We report the development of an experimental approach to efficiently determine the energy level structure of an individual silicon vacancy (SiV) center in a magnetic field along an arbitrary direction. This approach uses two coupling rates (one each for the ground and the excited states) to characterize the combined effects of static strain and dynamic Jahn-Teller coupling and exploits the fact that orbital Zeeman effects vanish when the magnetic field is normal to the SiV axis. With an analytical expression for the energy level structure of the SiV under a transverse magnetic field, the two coupling rates can be directly derived from two measurements: one on the frequency separation between two spin-conserved transitions and the other on the coherent population trapping resonance of the SiV ground spin states. A detailed comparison between the numerical calculation and the experimental result on the dependence of the spin-conserved splitting on both the amplitude and direction of the magnetic field further reveals unequal orbital magnetic coupling for the ground and excited states, indicating that unequal orbital quenching factors are needed for an accurate description of the SiV energy level structure in a magnetic field.

We experimentally study the dispersion of localized acoustic surface waves (ASWs) supported by an array of coupled membrane-capped cavities. We design, simulate, and characterize a metasurface with a unit cell comprising a simple cylindrical air-filled cavity resonator topped with a tensioned membrane. We show that by tuning the resonance of constituent membrane or cavity, the behavior of the coupled system can reduce the frequency of the lowest supported surface mode by half compared to cavities without membranes. Experimentally obtained dispersion of the ASWs supported by the sample are compared with numerical predictions. With this mechanism, the operating frequency of acoustic surface modes can readily be altered by changing the physical parameters of constituent elements to tune the resonant frequency of the coupled cavity-membrane system.

Exploring valley physics in materials with nonhexagonal crystal structures is a promising avenue for advancing two-dimensional valleytronics. The valley-related Hall effect enables precise electron control by manipulating the valley degree of freedom. Here, we explore the operability of layer-locked multiple valley Hall effects (VHEs) realized in tetragonal altermagnetic/ferromagnetic monolayers $M_2\mathrm{SiC}{X}_2$ (M is a transition metal atom; $X=\mathrm{S}, \mathrm{Se}$). Using tetragonal monolayers ${\mathrm{Cr}}_2\mathrm{SiC}{X}_2$ as examples, we examine their collinear altermagnetic trivial state and collinear ferromagnetic nontrivial state through first-principles calculations. The net layer-locked VHE and anomalous dual VHE arise from valley-layer coupling, nonzero Berry curvature, and spin splitting. Additionally, the net layer-locked anomalous VHE can also be realized and switched by applying a vertical external electric field or uniaxial strain. Our results provide a platform for layer-locked multiple VHEs and highlight the potential of these materials in low-power-consumption spin valleytronic devices.

Multilayer and bulk transition metal dichalcogenides (TMDs) have become alternative platforms for strong light-matter coupling due to their high refractive index and the ability to excite optical modes. In particular, strong coupling between intrinsic excitons and the anapole mode (AM) excited by bulk TMDs has received widespread attention due to the suppressed far-field radiation and enhanced near-field confinement caused by AM. Here, we propose an all-dielectric self-hybridizing disk-ring resonator made of bulk TMD material. We demonstrate that an abnormal anapole mode (AAM) can be excited by the interaction of the AM excited by a single disk with the magnetic quadrupole $\left(Q_m\right)$ mode excited by a single ring. Importantly, we conduct a detailed analysis of the coherent and incoherent strong-coupling processes involving AAM, AM, and intrinsic excitons. Our findings indicate that the AM-exciton strong coupling exhibits reduced incoherent coupling, which we qualitatively attribute to the suppression of radiation decay in AM compared to AAM, thereby inhibiting energy exchange between the system and the continuum base. Furthermore, we demonstrate the robustness of the strong coupling in this system concerning structural parameters, and we explain that this robustness arises from the relatively small contribution of the $\left(Q_m\right)$ mode excited by the ring in the coupling process. Such a self-hybridizing nanostructure provided by this theoretical work may not only offer an attractive platform to explore light-matter interaction in the strong-coupling regime, but it may also show potential applications in realizing novel nanophotonic optical devices.

