The spin Hall effect with nonzero transverse spin current but vanishing charge current has important applications in spintronics. Owing to the half-spin nature of electrons, the spin transport has hitherto been restricted to the rank-1 spin vector, whereas higher-rank spin tensors exist and play important roles in larger-spin ($\ge 1$) systems. For instance, there are five linearly independent rank-2 spin quadrupole tensors, characterizing the spin nematics, in a spin-1 system. While these internal spin-tensor degrees of freedom substantially enrich the quantum phases and dynamics of large-spin ultracold gases, the quantum transport of spin tensors remains largely unexplored yet. Here we investigate the higher-rank spin tensor current and introduce the concept of the spin tensor Hall effect (STHE) in a large-spin system. We find that a net transverse spin tensor current can be driven by an external field in the longitudinal direction, while no lower-rank spin or charge current exists. Significantly, we identify a universal rank-2 spin tensor Hall conductivity $q/8\pi$ (with the carrier charge $q$) in a spin-1 model with intrinsic spin-orbit coupling, which is independent of the detailed model parameters. The STHE requires the violation of time-reversal symmetry (TRS) but can be protected by a unique pseudo-TRS associated with the rank-2 spin tensor. An experimental scheme is proposed to realize and detect the STHE with pseudospin-1 ultracold fermionic atoms and through the spin tensor accumulation. A general route towards the generalization of the STHE for larger spins is provided, using the SU(2) subalgebra and generalized Gell-Mann matrix representation of the $\mathrm{SU}(N$) group. Our work reveals an intrinsic spin tensor transport phenomenon and introduce a new member to the Hall effect families, which may pave the way to spin-tensor-tronics.

Layer-polarized anomalous Hall effect (LPAHE) is an attractive phenomenon in condensed-matter physics from the standpoints of both fundamental interest and device applications. The current LPAHE research is based on the extrinsic paradigm of using external electric fields, in which the generation and control of LPAHE are not straightforward. Here, we propose a mechanism that realizes intrinsic LPAHE in bilayer lattices, through the mediation of sliding physics and Berry curvature. Moreover, this mechanism can render the LPAHE in a controllable and reversible fashion. We analyze the symmetry requirements for a system to host such intrinsic LPAHE. Its validity is further demonstrated in a real material of bilayer $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$. By stacking with broken inversion symmetry, the layer-locked Berry curvature enables the intrinsic LPAHE in bilayer $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$, and the switchable control of its LPAHE is achieved by sliding ferroelectricity. Our work opens a significant alternative direction for LPAHE and two-dimensional materials research.

Parametric scattering dynamics are general and of crucial importance for cavity exciton polaritons. Here, parametric scattering process driven by exciton polariton condensates has been revealed in a 1D ZnO microcavity between the whispering-gallery mode and quasiwhispering-gallery mode. When the occupation of the produced polariton condensate is dense enough, polariton condensates formed on quasiwhispering-gallery mode can be scattered towards the ground state of the adjacent whispering-gallery modes at higher and lower energies. By using the femtosecond angle-resolved spectroscopic imaging technique, the ultrafast dynamics of this intermode polariton parametric scattering have been explicitly observed. The scattering towards a higher mode occurs faster than that to a lower-energy mode by less than a picosecond. The revealed dynamics can not only expand the present investigations on polariton parametric scattering, but also promote the potential applications in, e.g., quantum information processing.

$\mathrm{U}{\mathrm{Te}}_2$ is a recently discovered spin-triplet superconductor. One of the characteristic features of $\mathrm{U}{\mathrm{Te}}_2$ is a magnetic field ($H$)-boosted superconductivity >16 T when $H$ is applied exactly parallel to the $b$ axis. To date, this superconducting (SC) state has not been thoroughly investigated, and the SC properties as well as the spin state of this high-$H$ SC (HHSC) phase are not well understood. In this letter, we performed AC magnetic susceptibility and nuclear magnetic resonance measurements and found that, up to 24.8 T, the HHSC state has bulk nature and is quite sensitive to the $H$ angle and that its SC character is different from that in the low-$H$ SC (LHSC) state. The dominant spin component of the spin-triplet pair is along the $a$ axis in the LHSC state but is changed in the HHSC state along the $b$ axis. Our results indicate that $H$-induced multiple SC states originate from the remaining spin degrees of freedom.

