The Landau free energy of a compound that benefits from a linear coupling of an electric field and a magnetic field includes a product of the two fields, one polar and time even and one axial and time odd. Evidently, the coefficient of the product of fields is unchanged by a simultaneous change in the directions of space and time, a symmetry operation labeled anti-inversion. Invariance with respect to anti-inversion is the defining symmetry of the linear magnetoelectric (ME) effect included in 58 of 122 magnetic crystal classes, 19 of which prohibit higher-order (nonlinear) contributions to the free energy. In ME compounds, expectation values of some atomic magnetic tensors are invariant with respect to anti-inversion. An invariance shared by the Dirac monopole (an element of charge allowed in Maxwell's equations that has not been observed) and a Zel'dovich anapole, is also known as a Dirac dipole. From the science of materials perspective, it has been established that Dirac multipoles contribute to the diffraction of x rays and neutrons. We identify Dirac monopoles in bulk magnetic properties of iron tellurate (${\mathrm{Fe}}_2\mathrm{Te}{\mathrm{O}}_6$) and a spin ladder ($\mathrm{Sr}{\mathrm{Fe}}_2{\mathrm{S}}_2\mathrm{O}$). They are visible in the diffraction of light using an iron electric dipole–magnetic dipole absorption event. Both cited compounds present a simple antiferromagnetic configuration of axial dipoles, and their different magnetic crystal classes allow a linear ME effect. However, the Kerr effect is symmetry allowed in the spin ladder and forbidden in iron tellurate. Anapoles are forbidden in iron tellurate and allowed in the spin ladder compound, a difference evident in diffraction patterns fully informed by symmetry. More generally, we identify a raft of Dirac multipoles, and axial multipoles beyond dipoles, visible in future experiments using standard techniques with beams of neutrons or x rays tuned in energy to an iron atomic resonance. ME invariance imposes a phase relationship between nuclear (charge) and magnetic contributions to neutron (x-ray) diffraction amplitudes. In consequence, intensities of Bragg spots in an x-ray pattern do not change when helicity in the primary beam is reversed. A like effect occurs in the magnetic diffraction of polarized neutrons.

We propose a compact and highly efficient scheme for solid-state photonic quantum gates. At the core of our scheme is a $SWA{P}^{\varphi }$ gate based on giant Cooper-pair-based optical nonlinearity we predict in a semiconductor-superconductor structure, selectively introducing a phase to the $|{\mathrm{\Psi }}_{+}\rangle$ Bell state. We theoretically demonstrate this scheme on a practical device based on a superconducting contact coupled to a GaAs/AlGaAs waveguide structure. We model the Cooper-pair-induced nonlinear change of the refractive index showing strong nonlinearities at energies close to the superconducting gap inside a semiconductor band. We calculate the fidelity of the proposed $SWA{P}^{\varphi }$ gate, as well as the sensitivity of the gate to device parameters. As short photon wave packets are crucial for efficient higher-order interactions, we investigate the integrated fidelity for short wave packets with different central wavelengths and bandwidths, providing limiting factors as well as possible optimizations. This theoretically demonstrated concept can pave the way toward practical realizations of scalable photonic quantum circuits.

The recent measurement of the de Haas–van Alphen effect in the spin-triplet superconductor ${\mathrm{UTe}}_2$ [D. Aoki et al., J. Phys. Soc. Jpn. 91, 083704 (2022)] supports cylindrical electron and hole Fermi surfaces, which implies that ${\mathrm{UTe}}_2$ is trivial as a 3D time-reversal-invariant topological superconductor. Inspired by this observation, we investigate the possible realization of a topological crystalline superconductor protected by the crystalline symmetry of ${\mathrm{UTe}}_2$. We examine Majorana surface states protected by mirror and twofold rotational symmetries for all symmetry-allowed odd-parity pairing states with time-reversal symmetry and clarify the corresponding topological invariants. It is found that topological crystalline superconductivity can be realized for all irreducible representations of odd-parity pairing states of ${\mathrm{UTe}}_2$, even for cylindrical Fermi surfaces.

