${\mathrm{CrI}}_2$ is a van der Waals layered material that exhibits helimagnetism that propagates along ribbon chains. This is determined from neutron time-of-flight diffraction measurements. Below $T_N=17$ K in the orthorhombic structure, a screwlike helimagnetic order develops with an incommensurate wave vector of $\mathbf{q}\approx (0.2492,0,0)$ at 8 K. Using density functional theory ($\mathrm{DFT})+U$ calculations, the $J_1\text{−}{J}_2$ model is leveraged to describe the helimagnetism, where $J_1(>0)$ and $J_2(<0)$ correspond, respectively, to a ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor intrachain interaction. The $\mathrm{DFT}+U$ calculations suggest that orthorhombic ${\mathrm{CrI}}_2$ satisfies conditions that favor formation of helimagnetic order.

We report x-ray diffraction and magnetic susceptibility studies of the structural phase transition in $\alpha \text{−}{\mathrm{RuCl}}_3$. By utilizing a single crystal sample with a predominantly single-twin domain, we show that $\alpha \text{−}{\mathrm{RuCl}}_3$ goes from a high-temperature $C2/m$ structure to a rhombohedral structure with $R\overline{3}$ symmetry at low temperature. While the defining feature of the structural transition is changing the stacking direction from the monoclinic $a$ axis to the $b$ axis, bond-length anisotropy disappears when the structural change occurs, indicating that the local $C_3$ symmetry is restored within the honeycomb layer. The symmetry change is corroborated by the vanishing magnetic anisotropy in the low-temperature structure. Our study demonstrates that the magnetic interaction is extremely sensitive to the structural details in $\alpha \text{−}{\mathrm{RuCl}}_3$, which could explain the sample dependence found in this material.

Rare-earth tritellurides are van der Waals antiferromagnets which have been attracting attention as materials not only with high mobility, but also with various states such as superconductivity under high pressure, incommensurate charge density wave (CDW) phase, and multiple antiferromagnetic phases. In this paper, we perform longitudinal resistivity and Hall resistivity measurements simultaneously in exfoliated $R{\mathrm{Te}}_3$ $(R=\mathrm{La}, \mathrm{Ce}, \mathrm{Tb})$ thin film devices, in order to investigate the influence of magnetic ordering on transport properties in van der Waals magnetic materials. We obtain carrier mobility and concentration using a two-band model, and we observe an increase in carrier mobility in the antiferromagnets ${\mathrm{CeTe}}_3$ and ${\mathrm{TbTe}}_3$ due to the magnetic transition. Especially in ${\mathrm{CeTe}}_3$, the carrier concentration changes drastically below the magnetic transition temperature, suggesting the interaction between the CDW and antiferromagnetic phases. In addition, the analysis of the Shubnikov–de Haas oscillations in ${\mathrm{CeTe}}_3$ supports the possibility of Fermi surface modulation by magnetic ordering. This research will pave the way not only for spintronic devices that take advantage of high mobility, but also for the study of the correlation between CDW and magnetism states in low-dimensional materials.

In BCS superconductors, the superfluid stiffness is virtually constant at low temperature and only slightly affected by the exponentially low density of thermal quasiparticles. Here, we present an experimental and theoretical study on the temperature dependence of superfluid stiffness $\mathrm{\Theta }\left(T\right)$ in a strongly disordered pseudogaped superconductor, amorphous ${\text{InO}}_x$, which exhibits non-BCS behavior. Experimentally, we report an unusual power-law suppression of the superfluid stiffness $\delta \mathrm{\Theta }\left(T\right)\propto T^b$ at $T\ll T_c$, with $b\sim 1.6$, which we measured via the frequency shift of microwave resonators. Theoretically, by combining analytical and numerical methods to a model of a disordered superconductor with pseudogap and spatial inhomogeneities of the superconducting order parameter, we found a qualitatively similar low-temperature power-law behavior with exponent $b\sim 1.6–3$ being disorder-dependent. This power-law suppression of the superfluid density occurs mainly due to the broad distribution of the superconducting order parameter that is known to exist in such superconductors [B. Sacépé et al., Nat. Phys. 7, 239 (2011)], even moderately far from the superconductor-insulator transition. The presence of the power-law dependence $\delta \mathrm{\Theta }\left(T\right)\propto T^b$ at low $T\ll T_c$ demonstrates the existence of low-energy collective excitations; in turn, it implies the presence of a new channel of dissipation in inhomogeneous superconductors caused by subgap excitations that are not quasiparticles. Our findings have implications for the use of strongly disordered superconductors as superinductance in quantum circuits.