We explore the nontrivial thermoelectric properties of two-dimensional topological systems. For the Chern insulator, we show that the Seebeck coefficient is fully determined by the Kelvin formula, while the Nernst coefficient vanishes. For a two-dimensional electron gas with Rashba spin-orbit interactions, we reveal how the Berry curvature affects the thermoelectric coefficients, and derive the Mott-like equation for thermopower. We predict a strong variation of the thermopower of a two-dimensional topological insulator with time-reversal symmetry in the ballistic and dissipative regimes. The Kelvin formula applies in the ballistic regime, while the Mott formula holds in the dissipative regime. Importantly, in a system with trapezoidal geometry, the combination of ballistic and dissipative regimes leads to the anomalous Nernst effect. Finally, we analyze a two-dimensional Anderson insulator, where edge modes show distinct temperature behavior of the Seebeck coefficient near the weak localization-strong localization transition temperatures. In the trivial phase, the thermopower exhibits a strong power law temperature dependence, while in the topological phase, both power law and exponential dependencies coexist.

We have investigated cyclotron resonance (CR) in a disk-shaped two-dimensional electron system (2DES) with different environments. We find that the metallic reflector at the back side of the semiconductor substrate leads to significant oscillations in the CR radiative decay rate with frequency. We prove that the discovered effect stems from the modulation of the electric field and photonic density of states at the location of the 2DES. Thus, we observe the Purcell effect for the cyclotron magnetoplasma mode. Our experimental results open a disruptive approach toward boosting the terahertz emission in solid-state devices.

Low-temperature expansion of Ising model has long been a topic of significant interest in condensed matter and statistical physics. In this paper we present new results of the coefficients in the low-temperature series of the Ising partition function on the square lattice, in the cases of a zero field and of an imaginary field $i(\pi /2)k_{B}T$. The coefficients in the low-temperature series of the free energy in the thermodynamic limit are represented using the explicit expression of the density function of the Fisher zeros. The asymptotic behavior of the sequence of the coefficients when the order goes to infinity is determined exactly, for both the series of the free energy and of the partition function. Our analytic and numerical results demonstrate that the convergence radius of the sequence is dependent on the accumulation points of the Fisher zeros, which have the smallest modulus. In the zero field case this accumulation point is the physical critical point, while in the imaginary field case it corresponds to a nonphysical singularity. We further discuss the relation between the series coefficients and the energy state degeneracies, using the combinatorial expression of the coefficients and the subgraph expansion.

Determining the electronic phase diagram of a quantum material as a function of temperature ($T$) and applied magnetic field ($H$) forms the basis for understanding the microscopic origin of transport properties, such as the anomalous Hall effect (AHE) and topological Hall effect (THE). For many magnetic quantum materials, including $\mathrm{Eu}{\mathrm{Al}}_4$, a THE arises from a topologically protected magnetic skyrmion lattice with a nonzero scalar spin chirality. We identified a square skyrmion lattice (sSkL) peak in $\mathrm{Eu}{\left({\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\right)}_4$ ($x=0.9$) identical to the peak previously observed in $\mathrm{Eu}{\mathrm{Al}}_4$ by performing neutron-scattering measurements throughout the phase diagram. Comparing these neutron results with transport measurements, we found that in both compounds the maximal THE does not correspond to the sSkL area. Instead of the maximal THE, the maximal magnetocaloric-effect boundaries better identify the sSkL lattice phase observed by neutron-scattering measurements. The maximal THE therefore arises from interactions of itinerant electrons with frustrated spin fluctuations in a topologically trivial magnetic state.