Quantum machine learning offers a promising advantage in extracting information about quantum states, e.g., phase diagram. However, access to training labels is a major bottleneck for any supervised approach, preventing getting insights about new physics. In this Letter, using quantum convolutional neural networks, we overcome this limit by determining the phase diagram of a model where analytical solutions are lacking, by training only on marginal points of the phase diagram, where integrable models are represented. More specifically, we consider the axial next-nearest-neighbor Ising Hamiltonian, which possesses a ferromagnetic, paramagnetic, and antiphase, showing that the whole phase diagram can be reproduced.

Semiconductor excitons are commonly seen as hydrogen atom. This analogy requires a unique hole mass. In reality, this is not so due to the complexity of the semiconductor band structure. The precise consequences on the exciton physics of the Coulomb coupling between heavy and light holes remain a tricky open problem. Through an “optimized perturbative” approach that uses excitons with a flexible hole mass as a basis, we show that for zero exciton wave vector, the heavy-light hole mass difference does not split the $(2\times 4)$ exciton degeneracy in zinc-blende-like semiconductors, the hole mass for binding energy being close to the average mass inverse. By contrast, for nonzero exciton wave vector that physically breaks the crystal symmetry, the exciton degeneracy splits into two branches quantized along the exciton wave vector, with nontrivial center-of-mass dependence not only on the heavy and light hole masses, but also on the electron mass.

We report a combined theoretical and experimental investigation devoted to getting deeper insights into the exotic magnetic properties of the low-dimensional ${\mathrm{SeCuO}}_3$ system, for which the two inequivalent Cu(1) and Cu(2) sites show different quantum dynamics. First-principles calculations based on the density functional theory were performed to extract the magnetic exchange couplings. Briefly, we notably find that (i) the magnetic structure can be decomposed into two subsystems made of strongly antiferromagnetically coupled Cu(1) singlet state dimers and weak antiferromagnetic Cu(2) spin chains and (ii) weak ferromagnetic interactions between the two subsystems lead to magnetic frustration. The present model allows us to reproduce both magnetic susceptibility and torque magnetometry measurements. In addition, high-magnetic-field experiments and density-matrix renormalization-group simulations evidence a half-magnetization plateau at 40–45 T associated with the polarization of the Cu(2) spin chains, while the Cu(1) dimers are expected to reach the triplet state at 210–220 T.

The search for topological magnetism in two-dimensional (2D) magnetic materials is one of the hot topics in spintronics. We present comprehensive studies of magnetic phases in a series of Janus monolayers $\mathrm{Mn}XZ$ (MnAsBr, MnAsI, MnPBr, and MnPCl) and $\mathrm{Cr}YZ$ ($Y=\mathrm{Se}$, Te; and $Z=\mathrm{Cl}$, Br, I) via combining first-principles calculations and atomistic spin model simulations. Sizable Dzyaloshinskii-Moriya interaction can be realized in the $\mathrm{Mn}XZ$ and $\mathrm{Cr}YZ$ monolayers due to their intrinsic inversion symmetry breaking. More interestingly, the $\mathrm{Mn}XZ$ and $\mathrm{Cr}YZ$ monolayers exhibit different degrees of magnetic frustration and isotropic higher-order interactions. Lastly, our atomistic spin model simulations demonstrate that a variety of topological spin textures can be generated by the interplay among complex magnetic interactions. These results provide valuable information and fundamental understanding for topological magnetism in 2D magnets.

