtained can be interpreted within a rectangular potential-well model, with characteristic parameters derived from ab initio band structures of hexagonal Ge and ${\mathrm{Si}}_{0.25}{\mathrm{Ge}}_{0.75}$, as well as their strained multiquantum well structures, properly aligned via the branch point energies. Besides confinement energies and subbands, optical transition strengths are also discussed.

Exceptional points (EPs) are special spectral degeneracies of non-Hermitian operators: at the EP, the complex eigenvalues coalesce, i.e., they become degenerate in both their real and imaginary parts. In two-dimensional (2D) photonic crystal lattices, these elements can be tailored through structural engineering. In particular, it is known that a quadratic degeneracy in the photonic band structure can be split into a pair of Dirac points (DPs) by breaking one of the unit-cell symmetries, and each DP can be further split into a pair of EPs by introducing losses. Each EP of the pair is then connected by an open isofrequency curve, called the bulk Fermi arc (BFA). In this work, we introduce a simplified effective Hamiltonian model accounting for the main physical properties of these EPs and BFAs. Then, we systematically investigate, through numerical simulations, how EPs as well as the related BFA depend on the type and amount of broken symmetries in the given 2D unit cell of a realistic photonic crystal slab implementation. Our results show that it is possible to tailor the position and distance of the EP pair in reciprocal space, as well as the curvature and orientation of the associated BFA, by deterministically tuning the unit-cell structure. Importantly, the symmetry-breaking strategy we propose is general and can be applied to a broad range of photonic crystal designs beyond the specific example studied here. This approach opens interesting possibilities for exploiting EPs in applications involving photonic crystal lattices in, e.g., light-emitting devices or fundamental physics studies.

Based on the Bogoliubov-de Gennes theory, we investigate the topological-defect states in a mesoscopic superconducting square with coexisted $d$-wave and extended $s$-wave condensates when the Dresselhaus spin-orbit (SO) interaction and competing antiferromagnetic order are introduced. In the topologically trivial time-reversal symmetry breaking $s+id$ superconducting regime, the single-flux quantum vortex with composite point-like cores undergoes splitting and favors to exhibit the coreless skyrmionic pattern with varying the SO coupling and next-nearest-neighbor (nnn) hopping strengths as well as the temperature. The one-quanta vortex splitting behavior can also be realized by suitable tuning the strength and direction of Zeeman fields. Moreover, when the $s+id$ system evolves into the second-order topological superconducting phase, the zero-energy Majorana corner states remain robust against vortex bound states near half filling. A continuous change in the chemical potential can lead to the modulation of the number and location of Majorana corner modes because of the nucleation of extra fractional-flux one-component vortices inside the mesoscopic sample. Interestingly, an appropriate nnn-hopping strength can lead to the formation of zero-energy fractional vortices, which are expected to host Majorana zero modes. The evolution of low-energy vortex states is also temperature dependent, and the application of an out-of-plane Zeeman field can give rise to a coexisting Majorana-skrymion mode.

We investigate resonant photoluminescence arising from incompressible quantum liquids formed in two-dimensional electron systems. We demonstrate that, for excitons composed of a photoexcited electron occupying the upper spin sublevel of the zeroth Landau level and a valence-band hole, the influence of disorder potential fluctuations on optical recombination is strongly suppressed, indicating complete screening of the disorder. We identify an optical invariant quantity that is insensitive to excitation energy yet strongly dependent on electron temperature, serving as a probe of exciton recombination in quantum liquids. Analysis of this quantity reveals that quantum-liquid formation initiates at $\nu =1/3$ as the electron temperature decreases, consistent with the Laughlin state. Upon further cooling, the range of filling factors exhibiting quantum-liquid behavior expands continuously from $\nu =1/3$ toward $\nu =1/2$. Transitions between distinct incompressible quantum-liquid states occur smoothly, without well-defined phase boundaries separating insulating and conducting regimes. Locally, the system retains quantum-liquid characteristics even as bulk transport measurements indicate finite conductivity. Finally, we present a phase diagram delineating the stability region of incompressible quantum liquids relative to conductive phases.