Hydrides are famous for the possibility of reaching high-$T_{\mathrm{c}}$ superconductivity under high pressure within a conventional mechanism. Here we propose ternary nickel hydrides $M\mathrm{Ni}{\mathrm{H}}_2$ ($M=\mathrm{Li}$, Na) as materials that mirror key aspects of unconventional superconducting cuprates and nickelates while presenting unique characteristics. Compared to Ni oxides, Ni-H bands are wider due to shorter bond lengths and show a smaller charge-transfer energy. This leads to a larger scale of magnetic interactions than for $\mathrm{LaNi}{\mathrm{O}}_2$, which previous works in cuprates suggest should lead to a larger $T_{\mathrm{c}}$. The presence of an interstitial anionic electron orbital, which hybridizes with the $d_{z^2}$ band, induces self-doping in the Ni $d_{x^2-y^2}$ band, enabling metallicity and superconductivity in stoichiometric forms. A $t-J$ model computation yields dominant $d_{x^2-y^2}$ superconducting symmetry for all doping levels. This, combined with the improved thermodynamic stability over known $\mathrm{N}{\mathrm{i}}^{1+}$ oxides, positions $M\mathrm{Ni}{\mathrm{H}}_2$ as compelling materials for unconventional high-$T_{\mathrm{c}}$ superconductivity under standard conditions.

Electric resistivity is examined in the constrained Hilbert space of a doped Mott insulator, which is dictated by a non-Ioffe-Larkin composition rule due to the underlying mutual Chern-Simons topological gauge structure. In the low-temperature pseudogap phase, where holons remain condensed while spinons proliferate, charge transport is governed by chiral spinon excitation, comprising a bosonic spin-$\frac{1}{2}$ at the core of a supercurrent vortex. It leads to vanishing resistivity with the confinement of the spinons in the superconducting phase but low-$T$ divergence of the resistivity once the spinon confinement is disrupted by external magnetic fields. In the latter, the chiral spinons will generate a Hall number $n_H=$ doping concentration $\delta$ and a Nernst effect to signal underlying long-range entanglement between the charge and spin degrees of freedom. Their presence is further reflected in thermodynamic quantities such as specific heat and spin susceptibility. Finally, in the high-temperature spin-disordered phase, it is shown that the holons exhibit linear-$T$ resistivity by scattering with the spinons acting as free local moments, which generate randomized gauge fluxes as perceived by the charge degree of freedom.

The boundary critical behavior of the two-dimensional (2D) quantum antiferromagnetic (AF) XXZ model coupled with either a dangling $\mathrm{spin}\text{−}1/2$ XXZ chain or a dangling two-leg ladder on the boundary is studied with the bosonization and renormalization group analysis. A rich boundary phase diagram is obtained in each case. In the dangling chain case, the boundary either develops a long-range AF order in the easy-plane or the easy-axis direction with extraordinary critical behavior or has a valence bond solid order with ordinary boundary critical behavior. In the case of a dangling two-leg ladder, besides the possible easy-plane or easy-axis AF-ordered phases on the boundary with extraordinary critical behavior, the boundary can form a singlet phase with ordinary critical behavior without breaking any symmetry. These results are consistent with recent numerical simulations on the boundary critical behavior of 2D quantum spin models.

We study the topological order that arises from chiral states with SU(N) or SO(N) edge-state symmetry. This extends our previous study of topological orders that descend from the bosonic $E_8$ quantum Hall state. We use exactly solvable models of coupled electron wires to construct states with $\mathrm{SU}{\left(m\right)}_n, \mathrm{SO}{\left(m\right)}_n$, or $\mathrm{Sp}{\left(m\right)}_n$ topological order for various levels $n$. We use our constructions to write down string operators for various non-Abelian anyons. We thereby provide a systematic, model derivation of quantum Hall states, topological superconductors, and spin liquids with emergent non-Abelian quasiparticle excitations, including those of Ising, metaplectic, and Fibonacci type.