We experimentally study how the magnetic correlations develop in a binary alloy close to the ferromagnetic quantum critical point with small-angle neutron scattering (SANS). Upon alloying the itinerant ferromagnet nickel with vanadium, the ferromagnetic order is continuously suppressed. The critical temperature $T_c$ vanishes when vanadium concentrations reach the critical value of $x_c=0.116$ indicating a quantum critical point separating the ferromagnetic and paramagnetic phases. Earlier magnetization and $\mu \mathrm{SR}$ data have indicated the presence of magnetic inhomogeneities in ${\mathrm{Ni}}_{1-x}{\mathrm{V}}_x$ and, in particular, recognize the magnetic clusters close to $x_c$, on the paramagnetic and on the ferromagnetic sides with nontrivial dynamical properties [R. Wang et al., Phys. Rev. Lett. 118, 267202 (2017)]. We present the results of SANS study with full polarization analysis of polycrystalline ${\mathrm{Ni}}_{1-x}{\mathrm{V}}_x$ samples with $x=0.10$ and $x=0.11$ with low critical temperatures $T_c<50$ K. For both Ni-V samples close to $x_c$ we find isotropic magnetic short-range correlations on the nanometer scale persisting at low temperatures. They are suppressed gradually in higher magnetic fields. In addition, signatures of long-range ordered magnetic domains are present below $T_c$. The fraction of these magnetic clusters embedded in the ferromagnetic ordered phase grows toward $x_c$ and agrees well with the cluster fraction estimate from the magnetization and $\mu \mathrm{SR}$ data. Our SANS studies provide new insights into the nature of the inhomogeneities in a ferromagnetic alloy close to a quantum critical point.

The two-dimensional layered insulator $\alpha \text{−}{\mathrm{RuCl}}_3$ is a candidate material for a quantum spin-liquid state, which may be realized when a magnetic field suppresses the antiferromagnetic order present at low temperature. Oscillations in the field dependence of the thermal conductivity, observed for an in-plane magnetic field $B$ up to a critical field $B^{★}$, have been attributed to exotic charge-neutral fermions, viewed as evidence of a quantum spin-liquid state between the critical field $B_c\simeq 7$ T at which the antiferromagnetic phase ends and $B^{★}$. Here we report measurements of the thermal conductivity of $\alpha \text{−}{\mathrm{RuCl}}_3$ as a function of magnetic field up to 15 T applied in two distinct in-plane directions: parallel and perpendicular to the Ru-Ru bond. We find that the number of oscillations between $B_c$ and $B^{★}$ is the same for the two field directions even though the field interval between $B_c$ and $B^{★}$ is different. In other words, the period of the oscillations is controlled by the transition fields $B_c$ and $B^{★}$. We conclude that these are not true oscillations—coming from putative fermions in a spin-liquid state—but anomalies associated with a sequence of magnetic transitions.

Using the reflection positivity method, we provide rigorous proof of the existence of long-range magnetic order for the XY model on the honeycomb lattice for large spins $S\ge 2$. This is in contrast with the result obtained using the same method but on the square lattice—which gives a stable long-range order for spins $S\ge 1$. We suggest that the difference between these two cases stems from the enhanced quantum spin fluctuations on the honeycomb lattice. Using linear spin-wave theory, we show that the enhanced fluctuations are due to the overall much higher kinetic energy of the spin waves on the honeycomb lattice (with Dirac points) than on the square lattice (with good nesting properties).

Dynamic and static crystal lattice properties of ${\mathrm{SrCu}}_2{\left({\mathrm{BO}}_3\right)}_2$ are studied by means of Raman scattering, magnetostriction, and thermal expansion measurements in magnetic fields to 45 T. Raman experiments versus temperature reveal that some phonon modes show an unusual behavior: their frequencies soften (modes at 200 and 450 ${\mathrm{cm}}^{-1}$) while others harden (modes at 385 and 478 ${\mathrm{cm}}^{-1}$) when decreasing the temperature below 15 K. Magneto-Raman experiments show that their field dependence correlates with their respective temperature dependencies; e.g., modes that are hardened with increasing temperature also harden with applied magnetic fields and modes that become softer with temperature also soften with applied fields. We use density functional theory to successfully model and compute the energies of these modes, classifying them into two types: pantograph (modes that soften when decreasing the temperature) and nonpantograph. We conclude that the former involves the modification of the intradimer exchange interaction $J$ and the latter the interdimer $J^{\prime }$. Finally, dilatometry is used to correlate field-dependent Raman modes to the closing of the spin gap as well as fractional-magnetization stripe states $M=1/4$ $M_s$ and $M=1/3$ $M_s$, where $M_s$ is the saturation magnetization.