We theoretically investigate the generation and Josephson current signatures of Floquet Majorana end modes (FMEMs) in a periodically driven altermagnet (AM) heterostructure. Considering a one-dimensional (1D) Rashba nanowire (RNW) proximitized to a regular $s$-wave superconductor (SC) and a $d$-wave AM, we generate both 0- and $\pi$-FMEMs by driving the nontopological phase of the static system. Interestingly, the static counterpart hosts both topological Majorana zero modes (MZMs) and inquisitive nontopological accidental zero modes (AZMs) not originating from any metal-SC interface but rather intrinsic to the bulk of the isolated system. The periodic drive can gap out the static AZMs and generate robust $\pi$-FMEMs, termed as topological AZMs. We topologically characterize the emergent FMEMs via dynamical winding numbers exploiting chiral symmetry of the system. Moreover, we consider a periodically driven Josephson junction comprising a RNW/AM-based 1D topological superconduting setup. We identify the signature of MZMs and FMEMs utilizing the $4\pi$-periodic Josephson effect, distinguishing them from trivial AZMs exhibiting $2\pi$ periodicity, in both static and driven platforms. This Josephson current signal due to Majorana modes survives even in the presence of finite disorder. Our Letter establishes a route to realize and identify FMEMs in AM-based platforms through Floquet engineering and Josephson current response.

This work investigates the electronic and vibrational structures of the pseudo Jahn-Teller (PJT) compound ${\mathrm{Rb}}_2{\mathrm{CuCl}}_4{\left({\mathrm{H}}_2\mathrm{O}\right)}_2$, along with their pressure dependence using optical absorption and Raman spectroscopy. The rhombic $\left({\mathrm{D}}_{2\mathrm{h}}\right)$ local structure of the ${\mathrm{CuCl}}_4{\left({\mathrm{H}}_2\mathrm{O}\right)}_2^{2-}$ complex undergoes a progressive pressure-induced transformation, in which the two short and two long Cu-Cl bonds (perpendicular to the ${\mathrm{H}}_2\mathrm{O}\text{−}\mathrm{Cu}\text{−}{\mathrm{OH}}_2$ axis) converge in length, ultimately suppressing the PJT distortion at 10 GPa. This yields a tetragonal $\left({\mathrm{D}}_{4\mathrm{h}}\right)$ symmetry with four equivalent Cu-Cl bonds. The spectra reveal the crystal-field electronic structure of the complex in both ${\mathrm{D}}_{4\mathrm{h}}$ and PJT-distorted ${\mathrm{D}}_{2\mathrm{h}}$ geometries. Their energies, calculated via the angular overlap model (AOM), accurately describe the ground state and the excited states. Notably, the first crystal-field transition—between PJT-active levels ${\mathrm{a}}_{1\mathrm{g}}(3z^2-r^2)$ and ${\mathrm{b}}_{1\mathrm{g}}(x^2-y^2)$ of ${\mathrm{Cu}}^{2+}$—occurs at 1.32 eV in the PJT-distorted $\left({\mathrm{D}}_{2\mathrm{h}}\right)$ phase but shifts to 1.09 eV in the undistorted ${\mathrm{D}}_{4\mathrm{h}}$ phase, directly quantifying the PJT-induced splitting. The vibrational modes exhibit unusual pressure dependence: The frequency associated with the long Cu-Cl bond in ${\mathrm{D}}_{2\mathrm{h}}$ shows a large pressure shift, while the short Cu-Cl bond mode shifts slightly. These converge at the transition pressure ($P_t$ = 10 GPa), confirming the progressive suppression of the PJT distortion (from $Q_{{\mathrm{b}}_{1\mathrm{g}}}^0=0.7$ Å at ambient pressure to $Q_{{\mathrm{b}}_{1\mathrm{g}}}^0=0$ at $P_t$). A Grüneisen-type model correlates the pressure-dependent Cu-Cl stretching frequencies with bond-distance variations, providing an alternative method to track PJT distortion under pressure. The local volume $V\left(P\right)$ of the complex, derived from this approach, follows a Murnaghan equation of state with a bulk modulus $B_{\mathrm{loc}}=22\left(2\right)$ GPa, consistent with the x-ray diffraction value $(B_{\mathrm{cryst}}=20.5 \mathrm{GPa})$.

