Spin-orbit coupling (SOC) leads to splitting of otherwise spin-degenerate bands in noncentrosymmetric materials, even if time-reversal symmetry is present. While this gives rise to well-known phenomena such as the Rashba and Dresselhaus effects, various other terms are allowed based on the point group of the crystal and the electronic Hamiltonian. In this study, we utilize point group representations to illustrate that four different types of SOC terms (Rashba, Dresselhaus, Weyl, and Ising) can emerge in periodic solids. We construct reciprocal-space energy expressions for each type of SOC-induced splitting of opposite-spin bands, and follow a similar procedure to also obtain minimal tight-binding models that capture all types of spin splittings for subgroups of two high-symmetry groups $m\overline{3}m$ and $6/mmm$. Furthermore, we also obtain a complete list of nodal features in the electronic band structure in these systems, distinguishing between crystallographic-symmetry-imposed nodal lines and those imposed by time-reversal symmetry only. Finally, we conclude by presenting a list of materials that host each type of inversion-breaking SOC effects. Our classification of the spin-splitting symmetries in nonmagnetic systems with SOC is the counterpart of the recent classification of spin-splitting symmetries in unconventional magnetic systems without SOC, such as altermagnets and odd-parity magnets. More broadly, our work provides a basis for studying superconductivity and other collective electronic phenomena that are impacted by SOC-induced band splittings in noncentrosymmetric materials.

The evaluation of the electrostatic potential is fundamental to the study of condensed phase systems. We discuss the calculation of the relevant lattice summations by Ewald-type techniques. A model charge density is introduced, that cancels multipole moments of the crystalline charge distribution up to a desired order, for accelerating convergence of the Ewald sums. The method is applicable to calculations of bulk systems, employing arbitrary unit cells in a classical or quantum context, and with arbitrary basis functions to represent the charge density. The efficacy of the method is demonstrated on the calculation of the fundamental gap of the gallium arsenide bulk semiconductor, as a prototype example, where significantly accelerated convergence is numerically confirmed, due to a reduction of the number of two-electron integrals that need to be computed. The approach clarifies a decades-old implementation in the crystal code.

Conventional luminescence intensity ratio (LIR) thermometry based on two thermally coupled levels (TCLs) suffers from an intrinsic trade-off between a large energy gap (ΔE), which is required for high relative sensitivity ($S_r$), and the strong thermal coupling needed to maintain Boltzmann equilibrium. Nonthermally coupled thermometers can also provide high sensitivity and robust performance after appropriate calibration, but their temperature response is generally more system specific because it is not directly constrained by a simple Boltzmann relation. Here, we implement a three-level thermal-coupling scheme in ${\mathrm{Nd}}^{3+}$-doped ${\mathrm{NaYF}}_4$ microparticles to mitigate this sensitivity-thermalization trade-off. The intermediate ${}^4\mathrm{F}_{5/2}$ manifold partitions the ∼1700 ${\mathrm{cm}}^{-1}$ separation between ${}^4\mathrm{F}_{3/2}$ and ${}^4\mathrm{F}_{7/2}$ into two moderate adjacent subgaps of about 800–900 ${\mathrm{cm}}^{-1}$, which is expected to facilitate thermally assisted population redistribution while retaining a large effective $\mathrm{\Delta }E$. At the same time, a thermally enhanced anti-Stokes emission at 753 nm (${}^4\mathrm{F}_{7/2}\to {}^4\mathrm{I}_{9/2}$) and a thermally quenched Stokes emission at 1061 nm (${}^4\mathrm{F}_{3/2}\to {}^4\mathrm{I}_{11/2}$) are combined to construct the LIR, making the intensity ratio strongly temperature dependent and producing a steep absolute LIR response, as reflected by absolute sensitivity ($S_a$). Notably, the 753 nm anti-Stokes emission lies in the NIR-I region, whereas the 1061 nm Stokes emission is located in the NIR-II region. This NIR-I/NIR-II-separated configuration reduces spectral overlap and cross-talk between the two thermometric channels, allowing the thermally enhanced and thermally quenched emissions to be tracked independently in the anti-Stokes/Stokes ratiometric readout. Experimentally, the resulting near-infrared thermometer operates reliably from 298 to 548 K, reaching a maximum $S_r$ of 2.73% ${\mathrm{K}}^{-1}$ at 298 K, while the selected fixed anti-Stokes/Stokes readout exhibits an $S_a$ value of 29.81% ${\mathrm{K}}^{-1}$ at 548 K, with consistent performance under both 864 and 808 nm excitation. Compared with a simple two-level TCL description, this three-level strategy offers a practical way to use a larger overall energy separation while retaining a Boltzmann-type interpretation of the temperature-dependent LIR. This work provides an energy-level engineering approach for designing high-sensitivity luminescent thermometers based on sequential thermal coupling.

