Discrete time crystals are a special phase of matter in which time translational symmetry is broken through a periodic driving pulse. Here, we first propose and characterize an effective mechanism to generate a stable discrete time crystal phase in a disorder-free many-body system with indefinite persistent oscillations even in finite-size systems. Then we explore the sensing capability of this system to measure the spin exchange coupling. The results show strong quantum-enhanced sensitivity throughout the time crystal phase. As the spin exchange coupling varies, the system goes through a sharp phase transition and enters a non-time-crystal phase in which the performance of the probe considerably decreases. We characterize this phase transition as a second-order type and determine its critical properties through a comprehensive finite-size scaling analysis. The performance is independent of the initial states and may even benefit from imperfections in the driving pulse. A simple set of projective measurements can capture the quantum-enhanced sensitivity.

Using near-edge x-ray absorption fine structure (NEXAFS) and resonant inelastic x-ray scattering (RIXS) at the C $K$-edge, we have studied the carbon environment and dynamics in $\kappa {\text{-(BEDT-TTF)}}_2{\mathrm{Cu}}_2{\left(\mathrm{CN}\right)}_3$ and supplemented them by density functional theory calculations. The maximum in the NEXAFS pre-edge is identified to originate mainly from nonequivalent carbon sites of the BEDT-TTF molecule, whereas the anionic carbons contribute to the intensity at higher energy. RIXS spectra show resonant reinforcement of the interorbital excitations, but without a clear set of vibrational harmonics, previously detected in our N $K$-edge RIXS study. This finding points to the strong multimode vibrational excitation of all carbon sites in both (BEDT-$\mathrm{TTF}){{}_2}^{+}$ molecular and ${\mathrm{Cu}}_2\left(\mathrm{CN}\right){{}_3}^{-}$ anionic subsystems, thus demonstrating a strongly disordered environment which might have important implications for the electronic state of the $\kappa {\text{-(BEDT-TTF)}}_2{\mathrm{Cu}}_2{\left(\mathrm{CN}\right)}_3$.

Time interfaces consist of abrupt and spatially uniform changes in the optical properties of a medium. Their periodic occurrence forms photonic time crystals, which offer opportunities to tailor classical and quantum light-matter interactions. Here we explore one-dimensional photonic time quasicrystals, formed when time interfaces occur in a quasiperiodic fashion featuring long-range order. We unveil the emergence of topological phases and Hofstadter butterfly spectra in these systems, and demonstrate that their temporal response emulates the localization of topological edge states, enabling the temporal analog of topological Thouless pumping. Our findings open avenues for topological photonics leveraging time as a synthetic dimension, with functionalities that go beyond their spatial counterparts.

The Brillouin Klein bottle induced by ${\mathbb{Z}}_2$ gauge field has been recently proposed and has sparked growing interest. The momentum-space nonsymmorphic symmetry that it respects fundamentally modifies the Bloch band theory and expands the topological classification. Previous works limited to systems under ${\mathbb{Z}}_2$ gauge field have been developed, leaving the interaction between non-Abelian gauge fields and symmetries untouched. Here, we report theoretical and experimental realization of entwined Klein bottles with two orthogonal sub-bottles induced by $U_2$ non-Abelian gauge field, which stems from the hopping between two inseparable pseudospins. The bilayer acoustic crystals with non-Abelian coupling are constructed here to explore different topologies from the traditional Klein bottles under the Abelian fields. This research sheds light on both first-order and higher-order topologies unexplored in non-Abelian gauge fields, and enriches the topological classification with gauge symmetry beyond the existing paradigms.

We calculate the thermoelectric transport properties of the inverse Heusler compound ${\mathrm{Li}}_2\mathrm{AgSb}$ by first principles calculation, combining self-consistent phonon theory, compression sensing technique, and Boltzmann transport theory. Due to the influence of atomic mass differences, bonding characteristics, and atomic vibrations, the frequency range of the phonon spectrum of the material is expanded, forming multiple band gaps. These band gaps limit some three-phonon (3ph) scattering channels and enhance the four-phonon (4ph) scattering process, thereby significantly improving the anharmonicity of ${\mathrm{Li}}_2\mathrm{AgSb}$. In addition, multiple band gaps also lead to scattering partitioning, and phonon recombination processes occur in the ultrahigh-frequency region. In order to accurately reveal the impact of third-order anharmonicity on material properties, we introduced a bubble diagram to correct phonon self-energy and found that it has a significant impact on thermal conductivity. Furthermore, by combining multiple scattering mechanisms and spin-orbit coupling (SOC), we calculated the electrical transport properties of a direct semiconductor material with multiple band gaps that exhibits a unique band structure, including a highly dispersed multivalley conduction band minimum value and a flat, highly degenerate valence band maximum, resulting in ultrahigh power factors. The result shows that at 900 K and considering SOC, $n$-type ${\mathrm{Li}}_2\mathrm{AgSb}$ can reach a maximum $ZT$ value of 5.86 under consideration of the bubble diagram, while $p$-type ${\mathrm{Li}}_2\mathrm{AgSb}$ can reach a maximum $ZT$ value of 4.96 under consideration of the bubble diagram, so the thermoelectric properties of $n$-type ${\mathrm{Li}}_2\mathrm{AgSb}$ are much better.