We explore the properties of a Gross-Pitaevskii chain subject to an incommensurate periodic potential, i.e., a nonlinear Aubry-André model. We show that the condensate crucially impacts the properties of the elementary excitations. In contrast to the conventional linear Aubry-André model, the boundary between localized and extended states (mobility edge) exhibits nontrivial branching. For instance, in the high-density regime, “tongues” of extended phases at intermediate energies penetrate the domain of localized states. In the low-density case, the situation is opposite, and tongues of localized phases emerge. Moreover, intermediate critical (fractal) states are observed. The low-energy phonon part of the spectrum is robust against the incommensurate potential. Our study shows that accounting for interactions, already at the classical level, leads to highly nontrivial behavior of the elementary excitation spectrum.

In crystalline systems, chiral crystals cannot interconvert to their enantiomorph postsynthesis without undergoing melting-recrystallization processes. However, recent work indicates that ultrafast terahertz-polarized light has been shown to enable dynamic control of structural chirality in the antiferrochiral boron phosphate $\left({\mathrm{BPO}}_4\right)$ crystal. Here, using first-principles calculations combined with nonlinear phonon dynamics simulations, we investigate the underlying physics of phonon chirality in this system. The results demonstrate that polarized optical pumping not only induces chiral phonons but also establishes a chirality-selective filtering mechanism, both of which can be reversibly switched by tuning the polarization of the excitation pulse. Furthermore, under a temperature gradient, the pump-induced chiral phonons give rise to ultrafast phonon magnetization, with its direction also controllable via light polarization. Our findings establish a new paradigm for ultrafast optical control of phonon chirality via dynamic chirality switching, offering promising opportunities for chiral information transfer and the design of chiral phononic devices.

Recent advancements in spintronics and fundamental physical research have brought increased attention to the rare-earth-based magnetically ordered materials. One of the important properties of these materials is the temperature dependence of the spontaneous magnetization $M\left(T\right)$. Recently, a successful framework was proposed for the theoretical description of $M\left(T\right)$ across the entire temperature range from $T=0\mathrm{K}$ to the Curie temperature $T_{{}_{\mathrm{C}}}$ in simple cubic ferromagnetics, EuO and EuS. We extend this approach to compute and analyze $M\left(T\right)$ for a more complex magnetic material: multi-sublattice collinear ferrimagnets such as yttrium iron garnet (YIG) ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$. YIG is a unique material that has a high Curie temperature well above room temperature. It features a cubic crystallographic structure characterized by low anisotropy and minimal spin-orbit interaction. These properties result in an exceptionally low spin-wave damping, which is important for fundamental studies as well as engineering applications. The primary challenge in describing ferrimagnets theoretically arises from its intricate magnetic structure, characterized by multiple magnetic sublattices. We analyzed and generalized for multi-sublattice collinear ferrimagnets two well-known approximations describing $M\left(T\right)$. The first approach is the Bloch $\frac{3}{2}$-law, which describes the suppression of $M\left(T\right)$ due to spin-wave excitation, and is valid in the low-temperature limit $T\ll T_{{}_{\mathrm{C}}}$. The second one is Weiss's mean-field approximation, which provides a reasonable description of $M\left(T\right)$ near $T_{{}_{\mathrm{C}}}$. Using a single tuning parameter, we combine these two approaches to describe $M\left(T\right)$ for any $0\le T\le T_{{}_{\mathrm{C}}}$. The theoretical result for $M\left(T\right)$ aligns well with our measurements and the previously available experimental data across the entire temperature range. We also demonstrate that experimental and theoretical dependencies $M\left(T\right)$ follow the mean-field prediction $\sqrt{{T_{{}_{\mathrm{C}}}-T}^{\phantom{\int }}}$ for almost all temperatures.