We compute the second-harmonic response of two-dimensional topological Dirac semimetals subjected to an in-plane magnetic field. The quantum kinetic equation for the Wigner distribution function is derived and then solved to compute the second-order electric-field contributions to the current density. Both the Berry curvature dipole and the field-induced terms in the current are analyzed across a broad range of model parameters. We propose that our theory can be tested experimentally by measuring the dependence of the anomalous Hall resistivity on the in-plane magnetic field in the surface states of the topological insulator SnTe, in ${\mathrm{WTe}}_2$ and ${\mathrm{WSe}}_2$ monolayers, as well as under applied uniaxial stress in the Kondo lattice material ${\mathrm{Ce}}_3{\mathrm{Bi}}_4{\mathrm{Pd}}_3$ at very low temperatures.

Frustrated Kondo spin-lattice systems away from the antiferromagnetic ground state have been found to display strange metal behavior. In two dimensions (2D), where deviations from bulk systems are expected, the emergence of Kondo spin lattices has recently been observed in van der Waals systems. Metallomolecular interfaces of supramolecular lattices have also been suggested as an alternative 2D Kondo spin-lattice system where a single-ion Kondo effect, as well as an inter-spin-site Ruderman-Kittel-Kasuya-Yosida coupling, has been demonstrated in scanning tunneling microscopy studies. Here, going beyond ultrahigh-vacuum STS studies in metallomolecular interfaces, we report a metastable frustrated antiferromagnetic state, with ultrahigh spin-freezing temperatures $T_{\mathrm{f}}$ ranging from 240 to 300 K on the interfaces of highly textured Pt(111) and Pt(111)/Co films with organic molecules grown in an ultrahigh vacuum of approximately ${10}^{-10}\mathrm{mbar}$. A signature of the expected strange metal behavior in correlated systems is a large Nernst response. In the vicinity of the spin-freezing transition, we measure a large anomalous Nernst effect in the Pt/Co/molecule heterostructures that we attribute to the frustrated 2D Kondo spin lattice interface, with an anomalous Nernst coefficient of at least $3\mu \mathrm{V}/\mathrm{K}$.

We show that the Bell-state phase of a polarization-entangled photon pair controls the biexciton eigenstate distribution produced by entangled two-photon absorption in monolayer ${\mathrm{WSe}}_2$. In a frequency-nondegenerate ladder scheme, two independent valley pathways ($K$ and $K^{\prime }$) share no intermediate state, so the biphoton phase sets the relative amplitude between them. Within the valley-symmetric limit, the phase dependence is contained in the prefactors $1\pm e^{i\phi }$, which are independent of the material response. The resulting selection rule partitions the excitation among biexciton eigenstates according to the Bell-state phase $\phi$. The symmetric Bell state ($\phi =0$) selectively drives bright eigenstates, while the antisymmetric state ($\phi =\pi$) drives the exchange-dark eigenstate. No separable polarization state reproduces this $\phi$-dependent eigenstate distribution. At equal total pair flux, the dark-state pumping rate of the Bell state is twice the upper bound for any separable polarization state. Exceeding this bound certifies polarization entanglement of the source. Including valley dephasing, intervalley scattering, source imperfections, and residual amplitude errors at 4 K, the estimated phase-scan visibility of the eigenstate-resolved pair-absorption rates is $V\gtrsim 0.95$ for broadband spontaneous parametric down-conversion (entanglement time $T_e\sim 100$ fs) with high source concurrence and picosecond-scale valley coherence.

A resistance upturn that occurs in ${\mathrm{SrTiO}}_3$-based two-dimensional electron gases at low temperatures is often attributed to Kondo scattering of carriers from localized spins. We show that the low-temperature transport behavior of the electron gas that forms at the $\gamma \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3/{\mathrm{SrTiO}}_3$ interface is governed by a whole hierarchy of quantum corrections in addition to the Kondo contribution. Upon cooling, the resistance shows a typical Kondo-like upturn, but then decreases due to weak antilocalization, and finally vanishes at the superconducting transition. When superconductivity is suppressed by applying a magnetic field or by reducing the carrier density, a logarithmic correction due to electron-electron interactions appears at millikelvin temperatures. These results show that the low-temperature resistance behavior cannot be accounted for by a Kondo-only interpretation, but requires consideration of several quantum corrections.