We provide a framework to determine the upper bound for the complexity of computing the exact Heisenberg representation of a given operator with respect to a Hamiltonian. Working in the Heisenberg picture, we show that each Hamiltonian defines an equivalence relation, causing the operator space to be partitioned into equivalence classes. Any operator within a specific class never leaves it during the evolution. We provide a method to determine the dimension of the equivalence classes and evaluate it for various models, such as the $XY$ chain and Kitaev model on trees. For classes with a dimensionality that is not excessively large, one can use our framework to compute the exact Heisenberg representation of any operator within that class. Our findings reveal that the complexity of operator evolution in these models grows from the edge to the bulk, which is physically manifested as suppressed relaxation of qubits near the boundary. Our methods serve to reveal several new cases of simulable quantum dynamics, such as $XY$ evolution augmented with certain non-Clifford single-qubit gates. We also introduce an $XY\text{−}ZZ$ model where the dimension of an equivalence class, while exponential in the system size, grows considerably slower than might be naively anticipated, which entails a practical computational advantage when simulating finite systems. Furthermore, we demonstrate how to apply our method to time-dependent Hamiltonians and dissipative systems.

The quest for topological superconductors triggers revived interests in resolving non-$s$-wave pairing channels mediated by phonons. While density functional theory and density functional perturbation theory have established a powerful framework to calculate electron-phonon couplings in real materials in a first-principles way, its application is largely limited to conventional $s$-wave superconductivity. Here, we formulate an efficient and simple-to-use algorithm for first-principles pairing channel analysis, and apply it to several representative material systems.

Recently, altermagnetism (AM) has emerged as a new category of magnetism, alongside conventional antiferromagnetism (AFM) and ferromagnetism. In an AM, superconductivity (SC) is faced with a dilemma that the spin-polarized bands, induced by the broken time reversal ($\mathcal{T}$) symmetry, dominantly support spin-triplet pairing. In contrast, AM spin fluctuations routinely facilitate spin-singlet pairing as in AFM. Consequently, unconventional SC is either absent or weak in AM materials. Here, we propose that stacking two-dimensional (2D) AM materials could resolve this dilemma. Stacked 2D materials have yielded a variety of new electronic properties by altering the symmetries inherent in the monolayer. In a 2D anisotropic Hubbard model, we investigate the general energy dispersions of both single-layer and stacked AM materials. We demonstrate that AM sheet stacking can alter the original symmetries, consequently affecting the energy dispersion. The interlayer magnetic coupling enhances the low $\mathbf{q}$ magnetic fluctuations. $\mathcal{T}$ symmetry is restored in the AA stacking with an antiferromagnetic interlayer coupling and then both the energy dispersion and pairing interaction are in favor of spin-singlet SC. The ferromagnetic interlayer coupling in the AB stacking not only recovers $\mathcal{T}$ symmetry but also supports spin-triplet pairing. It is further anticipated that twisted bilayer AM sheets could exhibit additional novel electronic properties, including topology, flat bands, and collective excitations. Our work illustrates that stacking sheets of AM materials could open up a unique research domain in exploring novel quantum phenomena and offer a fertile ground for potential electronic applications.