The Cooper pair Bose metal (CPBM) is a nonsuperfluid quantum phase in which uncondensed fermion pairs form a “Bose surface” in momentum space. We investigate the CPBM in the two-dimensional spin-anisotropic attractive Hubbard model by tuning the next-nearest-neighbor (NNN) hopping $t^{\prime }$, carrier filling $n$, and spin anisotropy $\alpha$, using large-scale constrained-path quantum Monte Carlo simulations. A moderate NNN hopping $t^{\prime }/t=0.2$ substantially enlarges the CPBM region: the phase extends into weaker anisotropy regimes and coexists with a commensurate charge-density wave (CDW) near half-filling $(n>0.95)$, where CDW order would otherwise dominate at $t^{\prime }=0$. Interestingly, $t^{\prime }$ suppresses the overall CDW peak amplitude and introduces a geometric correlation between the orientations of the Fermi and Bose surfaces: for weak Fermi-surface rotations, the Bose surface remains aligned with the lattice axes, while larger distortions drive both surfaces to rotate in tandem. Momentum-resolved pairing distributions reveal that the bosonic pairing channels are jointly controlled by $t^{\prime }$ and carrier filling $n$. For small $t^{\prime }$, $d_{xy}$-wave correlations dominate across the entire filling range. In contrast, for larger $t^{\prime }$, the dominant pairing symmetry varies with $n$, reflecting a nontrivial interplay between frustration and density. These findings establish carrier filling and NNN hopping as complementary levers for manipulating CPBM stability and provide concrete criteria for identifying nonsuperfluid bosonic matter in cold-atom and correlated-electron systems.

The recent discovery of superconductivity in the bilayer Ruddlesden-Popper nickelate ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ under high pressure has generated much interest in the superconducting pairing mechanism of nickelates. Despite extensive work, the superconducting pairing symmetry in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ remains unresolved, with conflicting results even for identical methods. We argue that different superconducting states in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ are in close competition and highly sensitive to the choice of interaction parameters as well as pressure-induced changes in the electronic structure. Our study uses a multiorbital Hubbard model, incorporating all Ni $3d$ and O $2p$ states. We analyze the superconducting pairing mechanism of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ within the random phase approximation and find a transition between $d$-wave and sign-changing $s$-wave pairing states as a function of pressure and interaction parameters, which is driven by spin fluctuations with different wave vectors. These spin fluctuations with incommensurate wave vectors cooperatively stabilize a superconducting order parameter with $d_{x^2-y^2}$ symmetry for realistic model parameters. Simultaneously, their competition may be responsible for the absence of magnetic order in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$, demonstrating that magnetic frustration and superconducting pairing can arise from the same set of incommensurate spin fluctuations.

Inorganic halide perovskites possessing noncentrosymmetric (NCS) structures are highly desirable for anomalous photovoltaic, ferroelectric, and nonlinear optical (NLO) applications. In this work, we investigate the Ruddlesden-Popper (RP) germanium (Ge) halide perovskites ${\mathrm{Cs}}_2\mathrm{Ge}{X}_4$ ($X=\mathrm{Cl}$, Br, I) to identify low-energy NCS phases and evaluate their NLO properties via first-principles calculations. Starting from the centrosymmetric $I4$/mmm parent phase, we systematically introduce 40 symmetry-allowed structural distortion modes, including 37 octahedral rotation/tilt modes and 3 polar displacement modes, to generate a set of low-symmetry configurations. Our results reveal that NCS configurations are energetically favored in ${\mathrm{Cs}}_2\mathrm{Ge}{X}_4$ relative to their centrosymmetric counterparts, in contrast to analogous lead-based RP perovskites, which tend to stabilize centrosymmetric structures. The lowest energy NCS structure is identified as the polar $\mathit{Pc}$ phase. Symmetry-mode analysis indicates that the polar ${\mathrm{\Gamma }}_5^{-}$ distortion in these Ge-based systems originates from the stereochemically active lone-pair electrons of $\mathrm{G}{\mathrm{e}}^{2+}$, which drives inversion-symmetry breaking and stabilizes the NCS structure. Furthermore, we compute the second-order nonlinear susceptibility and second-harmonic-generation response of $\mathit{Pc}$-phase ${\mathrm{Cs}}_2\mathrm{Ge}{X}_4$, confirming its promising NLO performance. This study provides mechanistic insight into lone-pair-induced noncentrosymmetry in layered germanium halide perovskites and underscores their potential for advanced nonlinear optical applications.

The hydrogen-induced phase transition of α-uranium to uranium hydride proceeds through a metastable intermediate $\alpha \text{−}\mathrm{U}{\mathrm{H}}_{3-x}$ phase, bridging the structural gap between α-U and $\alpha \text{−}\mathrm{U}{\mathrm{H}}_3$. Ab initio molecular-dynamics simulations combined with machine-learned smooth overlap of atomic positions descriptors reveal that elevated hydrogen concentrations promote a stepwise reorganization of uranium and hydrogen sublattices. This intermediate phase exhibits dynamical stability, with hydrogen preferentially occupying tetrahedral interstitial sites and uranium lattice symmetry evolving from orthorhombic to tetragonal and ultimately cubic. Moreover, the energy barriers for each phase transition step and the influence of hydrogen partial pressure and temperature on this process have been clarified. The study provides direct dynamical evidence of the metastable intermediate, elucidating the kinetic and symmetry-breaking pathways underlying the hydrogen-induced transformation. These insights advance the fundamental understanding of uranium hydride formation under realistic conditions and emphasize the critical role of intermediate phases in phase transitions.