Two-dimensional coherent spectroscopy (2DCS) probes the nonlinear optical response of correlated systems. An interesting application is the study of fractionalized excitations, which are challenging to distinguish unambiguously in linear response. Here we demonstrate how the sensitivity of optical matrix elements to variations in the photon polarization allows one to probe different aspects of low-lying excitations in models of the candidate fractionalized materials ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ and ${\mathrm{Nd}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$, which host effective one-dimensional spin chains when subjected to a [110] magnetic field. We show how both fractionalized spinon excitations or conventional magnons can be picked out in the 2DCS response and how the response from polarized spin chains can be used to probe the dipolar-octupolar mixing angle $\theta$ through the relative intensity of one- and two-magnon signals. Further, we find that a [001] polarization of the probe field is particularly sensitive to lower band edge of the spinon continuum and can be used as a measure of the proximity of a quantum critical point in ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$. 2DCS can thus be employed to provide invaluable and detailed information both on the constituent degrees of freedom of a quantum material and on their collective behavior.

We study the dynamical response of vacancy-induced quasiparticle excitations in the site-diluted Kitaev spin liquid with a magnetic field. Due to the flux-binding effect and the emergence of dangling Majorana fermions around each spin vacancy, the low-energy physics is governed by a set of vacancy-induced quasi-zero-energy modes. These localized modes result in unique characteristics of the dynamical spin correlation functions, which intriguingly mimic the single-quasiparticle density of states and further exhibit a quasi-zero-frequency peak. By recognizing the potential observability of these local correlation functions via scanning tunneling microscopy (STM), we show how the STM response is sensitive to the local flux configuration, the magnetic field strength, and the vacancy concentration. Constructing a simple model of the localized modes, we also elucidate how the local correlation functions can be interpreted in terms of the hybridization between these modes.

In the field of structured light, the study of optical vortices and their vectorial extension—vectorial vortex beams—has garnered substantial interest due to their unique phase and polarization properties, which make them appealing for many potential applications. Combining the advantages of vortex beams and anisotropic materials, unique possibilities for electromagnetic field tailoring and manipulation can be achieved in nonlinear optics, quantum and topological photonics. These applications call for a comprehensive modeling framework that accounts for properties of both anisotropic materials and vector vortex beams. In this paper, we describe a semianalytical model that extends the vectorial diffraction theory to the case of focused vortex beams propagating through a uniaxial slab, considering both the cases of scalar and vectorial vortices in the common framework of a Laguerre-Gaussian mode basis. The model aims to provide a comprehensive description of the methodology, enabling the implementation of complex beam transmission through, reflection from, and propagation in uniaxial anisotropic materials for specific applications. As a demonstration of its versatility, we apply the developed approach to describe propagation of high-order vortex beams in uniaxial materials with various dispersion characteristics, exploring the elliptic, hyperbolic and epsilon-near-zero regimes. We show how variations of the medium anisotropy modify the beam structure due to the vectorial nature of their interaction, which results from the different permittivities of the medium for transverse and longitudinal field components. The applicability of the approach can be extended to artificially structured media if they can be described by effective medium parameters. The developed formalism will be useful for modeling interaction of complex beams with uniaxial materials, allowing a common framework for a large variety of situations, which can also be extended beyond the electromagnetic waves.