Recent developments in spintronics have drawn renewed attention to the spin dynamics of cubic ferromagnetic crystals EuO and EuS. These ferromagnets have the simplest possible magnetic structure, making them the most suitable systems for testing various theoretical models of magnetic materials. A commonly used Weiss mean-field approximation (MFA) provides only a qualitative description of the magnetization temperature dependence $M\left(T\right)$. We develop a consistent theory for $M\left(T\right)$ based on the perturbation diagrammatic technique for spin operators. Our theory is in excellent quantitative agreement with the experimental dependence of $M\left(T\right)$ for EuO and EuS throughout the entire temperature range from $T=0$ to Curie temperature $T_{\mathrm{C}}$. In particular, our theoretical dependence $M\left(T\right)$ demonstrates a scaling behavior $M\left(T\right)\propto {(T_{\mathrm{C}}-T)}^{{\beta }_{*}}$ with the scaling index ${\beta }_{*}\approx 1/3$ in a wide range of temperatures, in agreement with the experimentally observed apparent scaling in EuO and EuS. The scaling behavior with ${\beta }_{*}\approx 1/3$ is manifested in the temperature range $T\lesssim T_{\mathrm{C}}$ where corrections to the magnetization due to its fluctuations $\delta M\left(T\right)\lesssim M\left(T\right)$. To distinguish it from the narrow “critical” range $T\approx T_{\mathrm{C}}$ with $\delta M\left(T\right)>M\left(T\right)$, we term this $T$-range “precritical.” The precritical corrections $\delta M\left(T\right)$ are still large enough to affect the $M\left(T\right)$ behavior. The index ${\beta }_{*}$ fundamentally differs from the “normal” scaling index ${\beta }_{\mathrm{MFA}}=1/2$ predicted by the MFA, which neglects the magnetization fluctuations. We refer to the apparent magnetization scaling with ${\beta }_{*}\approx 1/3$, which emerges in our theory, as “precritical anomalous.”

Most studies on the one-dimensional (1D) Hubbard model with transfer integral $t$ and on-site repulsion $U$ have assumed that for $u=U/4t>0$ and $h=\mu =0$, where $h$ denotes the magnetic field and $\mu$ the chemical potential, its global symmetry is $\mathrm{SO}\left(4\right)=[\mathrm{SU}\left(2\right)\times \mathrm{SU}\left(2\right)]/Z_2$. However, both in 1D and for the $U>0$ Hubbard model on any bipartite lattice it is actually larger and given by $[\mathrm{SU}\left(2\right)\times \mathrm{SU}\left(2\right)\times \mathrm{U}(1)]/Z_2^2=[\mathrm{SO}\left(4\right)\times \mathrm{U}(1)]/Z_2$. The studies of this paper account for the irreducible representations of that symmetry to identify both the spin and charge carriers that populate each of the energy eigenstates that span that model full Hilbert space. The global $\tau$-translational U(1) symmetry beyond $\mathrm{SO}\left(4\right)$ is found to describe the relative translational degrees of freedom of such spin and charge carriers, respectively. We show that important finite-temperature transport quantities as the $h>0$ spin and $\mu >0$ charge stiffnesses and the $h=0$ spin and $\mu =0$ charge diffusion constants are controlled by microscopic processes associated with the spin and charge elementary currents carried by these spin and charge carriers, respectively. We describe the model finite-temperature transport properties in terms of the microscopic processes associated with the spin and charge elementary currents carried by the corresponding carriers. We expect that the general $\tau$- and physical $\alpha$-spin representation used in our study is that suitable to address the open problems on finite-temperature transport in the 1D Hubbard model also discussed in this paper.

Spin-resolved dispersions for the topological insulator ${\mathrm{Mn}}_{1-x}{\mathrm{Ge}}_x{\mathrm{Bi}}_2{\mathrm{Te}}_4$ along the $\overline{K}\overline{\mathrm{\Gamma }}{\overline{K}}^{\prime }$ path of the Brillouin zone were studied using spin- and angle-resolved photoemission spectroscopy with laser radiation with varying Ge concentrations ($x$ from 0.1 to 0.8) for in-plane $\left(s_x\right)$ and out-of-plane $\left(s_z\right)$ spin orientations. Rashba-like states were observed, shifting to lower energies with increasing Ge content and dominating spin-dependent dispersions for $x$ from 50% to 75%. These states exhibit pronounced asymmetry in both in-plane $\left(s_y\right)$ and out-of-plane $\left(s_z\right)$ spin polarizations for opposite $\pm k_{\parallel }$ directions, arising from time-reversal and inversion symmetry breaking. Theoretical calculations confirmed this asymmetry along the $\overline{K}\overline{\mathrm{\Gamma }}{\overline{K}}^{\prime }$ path. Constant energy maps reveal a pronounced $s_z$ spin component along $\overline{\mathrm{\Gamma }}\overline{K}$, with a sign change crossing $\overline{\mathrm{\Gamma }}\overline{M}$. The observed spin polarization suggests potential applications in spin devices based on magnetic topological insulators.