Within a homologous series of cuprate superconductors, variations in the stacking of ${\mathrm{CuO}}_2$ layers influence the collective charge dynamics through the long-range Coulomb interactions. We use O $K$-edge resonant inelastic x-ray scattering to reveal plasmon excitations in the optimally doped trilayer ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{10+\delta }$. The observed plasmon exhibits nearly $q_z$-independent dispersion and a large excitation gap of approximately 300 meV. This mode is primarily ascribed to the ${\omega }_{-}$ mode, where the charge density on the outer ${\mathrm{CuO}}_2$ sheets oscillates out of phase while the density in the inner sheet remains unaltered at $q_z=0$. The intensity of the acoustic ${\omega }_3$ mode is relatively weak and becomes vanishingly small near $(q_x,q_y)=(0,0)$. This result highlights a qualitative change in the eigenmode of the dominant low-energy plasmon with the number of ${\mathrm{CuO}}_2$ layers.

We investigate the behavior of dark soliton solutions and their cloning in a nonresonant, incoherently pumped exciton-polariton condensate influenced by external potentials. The introduction of a Gaussian potential well enables the acquisition of multipole dark solitons. The power and stability of these solitons can be regulated by the properties of the potential. Notably, the one-pole dark soliton, due to its favorable characteristics, is used to facilitate soliton cloning. By employing multiple Gaussian potential wells and initially injecting a one-pole dark soliton into the leftmost wells, we achieve the “shearing clone” of a stable, identical soliton through a gain and loss mechanism. Different from periodically cloning by pumping, the cloned dark soliton from potential can maintain high fidelity over an extended period, even under quantum perturbations, making it a practical approach for stable dark soliton generation. However, successful soliton cloning requires careful control of the width and distance between the Gaussian potential wells, corresponding to a “clone area.” By modulating the number and spacing of the Gaussian potential wells, we can manipulate the “clone area” and the position of soliton cloning. Our investigation demonstrates that soliton cloning arises from the interactions between the solutions, the binding effect of the potential wells, and the gain and loss dynamics of the system. Our proposal offers a promising method for generating and controlling dark soliton, introducing a new approach to achieve soliton cloning in nonequilibrium systems. Additionally, soliton cloning offers potential applications in areas such as the synthesis of molecules and multisoliton clusters, quantum communication technologies.

Efficient carrier separation is a crucial factor in photocatalysis, typically achieved in type-II or $Z$-scheme heterostructures. However, in homostructures, carrier separation remains challenging due to degenerate band alignment. Here, we demonstrate enhanced photogenerated electron-hole separation at a homointerface, enabling superior water-splitting catalysis by leveraging the synergistic effects of sliding ferroelectricity and piezoelectricity. Using two-dimensional ${\beta }_2\text{−}M{A}_2{\mathrm{Z}}_4$ ($M$ = Zr, Hf; $A$ = Si, Ge; $Z$ = N) homostructures as a model system, we reveal that this synergy allows for precise control over the orientation and intensity of polarization. The interlayer vertical polarization increases from ∼2.5 to ∼8.8 pC/m, with a moderate polarization level facilitating Gibbs free-energy reduction toward zero, thereby enhancing the hydrogen evolution reaction (HER). Additionally, the reversible polarization characteristic enables dynamic modulation of carrier distribution across individual sublayers, enabling an ON-OFF switching mechanism for catalysis. Specifically, one polarization direction promotes HER, while the opposite favors the oxygen evolution reaction. Our findings provide a viable strategy for designing high-efficiency ferroelectric and piezoelectric catalysts for water splitting.