Recent studies identified spin-order-driven phenomena such as spin-charge interconversion without relying on the relativistic spin-orbit interaction. Those physical properties can be prominent in systems containing light magnetic atoms due to sizable exchange splitting and may pave the way for realization of giant responses correlated with the spin degree of freedom. In this paper, we present a systematic symmetry analysis based on the spin crystallographic groups and identify the physical property of a vast number of magnetic materials up to 1500 in total. By decoupling the spin and orbital degrees of freedom, our analysis enables us to take a closer look into the relation between the dimensionality of spin structures and the resultant physical properties and to identify the spin and orbital contributions separately. In stark contrast to the established analysis with magnetic space groups, the spin crystallographic group manifests richer symmetry including spin-translation symmetry and leads to emergent responses. For representative examples, we discuss the geometrical nature of the anomalous Hall effect and magnetoelectric effect and classify the spin Hall effect arising from the nonrelativistic spin-charge coupling. Using the power of computational analysis, we apply our symmetry analysis to a wide range of magnets, encompassing complex magnets such as those with noncoplanar spin structures as well as collinear and coplanar magnets. We identify emergent multipoles relevant to physical responses and argue that our method provides a systematic tool for exploring sizable electromagnetic responses driven by spin order.

Magnetic structures and spin excitations are studied across the phase diagram of the geometrically frustrated $S=3/2$ quantum antiferromagnet ${\mathrm{Cs}}_2{\mathrm{CoBr}}_4$ in magnetic fields applied along the magnetic easy axis, using neutron diffraction, inelastic neutron scattering, and terahertz absorption spectroscopy. The data are analyzed, where appropriate, using extended $\mathrm{SU}\left(4\right)$ linear spin wave theory. A minimal magnetic Hamiltonian is proposed based on measurements in the high-field paramagnetic state. It deviates considerably from the previously considered models. Additional dilatometry experiments highlight the importance of magnetoelastic coupling in this system.

We report on the coexistence of both normal and topological insulating phases in InAs/GaSb bilayer quantum well induced by the built-in electric field tuned optically and electrically. The emergence of topological and normal insulating phases is assessed based on the evolution of the charge carrier densities, the resistivity dependence of the gap via in-plane magnetic fields, and the thermal activation of carriers. For the Hall bar device tuned optically, we observe the fingerprints associated with the presence of only the topological insulating phase. For another Hall bar processed identically but with an additional top gate, the coexistence of normal and topological insulating phases is found by electrical tuning. Our finding paves the way for utilizing a different electro-optical tuning scheme to manipulate InAs/GaSb bilayer quantum wells to obtain trivial-topological insulating interfaces in the bulk rather than at the physical edge of the device.

The Mott insulator $\alpha \text{−}{\mathrm{RuCl}}_3$ has generated great interest in the community due to its possible field-induced Kitaev quantum spin liquid state. Despite enormous effort spent trying to obtain the form of the low-energy Hamiltonian, there is currently no agreed upon set of parameters which is able to explain all of the data. A key piece of missing information lies in the determination of the magnetic form factor of ${\mathrm{Ru}}^{3+}$, particularly for a true quantitative treatment of inelastic neutron scattering data. Here we present the experimentally derived magnetic form factor of ${\mathrm{Ru}}^{3+}$ in the low spin $4d^5$ state using polarized neutron diffraction within the paramagnetic regime on high-quality single crystals of $\alpha \text{−}{\mathrm{RuCl}}_3$. We observe strong evidence of an anisotropic form factor, expected of the spin-orbit coupled $j_{\text{eff}}=\frac{1}{2}$ ground state. We model the static magnetization density in increasing complexity from simple isotropic cases, to a multipolar expansion, and, finally, ab initio calculations of the generalized $j_{\text{eff}}=\frac{1}{2}$ ground state. Comparison of both single ion models and inclusion of ${\mathrm{Cl}}^{-}$ anions support the presence of hybridization of ${\mathrm{Ru}}^{3+}$ with the surrounding ${\mathrm{Cl}}^{-}$ ligands.