${\mathrm{V}}_2{\mathrm{O}}_3$, an archetypal Mott oxide, undergoes paramagnetic metal to paramagnetic insulator/antiferromagnetic insulator (PM-PI/AFI) transitions, which remain elusive due to the interplay of multiple degrees of freedom. Here, the variations of crystal field and orbital occupation across Mott transitions in ${\mathrm{V}}_2{\mathrm{O}}_3$ thin films are quantitatively identified using x-ray absorption spectroscopy (XAS) at the O $K$ and V $L$ edges. The isostructural PM-PI transition in the strained ${\mathrm{V}}_2{\mathrm{O}}_3$ thin films accompanies by dramatic changes in trigonal crystal field of 0.78–0.98 eV and $a_{1g}{e}_g^{\pi }$ orbital occupation of 54%–39%. Furthermore, the monoclinic distortion in the low-temperature AFI phase gives rise to a larger crystal field than the high-temperature PM and PI phases with the decrease of $a_{1g}{e}_g^{\pi }$ orbital occupation. Accordingly, the temperature- and strain-tuned PM-AFI transitions in the ${\mathrm{V}}_2{\mathrm{O}}_3$ thin films proceed in a similar manner. Our results directly demonstrate the importance of lattice and orbital degrees of freedom and their robust coupling to shed new light on the Mott transitions in ${\mathrm{V}}_2{\mathrm{O}}_3$.

As a typical nonradiative multiphonon transition in semiconductors, carrier capture at defects is critical to the performance of semiconductor devices. Its transition rate is usually calculated using the equal-mode approximation, which assumes that phonon modes and frequencies remain unchanged before and after the transition. Using the carbon substitutional defect $\left({\text{C}}_{\text{N}}\right)$ in GaN as a benchmark, here we demonstrate that the phonon renormalization can be significant during defect relaxation, which causes errors as large as orders of magnitude in the approximation. To address this issue, we consider (i) the Duschinsky matrix connecting the initial-state and final-state phonons, which accounts for the changes in phonon modes and frequencies, and (ii) the off-diagonal contributions in the total transition matrix element, which incorporates the cross terms of electron-phonon interactions between different modes. With this improvement, the calculated transition rates show agreement with experimental results within an order of magnitude. We believe the present method makes one step forward for the accurate calculation of the multiphonon transition rate, especially in cases with large defect relaxations.

The circularly polarized photoluminescence (PL) of excitons induced by application of a magnetic field is investigated experimentally and theoretically for an inhomogeneous ensemble of (In,Al)As/AlAs quantum dots with indirect band gap and type-I band alignment. We demonstrate that the circular polarization degree of the PL shows a nonmonotonic dependence on the dot size and the splitting of the oppositely polarized emission bands is significantly larger than the Zeeman splitting of the excitons in individual dots. The low-energy polarized luminescence band has lower intensity than the high-energy one. The polarization sign of the exciton emission coincides in large dots and the wetting layer, while it is opposite in small dots. A model description of this phenomenon that takes into account the equilibrium populations of long-lived exciton states is developed. The dependence of the exciton $g$ factor on the size of the quantum dot is obtained. Good agreement of the modeled spectra with the experimentally observed ones is achieved without any fitting parameters.

We compare three models of graphene electric conductivity: a nonlocal Kubo model, a local model derived by Falkovsky, and, finally, a nonlocal quantum field theory (QFT) polarization-based model. These models are supposed to provide consistent results since they are derived from the same Hamiltonian. While we confirm that the local model is a proper $\mathit{q}\to \mathit{0}$ limit of both the nonlocal Kubo and the nonlocal QFT model (once losses are added to this last model), we find hard inconsistencies in the nonlocal QFT model as derived and currently used in literature. In particular, in the genuine nonlocal region ($\mathit{q}\ne \mathit{0}$), the available QFT model shows an intrinsic nonphysical plasmalike behavior for the interband transversal electric conductivity at low frequencies (even after introducing the unavoidable losses). The Kubo model, instead, shows the expected behavior, i.e., an almost constant electric conductivity as a function of frequency $\omega$ with a gap for frequencies $\hslash \omega <\sqrt{{\left(\hslash v_{F}q\right)}^2+4m^2}$. We show that the Kubo and QFT models can be expressed using an identical polarization operator ${\mathrm{\Pi }}_{\mu \nu }(\omega ,\mathit{q})$, but they employ different expressions for the electric conductivity ${\sigma }_{\mu \nu }(\omega ,\mathit{q})$. In particular, the Kubo model uses a standard regularized expression, a direct consequence of Ohm's law and causality, as we rigorously rederive. We show that, once the standard regularized expression for ${\sigma }_{\mu \nu }(\omega ,\mathit{q})$ is used in the QFT model, and losses are included, the Kubo and QFT model coincide, and all its anomalies naturally disappear. Our findings show the necessity to appropriately define and regularize the electric conductivity to connect it with the available QFT model. This can be relevant for theory, predictions, and experimental tests in the nanophotonics and Casimir effect communities.