Topological spin textures exhibit a hierarchical nature. For instance, magnetic skyrmions, which possess a particlelike nature, can aggregate to form superstructures such as skyrmion strings and skyrmion lattices. Magnetic hopfions are also regarded as superstructures constructed from closed loops of twisted skyrmion strings, which behave as another type of independent particle. However, it remains elusive whether such magnetic hopfions can also aggregate to form higher-level superstructures. Here, we report a stable superstructure with three-dimensional periodic arrangement of magnetic hopfions in a frustrated spin model with easy-plane anisotropy. By comprehensively examining effective interactions between two hopfions, we construct the hopfion superstructure by a staggered arrangement of one-dimensional hopfion chains with Hopf number $H=+1$ and $H=-1$ running perpendicular to the easy plane. Each hopfion chain is threaded by a magnetic meron string, resulting in a nontrivial topological texture with skyrmion number $N_{\mathrm{sk}}=2$ per magnetic unit cell on any two-dimensional cut parallel to the easy plane. We show that this hopfion superstructure is metastable against angular noise, supported by an energy barrier comparable to the dominant exchange interaction, and remains robust across a range of the hopfion density. Furthermore, we demonstrate that superstructures with higher Hopf number can also be stabilized. Our findings extend the existing hierarchy of topological magnets and pave the way for exploring new quantum phenomena and spin dynamics.

Extrinsic scattering by impurities can alter the directions of flow and spin polarization of electrons, significantly advancing the generation and manipulation of electronic spin currents. It should also enable control of these properties of magnons, realizing the generation and manipulation of magnonic spin currents. However, no experimental observation of extrinsic scattering induced analogous magnon phenomenon has been made so far. Here, we report the observation of a thermal voltage converted from the extrinsic scattering induced magnon spin swapping effect in a ferrimagnetic insulator Bi-doped yttrium iron garnet $\mathrm{B}{\mathrm{i}}_1{\mathrm{Y}}_2\mathrm{F}{\mathrm{e}}_5{\mathrm{O}}_{12}$, triggered by an in-plane temperature gradient. The thermal voltage disappears without Bi dopants and shows nearly linear scaling with the Bi amount, leading to an unambiguous ascription of this magnon transport phenomenon to the extrinsic scattering by impurities and ruling out other possible thermoelectric mechanisms. Our study not only provides compelling evidence for the extrinsic scattering induced magnon spin swapping effect by Bi impurities doping, but it also expands the range of materials and the means for controlling magnon transport.

Two-dimensional (2D) van der Waals magnetic materials hold great potential for advancing ultraminiature spintronic and information storage devices. Nevertheless, existing candidates are often constrained by their low magnetic anisotropy energy (MAE) or relatively small magnetic moments. In this work, we predict monolayer ${\mathrm{MnIn}}_2{\mathrm{Se}}_3{\mathrm{I}}_2$ as a 2D magnetic material, exhibiting a substantial local moment of 4.41 μ${}_{\mathrm{B}}/\mathrm{Mn}$ together with a remarkably large MAE of up to $931\mu \mathrm{eV}/\mathrm{Mn}$. Phonon spectra and molecular dynamics simulations confirm that the crystal structure of ${\mathrm{MnIn}}_2{\mathrm{Se}}_3{\mathrm{I}}_2$ is both dynamically and thermodynamically stable. Owing to the pronounced anisotropy in magnetic exchange interactions along the two orthogonal in-plane directions, the system undergoes two distinct magnetic phase transitions at different temperatures. Overall, this study not only identifies ${\mathrm{MnIn}}_2{\mathrm{Se}}_3{\mathrm{I}}_2$ as a promising 2D magnetic candidate for future applications, but also elucidates the intrinsic correlation between its structural stability and magnetic tuning mechanisms.