The qualitative reliability of the dynamical mean-field theory (DMFT) is investigated for systems in which either the actual carrier density or the effective carrier density is low, by comparing the exact perturbative and dynamical mean-field expressions of electron-scattering rates and optical conductivities. We study two interacting systems: tight-binding models in which the chemical potential is near a band edge and Dirac systems in which the chemical potential is near the Dirac point. In both systems it is found that DMFT underestimates the low frequency, near-Fermi-surface single-particle scattering rate by a factor proportional to the particle density. The quasiparticle effective mass is qualitatively incorrect for the low density tight-binding model but not necessarily for Dirac systems. The dissipative part of the optical conductivity is more subtle: in the exact calculation vertex corrections, typically neglected in DMFT calculations, suppress the low frequency optical absorption, compensating for some of the DMFT underestimate of the scattering rate. The role of vertex corrections in calculating the conductivity for Dirac systems is clarified and a systematic discussion is given of the approach to the Galilean- or Lorentz-invariant low-density limit. Relevance to recent calculations related to Weyl metals is discussed.

We study the spin-$1/2$ Heisenberg model on the square lattice with the first- and second-nearest-neighbor antiferromagnetic couplings $J_1$ and $J_2$, as well as the three-spin scalar chiral coupling $J_{\chi }$. Using density matrix renormalization group calculations, we obtain a quantum phase diagram of this system for $0\le J_2/J_1\le 1.0$ and $0\le J_{\chi }/J_1\le 1.5$. We identify the Néel and stripe magnetic order phase at small-$J_{\chi }$ coupling. With growing $J_{\chi }$, we identify the emergent chiral spin liquid (CSL) phase characterized by the quantized spin Chern number $C=1/2$ and entanglement spectrum with the quasidegenerate group of levels agreeing with chiral SU(2)${}_1$ conformal field theory, which is an analog of the $\nu =1/2$ Laughlin state in the spin system. In the vicinity of the Néel and CSL phase boundary, our numerical results do not find evidence to support the coexistence of Néel order and topological order that was conjectured by mean-field calculations. In the larger-$J_2$ and -$J_{\chi }$ coupling regime, the entanglement spectrum of the ground state also exhibits the chiral quasidegeneracy consistent with a CSL, but the adiabatic flux insertion simulations fail to obtain the quantized Chern number. By analyzing the finite-size scaling of the magnetic order parameter, we find the vanished magnetic order suggesting a magnetic disorder phase, whose nature needs further studies. Different from the spin-$1J_1\text{−}{J}_2\text{−}{J}_{\chi }$ model, we do not find the coexistent stripe magnetic order and topological order. We also investigate the $J_{\chi }$ dominant regime and find a strong tendency of the system to develop a dimer order rather than the chiral spin magnetic order observed in the spin-1 model. Our results unveil interesting quantum phases in this spin-$1/2$ model and also demonstrate the drastic differences between the spin-$1/2$ and spin-1 cases.

The antiferromagnetic layered compound ${\mathrm{EuCd}}_2{\mathrm{As}}_2$ is widely considered a leading candidate of ideal Weyl semimetals, featuring a single pair of Weyl nodes in its field-induced ferromagnetic state. Nevertheless, this view was recently challenged by an optical spectroscopy study, which suggested that it is a magnetic semiconductor. In this study, we successfully synthesized highly insulating ${\mathrm{EuCd}}_2{\mathrm{As}}_2$ crystals with carrier density reaching as low as $2\times {10}^{15}{\text{cm}}^{-3}$. The magnetotransport measurements revealed a progressive decrease of the anomalous Hall conductivity (AHC) by several orders of magnitude as the carrier density decreases. This behavior contradicts what is expected from the intrinsic AHC generated by the Weyl points, which is independent of carrier density as the Fermi level approaches the charge neutrality point. In contrast, the scaling relationship between AHC and longitudinal conductivity aligns with the characteristics of variable-range hopping insulators. Our results suggest that ${\mathrm{EuCd}}_2{\mathrm{As}}_2$ is a magnetic semiconductor rather than a topological Weyl semimetal.