We investigate emergent odd-frequency pairs and proximity effect in nematic and chiral states of superconducting topological insulators (STIs), such as $M_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ ($M=$ Cu, Sr, Nb). The interplay of pairing symmetry, the orbital degrees of freedom, and strong spin-orbit interaction generates a variety of odd-frequency pairs in the bulk and surface of STIs. The nematic and chiral states are the prototypes of topological superconductors with and without time-reversal symmetry, respectively. We find that the Fermi surface evolution from a closed spheroidal to an open cylindrical shape changes the pairing symmetry from the nematic to chiral state, which causes the evolution of the odd-frequency pairings and surface Andreev bound states (SABSs). In addition, spin polarization of odd-frequency pairs and SABSs stems from the nonunitary pairing in the chiral state. The evolution and spin polarization of odd-frequency pairs and SABSs can be captured by tunnel conductance spectroscopy. Furthermore, we study the anomalous proximity effect in various irreducible representations of STIs. The anomalous proximity effect was originally predicted in spin-triplet superconductor junctions without spin-orbit interaction. Odd-frequency spin-triplet $s$-wave pairs penetrate into diffusive normal (DN) metals and induce a pronounced zero-energy peak of the local density of states in the DN region. Here we demonstrate that contrary to the well-known results, the anomalous proximity effect in STIs is not immune to nonmagnetic impurities. The fragility is attributed to the fact that the proximitized odd-frequency even-parity pairs are admixtures of $s$-wave and non-$s$-wave pairs due to strong spin-orbit interaction inherent to the parent materials.

We investigate resonant inelastic x-ray scattering (RIXS) at the O $K$ edge in insulating cuprates by means of three methods: cluster perturbation theory (CPT), Hartree-Fock approximation (HFA), and exact diagonalization (ED) method. We consider the three-band Hubbard model and show the overall momentum-dependence of the Zhang-Rice singlet (ZRS) excitation and charge-transfer excitation by the CPT combining with the perturbation scheme. A comparison of the RIXS spectra calculated using CPT and HFA reveals different momentum dependencies through the changes in the properties of the upper Hubbard band and the ZRS band. These findings are supported by analyses using the ED method on the RIXS spectra and dynamical charge structure factor.

Circuit complexity has been used as a tool to study various properties in condensed matter systems, in particular as a way to probe the phase diagram. However, compared with measures based on entanglement, complexity has been found lacking. We show that when imposing penalty factors punishing nonlocality, it becomes a much stronger probe of the phase diagram, able to probe more subtle features. We do this by deriving analytical solutions for the complexity in the XY chain with transverse field.

We provide a systematic real-space derivation of the continuum Hamiltonian for a graphene bilayer starting from a microscopic lattice theory, allowing for an arbitrary inhomogeneous smooth lattice deformation, including a twist. Two different microscopic models are analyzed: First, a Slater-Koster like model and, second, an ab initio derived model. We envision that our effective Hamiltonian can be used in conjunction with an experimentally determined atomic lattice deformation in twisted bilayer graphene in a specific device to predict and compare the electronic spectra with scanning tunneling spectroscopy measurements. As a byproduct, our approach provides electron-phonon couplings in the continuum Hamiltonian from microscopic models for any bilayer stacking. In the companion paper [J. Kang and O. Vafek, Phys. Rev. B 107, 075408 (2023)], we analyze in detail the continuum models for relaxed atomic configurations of magic angle twisted bilayer graphene.