Intercalation of epitaxial graphene on SiC(0001) with Sn results in a well-ordered Sn $(1\times 1)$ structure on the SiC surface with quasifreestanding graphene on top. While the electronic properties of the individual layers have been studied in the past, emerging phenomena arising from possible interlayer interactions between the 2D Sn layer and graphene remain unexplored. We use time- and angle-resolved photoemission spectroscopy to reveal a surprisingly short-lived nonequilibrium carrier distribution inside the Dirac cone of Sn-intercalated graphene. Further, we find that the graphene $\pi$ band exhibits a transient increase in binding energy that we attribute to charging of the graphene layer with holes. We interpret our results with support from density functional theory calculations of the graphene 2D Sn heterostructure that reveal a substantial hybridization between the graphene $\pi$ bands and Sn states, providing a channel for efficient ultrafast charge transfer between the layers. Our results on the graphene 2D Sn model system are expected to trigger similar investigations on related heterostructures obtained by intercalation of epitaxial graphene. Regarding the huge choice of materials that have been successfully intercalated in the past, we believe that the interlayer interactions revealed in the present paper only represent the tip of the iceberg, with many fascinating emerging phenomena to be discovered in the near future.

Tight-binding models provide great insight and are a low-cost alternative to ab initio methods for calculation of a material's electronic structure. These models are used to calculate optical responses, including nonlinear optical effects such as the shift current bulk photovoltaic effect. The validity of tight-binding models is often evaluated by comparing their band structures to those calculated with density functional theory. However, we find that band structure agreement is a necessary but not sufficient condition for accurate optical response calculations. We compute the shift current response and dielectric tensor using a variety of tight-binding models of ${\text{MoS}}_2$, including both Slater-Koster and Wannier tight-binding models that treat the Mo $4d$ orbitals and/or S $3p$ orbitals. We also truncate hoppings in the Wannier function models to next-nearest-neighbor, as is common in tight-binding methods, in order to gauge the effect on optical response. By examining discrepancies in energies and optical matrix elements, we determine the interpolation quality of the different tight-binding models and establish that agreement in both band structure and wave functions is required to accurately model optical response.

The influence of Coulomb interaction on the relaxation of the spin distribution function over the directions of electron momenta is studied by calculating the angular harmonics of the linearized electron-electron collision integral at low temperatures, when the electron gas is degenerate. It is shown that the relaxation rates of the spin distribution function of two-dimensional electron gas are substantially different for even and odd angular harmonics. For even harmonics, the relaxation rate of the spin distribution function is equal to the relaxation rate of the density distribution function, demonstrating a logarithmic increase with the number of harmonic and $T^2$ temperature dependence. For odd harmonics, the relaxation rate does not depend on the number of harmonic and depends on temperature as $T^{2}ln({\varepsilon }_F/T)$, where ${\varepsilon }_F$ is the Fermi energy. The results are used for theoretical investigation of the temperature dependence of spin accumulation rates relating the intensity of external spin pumping with nonequilibrium spin polarization in the electron gas with spin-orbit coupling. This dependence has a maximum when the collisional broadening energy governed by electron-electron scattering exceeds the spin splitting energy, and is sensitive to the difference in the relaxation rates for even and odd harmonics.

Quantum emitters are fundamental to advancing technologies such as secure quantum communication, high-resolution imaging, and quantum computing by enabling on-demand single-photon generation. Precise control over the spectral and radiation characteristics of quantum emitters is crucial for optimizing quantum devices and integrated photonic systems. Nevertheless, traditional designs based on passive materials impose fixed functionality postfabrication, limiting the ability to tune spontaneous emission dynamically. This study introduces time-varying Mie resonators as a dynamic means to achieve real-time control over the spontaneous emission of a quantum source. A theoretical framework combining the time-Floquet method with multipole expansion is developed to model light-matter interactions in time-modulated environments. Our findings reveal that time modulation enables precise control over multipolar resonant modes, compensating for frequency detuning in the quantum emitter's radiation through an optimal feedback strategy. Moreover, we demonstrate that time modulation can facilitate directional control of far-field emission by selectively exciting specific multipoles and manipulating their mutual coupling. We further show that transverse Kerker conditions enhance radiation directionality and that time modulation can convert nonradiating anapole states into radiating modes via symmetry breaking. Our findings provide a comprehensive framework for real-time manipulation of quantum emitter radiation and open up possibilities for unique applications in integrated quantum physics.