We study the magnetophotoluminescence of an optically trapped exciton-polariton condensate in a planar semiconductor microcavity with multiple ${\mathrm{In}}_{0.08}{\mathrm{Ga}}_{0.92}\mathrm{As}$ quantum wells. Extremely high condensate coherence time and continuous control over the polariton confinement are among the advantages provided by optical trapping. This allows us to resolve magnetically induced $\sim \mu \mathrm{eV}$ fine-energy shifts in the condensate and identify unusual dynamical regions in its parameter space. We observe polariton Zeeman splitting and, in small traps with tight confinement, demonstrate its full parametric screening when the condensate density exceeds a critical value, reminiscent of the spin-Meissner effect. For larger optical traps, we observe a complete inversion in the Zeeman splitting as a function of power, underlining the importance of condensate confinement and interactions with its background reservoir excitons.

Noncentrosymmetric superconductors can support flat bands of zero-energy surface states in part of their surface Brillouin zone. This requires that they obey time-reversal symmetry and have a sufficiently strong triplet-to-singlet-pairing ratio to exhibit nodal lines in the bulk. These bands are protected by a winding number that relies on chiral symmetry, which is realized as the product of time-reversal and particle-hole symmetry. We reveal a way to stabilize a flat band in the entire surface Brillouin zone, while the bulk dispersion is fully gapped. This idea could lead to a robust platform for quantum computation and represents an alternative route to strongly correlated flat bands in two dimensions, besides twisted bilayer graphene. The necessary ingredient is an additional spin-rotation symmetry that forces the direction of the spin-orbit-coupling vector not to depend on the momentum component normal to the surface. We define a winding number that leads to flat zero-energy surface bands due to bulk-boundary correspondence. We discuss under which conditions this winding number is nonzero in the entire surface Brillouin zone and verify the occurrence of zero-energy surface states by exact numerical diagonalization of the Bogoliubov–de Gennes Hamiltonian for a slab. In addition, we consider how a weak breaking of the additional symmetry affects the surface band, employing first-order perturbation theory and a quasiclassical approximation. We find that the surface states and the bulk gap persist for weak breaking of the additional symmetry but that the band does not remain perfectly flat. The broadening of the band strongly depends on the deviation of the spin-orbit-coupling vector from its unperturbed direction as well as on the spin-orbit-coupling strength and the triplet-pairing amplitude.

${}^{171}\mathrm{Yb}^{3+}$-doped ${\mathrm{Y}}_2{\mathrm{SiO}}_5$ (YSO) crystals are a promising platform for optical quantum memories in long-distance quantum communications. The relevance of this material lies in ${}^{171}\mathrm{Yb}$ long optical and spin coherence times, along with a large hyperfine splitting, enabling long quantum storage over large bandwidths. Mechanisms affecting the optical decoherence are, however, not precisely known, especially since low-temperature measurements have so far focused on the 2 to 4 K range. In this work, we performed two- and three-pulse photon echoes and spectral hole burning to determine optical homogeneous linewidths in two ${}^{171}\mathrm{Yb}$:YSO crystals doped at 2 and 10 ppm. Experiments were performed in the 40 mK to 18 K temperature range, leading to linewidths between 320 Hz, among the narrowest reported for rare-earth ions, and several MHz. Our results show that above $\sim 6$ K, the homogeneous linewidth ${\mathrm{\Gamma }}_h$ is mainly due to an elastic two-phonon process which results in a slow broadening with temperature, with ${\mathrm{\Gamma }}_h$ reaching only 25 kHz at 10 K. At lower temperatures, interactions with ${}^{89}\mathrm{Y}$ nuclear spin flips, paramagnetic defects or impurities, and also Yb-Yb interactions for the higher concentrated crystal are likely the main limiting factor to ${\mathrm{\Gamma }}_h$. In particular, we conclude that the direct effect of a spin and optical excited state lifetime is a minor contribution to optical decoherence in the whole temperature range that is studied. Our results indicate possible paths and regimes for further decreasing homogeneous linewidths or maintaining narrow lines at higher ${}^{171}\mathrm{Yb}$ concentration.