Dirac node lines (DNLs) are characterized by Dirac-type linear crossings between valence and conduction bands along one-dimensional node lines in the Brillouin zone (BZ). Spin-orbit coupling (SOC) usually shifts the degeneracy at the crossings thus destroys DNLs, and so far the reported DNLs in a few materials are noninteracting type, making the search for robust interacting DNLs in real materials appealing. Here, via first-principle calculations, we reveal that Kondo interaction together with nonsymmorphic lattice symmetries can drive a robust interacting DNLs in a Kondo semimetal ${\mathrm{CePt}}_2{\mathrm{Si}}_2$, and the feature of DNLs can be significantly manipulated by Kondo behavior in different temperature regions. Based on the density functional theory combining with dynamical mean-field theory $(\mathrm{DFT}+\mathrm{DMFT})$, we predict a transition to Kondo-coherent state at coherent temperature $T_{\mathrm{coh}}\approx 80$ K upon cooling, verified by temperature dependence of $\mathrm{Ce}\text{−}4f$ self-energy, Kondo resonance peak, magnetic susceptibility, and momentum-resolved spectral function. Below $T_{\mathrm{coh}}$, well-resolved narrow heavy-fermion bands emerge near the Fermi level, constructing clearly visualized interacting DNLs locating at the BZ boundary, in which the Dirac fermions have strongly enhanced effective mass and reduced velocity. In contrast, above a crossover temperature $T_{\mathrm{KS}}\approx 600$ K, the destruction of local Kondo screening drives noninteracting DNLs, which are comprised by light conduction electrons at the same location. These DNLs are protected by lattice nonsymmorphic symmetries thus robust under intrinsic strong SOC. Our proposal of DNLs, which can be significantly manipulated according to Kondo behavior provides an unique realization of interacting Dirac semimetals in real strongly correlated materials, and serves as a convenient platform to investigate the effect of electronic correlations on topological materials.

The dielectric properties of the various insulating phases in pure ${\mathrm{V}}_2{\mathrm{O}}_3$ and ${\left({\mathrm{V}}_{0.989}{\mathrm{Cr}}_{0.011}\right)}_2{\mathrm{O}}_3$ crystals have been investigated. Large dielectric constants on the scale of ${10}^3$ were obtained, which were attributed to the backflow effect of normal carriers and also the periodic charge configuration relevant to V-V dimers in an antiferromagnetic insulating state or the bond contraction of V-Cr-V in a paramagnetic insulating phase. We propose that if Cr dopants are arranged nearly uniformly, the charge density of ${\left({\mathrm{V}}_{0.989}{\mathrm{Cr}}_{0.011}\right)}_2{\mathrm{O}}_3$ in the paramagnetic insulating phase will exhibit a doping-induced wavelike distribution in real space, and thus the polarization of the system will be enhanced.

Bulk-boundary correspondence serves as an important feature of topological insulators, including Chern insulators and ${\mathbb{Z}}_2$ topological insulators. These topological insulators have spectral flow in the Wilson-loop spectrum, and they encounter Wannier obstruction. Recent studies show that the bulk topological features may not imply the existence of protected gapless boundary states. Here we address the opposite question: Does the existence of stably protected gapless edge states necessarily imply Wannier obstruction or Wilson-loop winding? We provide an example in which stably protected gapless edge states arise without the aforementioned bulk topological features. This trivialized topological insulator belongs to a new class of systems with non-$\delta$-like Wannier functions. Interestingly, the gapless edge states are not protected by crystalline symmetry; instead, the protection originates from mirror antisymmetry, a combination of chiral and mirror symmetries. Although the protected gapless edge states cannot be captured by bulk topological features, they can be characterized by the spectral flow in the entanglement spectrum.

Using the method developed in the companion paper [O. Vafek and J. Kang, Continuum effective Hamiltonian for graphene bilayers for an arbitrary smooth lattice deformation from microscopic theories, Phys. Rev. B 107, 075123 (2023)], we construct effective continuum theories for two different microscopic tight-binding models of twisted bilayer graphene at a twist angle of $1.{05}^{\circ }$, one Slater-Koster based and the other ab initio Wannier based. The energy spectra obtained from the continuum theory—either for rigid twist or including lattice relaxation—are found to be in nearly perfect agreement with the spectra from tight-binding models when the gradient expansion is carried out to second order, demonstrating the validity of the method. We also analyze the properties of the Bloch states of the resulting narrow bands, finding non-negligible particle-hole symmetry breaking near the $\mathrm{\Gamma }$ point in our continuum theory constructed for the ab initio-based microscopic model due to a term in the continuum theory that was previously overlooked. This reveals the difference with all existing continuum models where the particle-hole symmetry of the narrow band Hilbert space is nearly perfect.