We report the discovery of a dynamic magnetic ground state in the ${\mathrm{Yb}}^{3+}$ dimer-based compound ${\mathrm{Yb}}_2{\mathrm{Te}}_5{\mathrm{O}}_{13}$ through various characterization techniques down to sub-Kelvin temperatures. Magnetization measurements reveal the absence of long-range magnetic ordering down to 0.4 K and the onset of magnetic correlations below 1 K. Heat capacity data, measured down to 0.37 K, indicate a small finite energy gap in zero field, $\mathrm{\Delta }\left(0\right)\sim$ 0.55 K, and validate the presence of magnetic correlations with a Kramers doublet ground state ($J_{\text{eff}}$ = 1/2). Further insight is provided by zero-field muon spin relaxation ($\mu \mathrm{SR}$) measurements, which show a gradual slowdown of ${\mathrm{Yb}}^{3+}$ spin fluctuations below 30 K, indicating a dynamic state down to 44 mK. The temperature dependence of the relaxation rate, $\lambda$, confirms the presence of the Orbach process, which is mediated through various crystal electric field levels, complementing the $J_{\text{eff}}$ = 1/2 ground state. Furthermore, longitudinal field $\mu \mathrm{SR}$ measurements performed at 70 mK demonstrate that the ${\mathrm{Yb}}^{3+}$ spins remain dynamic even under an external field of 3200 Oe, with fluctuations becoming stronger with increasing magnetic field. Theoretical investigations further support the dynamic state, revealing competition between intra- and interdimer exchange interactions as the underlying cause. By integrating macroscopic and microscopic measurements with theoretical insights, we propose ${\mathrm{Yb}}_2{\mathrm{Te}}_5{\mathrm{O}}_{13}$ as a quantum spin liquid candidate, opening avenues for research in quantum magnetism.

We study the quasiparticles in chiral double layers with electron pairing within the framework of the Bogoliubov–de Gennes equation. In the presence of an edge it is demonstrated that the quasiparticle modes can be distinguished as edge modes and bulk modes, which appear at different energies. The bulk-edge correspondence is obtained by an analytic continuation from the in-gap edge modes to the bands of bulk modes. By varying the energy we find a transition from localized edge modes to delocalized bulk modes. We calculate the quasiparticle currents, discuss briefly how these currents couple to external currents, and predict how this can be used to control the quasiparticle modes.

The prevailing view on long-range correlations is that they typically attenuate uniformly with distance and temperature, as most interactions either exhibit short-range dominance or decay following a power law. In contrast to this belief, this Letter demonstrates that the intricate interplay between quasiperiodicity and the quasi-one-dimensional (1D) nature of subbands can result in strong long-range coupling without attenuation, a phenomenon referred to as an immortal interaction. Exemplifying a periodically stacked Fibonacci chain, we uncover an immortal interaction with greatly enhanced, persistent long-range coupling. Using negativity, it is shown that this interaction creates stable entanglement that endures over long distances and remains robust at finite temperatures. Additionally, unconventional logarithmic scaling entanglement is revealed, deviating from the traditional area law. These findings offer quasiperiodic quasi-1D systems as a prospective platform for sustaining stable entanglement across exceptionally long distances, even in the presence of finite-temperature effects.

Lithium-rich compounds offer exciting opportunities to explore novel high-pressure phenomena, with their structural, electronic, superconducting, and superionic behaviors attracting increasing attention. Here, using crystal structure prediction and first-principles calculations, we identify three stable Li-Bi compounds at high pressure, including $Fm\text{−}3m$ ${\mathrm{Li}}_3\mathrm{Bi}$, $R\text{−}3m$ ${\mathrm{Li}}_4\mathrm{Bi}$, and $P6/mmm$ ${\mathrm{Li}}_5\mathrm{Bi}$. Notably, ${\mathrm{Li}}_4\mathrm{Bi}$ and ${\mathrm{Li}}_5\mathrm{Bi}$ are identified as electrides, exhibiting metallic characteristics with significant contributions from Li and interstitial quasiatoms near the Fermi level. Electron-phonon coupling simulations predict superconducting transition temperatures of 5.8 K for ${\mathrm{Li}}_4\mathrm{Bi}$ and 6.5 K for ${\mathrm{Li}}_5\mathrm{Bi}$ at 100 GPa. High-temperature molecular dynamics simulations reveal superionic behavior in ${\mathrm{Li}}_4\mathrm{Bi}$ at 2400 K and 100 GPa, driven by cross-layer lithium diffusion, with further heating leading to a liquid phase transition. In contrast, ${\mathrm{Li}}_3\mathrm{Bi}$ is a pressure-tunable semiconductor, with an indirect band gap increasing from 0.73 eV at 50 GPa to 0.98 eV at 150 GPa. This study reveals the diverse physical properties of lithium-bismuth compounds under high pressures and provides a foundation for exploring their potential applications.