The metal-insulator transition is often accompanied by fascinating quantum phenomena, including superconducting domes, antiferromagnetic phase transitions, and quantum spin liquids. Concurrently, kagome materials are predominantly metallic, necessitating the realization of insulating states to fully exploit their significant potential in logic and optoelectronic device applications. To address this, we investigate the electronic transport and magnetic properties in correlated kagome systems with hopping disorder using the determinant quantum Monte Carlo method. Through comprehensive analysis of the kinetic energy, dc conductivity, and density of states at the Fermi level, we demonstrate that the cooperative interplay between hopping disorder and electron correlations promotes electron localization. Within the insulator, an increase in the disorder level reduces the Coulomb interaction required for the Mott transition. Additionally, while disorder partially suppresses antiferromagnetic ordering, it remains insufficient to induce a complete magnetic transition. Finally, we summarize two schematic regions distinguishing between antiferromagnetic metal, correlated Anderson insulator, and disordered Mott insulator. Our study advances the understanding of the metal-insulator transition in kagome systems by disorder and provides actionable insights for experimental control of these transitions.

We investigate Krylov spread complexity for the ground state of two-band Hamiltonians, where the reference state is a generic state on the Bloch sphere. The spread complexity is obtained by using a purely geometric formulation in terms of Bloch sphere data without constructing the circuit Hamiltonian. For generic reference states, the derivative of the spread complexity is logarithmically divergent at the topological phase transition in the Su-Schrieffer-Heeger (SSH) model. We demonstrate that the derivative of the spread complexity is bounded by fidelity susceptibility for general two-band models, indicating the sensitivity of the spread complexity to any gap closing (topological or trivial). This is illustrated in the massive Dirac Hamiltonian with a trivial gap closing. Finally, we introduce a nonunitary duality in the SSH model between the topological and trivial phases, which manifests itself in the spread complexity and fidelity susceptibility.

Energy renormalizations of resident carriers and excitons are studied theoretically, and compared with recent experiments of electrostatically doped ${\mathrm{WSe}}_2$ monolayers. The calculated energy renormalization of resident carriers, subjected to strong out of plane magnetic field, reveals the importance of dynamical screening in transition metal dichalcogenides. The energy renormalization of tightly bound excitons is analyzed through the exchange interaction between the electron (or hole) component of the exciton and resident carriers that share the same spin and valley quantum numbers. Our theory explains the weak energy shift of excitonic resonances despite the strong energy renormalization of resident carriers. We identify the dependence of the energy renormalization on the envelope function of a tightly bound exciton, showing that unlike free electron-hole pairs, this energy renormalization is not the added renormalizations of a resident electron and resident hole.

Resolving where a density-wave gap opens in momentum space is pivotal for identifying the microscopic origin of instabilities in layered nickelates. Using polarization- and symmetry-resolved electronic Raman scattering, we map the momentum dependence of the spin-density-wave (SDW) gap in trilayer ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$. Highly momentum-selective spectral-weight depletion below the SDW transition is observed, indicative of gap formation. Gap openings are observed on the $\alpha$ Fermi pocket at the Brillouin zone (BZ) center and near the BZ boundary region of the $\beta$ pocket, while a conspicuous absence of gap signatures along the diagonal direction of the BZ on the $\beta$ pocket places strong constraints on the underlying scattering mechanism. Comparison with the bilayer compound ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ reveals qualitatively different momentum selectivity of the SDW order, despite similar transition temperatures and energy scales. These results are difficult to reconcile with a scattering wave vector strictly along the $\mathrm{\Gamma }-M$ line and are consistent with a momentum dependent wave vector shifted away from the BZ diagonal. Our work establishes symmetry-resolved Raman scattering as a powerful two-particle probe of momentum-selective SDW instabilities and provides insights into the nature of magnetism in layered nickelates.

We study nonequilibrium mode selection in dissipative exciton-polariton condensates incoherently pumped through an excitonic reservoir in the presence of pure energy relaxation. For a confined system in which the pump profile selects a vortex mode at threshold, we show that energy relaxation qualitatively changes the condensation scenario: as the pump increases, the asymptotic state evolves from a vortex condensate to a periodic coherent two-mode state and then to a ground-state condensate. Pure energy relaxation thus reverses pump-selected excited-state condensation and provides a mechanism for relaxation-induced ground-state selection.