Fermion-to-qubit mappings play a crucial role in representing fermionic interactions on a quantum computer. Efficient mappings translate fermionic modes of a system to qubit interactions with a high degree of locality while using few auxiliary resources. We present a family of locality-preserving fermion-to-qubit mappings that require fewer auxiliary qubits than all existing schemes known to date. One instance requires only 1.016 qubits-per-fermion compared with 1.25 for the best-known locality-preserving mapping by Chen and Xu [PRX Quantum 4, 010326 (2023)]. Our family of mappings (parameterized by integer $n$) establishes a direct trade-off between the number of auxiliary qubits ($1/n^2$) and the circuit length $\left[O\right(logn\left)\right]$. Furthermore, we present a nonlocal variant that combines the strengths of the Jordan-Wigner and Bravyi-Kitaev mappings to give 98% shorter circuits than the Jordan-Wigner mapping. This is achieved by applying seemingly incompatible mappings at different scales, making it possible for their respective strengths to complement each other.

The phase behavior of rhodium (Rh) metal has been studied to 191 GPa and 2700 K using a combination of room-temperature isothermal compression and double-sided flash laser heating experiments. The isothermal compression data have been fitted with a second-order adapted polynomial of order L equation of state (EoS) with best-fitting parameters of $V_0=13.764\left(2\right){\AA }^3/\mathrm{atom}$, $K_0=258\left(3\right)\mathrm{GPa},$ and $K^{\prime }=5.36\left(9\right)$. Two-dimensional maps of the uniaxial stress component $t$ are presented for Rh at different pressures showing the spatial distribution of the local stress state of a relatively high-yield strength material encased in a Bi pressure medium. In addition, a simple, thermal pressure equation-of-state model, based on a single Einstein temperature, has been fitted to the high-pressure-temperature data up to 2700 K at 148 GPa and ambient-pressure thermal expansion data up to 1982 K. Also determined are the best-fitting parameters to reproduce the thermal EoS within the dioptas two-dimensional integration software. The optimized dioptas parameters are $V_0=13.764{\AA }^3/\mathrm{atom}$, $K_0=260.54\mathrm{GPa}$, $K^{\prime }=5.114$, ${\alpha }_T=2.99\times {10}^{-5}$ ${\mathrm{K}}^{-1}$, $\partial {\alpha }_T/\partial T=1.27\times {10}^{-9}$ ${\mathrm{K}}^{-2}$, $\partial K_0/\partial T=-6.43\times {10}^{-5}\mathrm{GPa}/\mathrm{K}$, and $\partial K^{\prime }/\partial T=-9.3\times {10}^{-10}{\mathrm{K}}^{-1}$.

Multipoint vertex functions, and the four-point vertex in particular, are crucial ingredients in many-body theory. Recent years have seen significant algorithmic progress toward numerically computing their dependence on multiple frequency arguments. However, such computations remain challenging and are prone to suffer from numerical artifacts, especially in the real-frequency domain. Here, we derive estimators for multipoint vertices that are numerically more robust than those previously available. We show that the two central steps for extracting vertices from correlators, namely, the subtraction of disconnected contributions and the amputation of external legs, can be achieved accurately through repeated application of equations of motion, in a manner that is symmetric with respect to all frequency arguments and involves only fully renormalized objects. The symmetric estimators express the core part of the vertex and all asymptotic contributions through separate expressions that can be computed independently, without subtracting the large-frequency limits of various terms with different asymptotic behaviors. Our strategy is general and applies equally to the Matsubara formalism, the real-frequency zero-temperature formalism, and the Keldysh formalism. We demonstrate the advantages of the symmetric improved estimators by computing the Keldysh four-point vertex of the single-impurity Anderson model using the numerical renormalization group.