Bound states in the continuum (BICs) have greatly impacted our ability to manipulate light-matter interactions at the nanoscale. However, in periodic structures, BICs are typically realized below the diffraction limit, thus leaving a broad spectral domain largely unexplored. Here, we introduce another type of at-$\mathrm{\Gamma }$ BICs of photonic crystal (PhC) slabs supporting higher-diffraction orders, which we call hybrid BICs (h-BICs), whereby symmetry protection and parameter tuning are utilized to suppress light emission in the zeroth- and higher-diffraction orders, respectively. By tuning certain structural parameters of the PhC slab, we fully characterize the dynamics of the topological structure of these h-BICs, including the generation, merging, splitting, and annihilation of circularly polarized states. We further show that the relative amount of light radiated in the first-order diffraction channels can be effectively controlled by simply breaking the $C_{4v}$ symmetry of the PhC slab. Our findings reveal a versatile approach to realize different types of BICs above the diffraction limit, and could potentially inspire efforts toward the development of photonic nanodevices, such as multivortex-beam generators, frequency converters, and lasers.

We consider a coupled system of a qubit and a magnon mode in which the qubit is weakly driven. We demonstrate that the spectral steady-state responses of both the qubit and the magnon show, in addition to two sidebands split by the coupling, also a peak at the driving frequency with virtually zero linewidth. This phenomenon, which persists at both strong and weak coupling, is an analog of the Heitler effect in atomic physics and shows the path towards building of coherent magnon sources.

The hexagonal MnTe is a prime material candidate for altermagnets, an emerging class of magnetic compounds characterized by the nontrivial interplay of antiparallel spin arrangements with their underlying crystal structures. Recognizing precise knowledge of crystal symmetry as the cornerstone of the spin-group classification scheme, we report here an inversion-symmetry-breaking structural distortion in this compound that has previously been overlooked. Through electron microscopy, second-harmonic-generation (SHG) polarimetry, and Raman spectroscopy experiments, we show that MnTe consistently exhibits local structural domains belonging to the $D_{3h}$ group, potentially resolving key inconsistencies in the earlier interpretations of Raman spectroscopy data. Our finding refines the symmetry analysis of MnTe within the altermagnetic class and sheds light on the mechanism of its magnetocontrollable Néel order.

Ultrafast birefringence oscillations observed in superfluid helium provide evidence for anisotropic quantum squeezing of quasiparticle pairs. The measured response is a superposition of contributions from all vibrational modes, with dominant contributions from rotons, maxons, and Pitaevskii's plateau. The nonzero initial phase follows naturally from multimode interference.

Non-Hermiticity fundamentally breaks conventional dimensional restrictions on localization and thus allows robust metallic states even in one-dimensional systems. However, the mechanism of Anderson localization in higher-dimensional non-Hermitian systems, especially anisotropic ones, remains largely elusive. Here, we demonstrate that the interplay between the non-Hermitian skin effect and complex disorder in a three-dimensional anisotropic Hatano-Nelson model drives direction-dependent phase transitions, referred to as anisotropic Anderson localization. As disorder increases, the system undergoes four distinct phases, in which the non-Hermitian skin effect emerges along certain spatial directions, while Anderson localization occurs along others. A reentrant localization transition appears near the spectral edge, driven by the imaginary parts of both energy and disorder. The coherent potential approximation analysis confirms the disorder-induced phase boundaries obtained from finite-size conductance calculations and naturally explains the origin of this reentrant behavior. Finally, complex energy-level statistics not only identify the complete localization threshold but also confirm that the system belongs to the symmetry class $\mathrm{A}$, which is associated with broken rotational symmetry.

We generalize the classic Néel diagram and identify another type of ferrimagnetic phase that remains fully magnetically compensated below the Curie temperature, forming a continuous line of compensated points. It exhibits zero net magnetization while retaining nonrelativistic, eV-scale reciprocal spin splitting. We further find a persistently enhanced intrinsic switching field over a broad temperature range near the fully compensated phase. Proximity to the compensated line is achieved by minimizing the net local moment while balancing exchange interactions with respect to the number of equivalent atoms in each sublattice. The resulting extended Néel diagram provides practical design rules for engineering fully compensated ferrimagnetic phases via targeted chemical substitution that combines atoms with robust and weak local moments, as demonstrated through density functional theory and Monte Carlo simulations for ${\mathrm{GdCo}}_5$-type ferrimagnets.