Rank-2 toric code (R2TC), a prototypical archetype of the discrete rank-2 symmetric gauge theory, has properties that differ from those of the standard toric code. Specifically, it features a blending of UV and IR in its ground state, restricted mobility of its quasiparticles, and variations in the braiding statistics of its quasiparticles based on their position. In this paper, we investigate various aspects of ${\mathbb{Z}}_N$ rank-2 gauge theory in $(2+1)$-dimensional spacetime. Firstly, we demonstrate that $U\left(1\right)$ rank-2 gauge theory can arise from $U\left(1\right)\times U\left(1\right)$ rank-1 gauge theory after condensing the gauge charges in a specific way. This construction scheme of $U\left(1\right)$ rank-2 gauge theory carries over to the ${\mathbb{Z}}_N$ case simply by Higgsing $U\left(1\right)$ to ${\mathbb{Z}}_N$, after which the resulting rank-2 gauge theory can be tuned to the R2TC. The holonomy operators of R2TC are readily identified using this scheme and are given clear physical interpretation as the pair creation/annihilation of various monopoles and dipoles. Explicit tensor network construction of the ground states of R2TC is given as two copies of the ground states of Kitaev's toric code that are “sewn together” according to the condensation scheme. In addition, through a similar anyon condensation protocol, we present a double semion version of rank-2 toric code whose flux excitations exhibit restricted mobility and semionic statistics. Finally, we identify the generalized discrete symmetries of the R2TC, which are much more complex than typical 1-form symmetries. They include conventional and unconventional 1-form symmetries, such as framed 1-form symmetries and what we call sublattice 1-form symmetries. Using these, we interpret the R2TC's unique properties (UV/IR mixing, position-dependent braiding, etc.) from the modern perspective of generalized spontaneous symmetry breaking and 't Hooft anomalies.

Topological crystalline insulators from the ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Se}$ family host textbook Dirac surface states that are nearly electron-hole symmetric and isotropic in momentum space. The high mobility of charge carriers possible in these materials allows one to reach the quantum limit at reasonably achievable magnetic fields. We exploit this advantage to combine magnetooptical Landau level spectroscopy, Shubnikov–de Haas transport measurement, and consistent modeling of the two experiments to precisely extract the band parameters of the topological states of this system along with their $g$ factor. We find an enhanced $g$ factor with field dependence compared with bulk states. This information is vital to the realization and understanding of novel quantized Hall effect, stemming from the mirror protected valley-degenerate Dirac states of this material family.

Rashba-type spin-orbit coupling is a long-term active topic due to its superiority of magnetic-field-free control of the electron spin. However, numerous Rashba-related works focus on improving the magnitude of the spin splitting that exhibits the traditional in-plane spin polarization. Very few studies concern manipulating the direction of the spin splitting, such as the generation of out-of-plane spin polarization especially in nonmagnetic materials. Intriguingly, this research field has recently become very appealing owing to its great prospects in high-density and energy-efficient spintronic applications. Here, we report a prominent out-of-plane spin polarization in the two-dimensional Dion-Jacobson (DJ) perovskite and reveal that it is the physical origin of the large Rashba spin splitting observed in both experiments and theoretical calculations. Consequently, the spin-split band structures of the studied system must be interpreted by a proposed three-dimensional Rashba model, with the spin polarization mainly along the out-of-plane direction. Moreover, the temperature-dependent Rashba spin splitting shows that both static and dynamical Rashba effects contribute to the total spin splitting, where the out-of-plane spin polarization always dominates the overall splitting. Such a robust generation of this unconventional spin component indicates the significant influence of the in-plane asymmetric crystal field on the spin-orbit interactions. It is worth emphasizing that it is this out-of-plane spin splitting, not the commonly considered in-plane ones, responsible for the reported large band splitting in DJ perovskites. These results present that the studied system may serve as a type of spin source material to explore the attractive out-of-plane spin polarization, which is highly desired for high-density magnetic switching as well as field-free spin-based computing. It also suggests that crystal symmetry engineering can be a promising strategy to manipulate the spin polarization.

The SU(2)-symmetric three-component spin-boson model (also Bose-Kondo model) exhibits different behavior of quantum phase and phase transition from its widely studied single-component counterpart. In this paper we proposed and theoretically studied a model of two separated spins coupled to a common bosonic bath. For our SU(2)-symmetric model, the stable fixed point representing the nonclassical phase and an unstable fixed point corresponding to the transition between the strong-coupling and nonclassical phases can be continuously tuned by the distance between the two spins. Thus the fixed-point collision and annihilation (FPCAA) could be achieved by simply changing the distance. We also studied in detail variations of the values of the two fixed points above as the distance is changed. Our work is essential for realization of FPCAA in such systems and paves the way for studying related physics such as deconfined criticality and quasiuniversality.

We show how to compute the orbital magnetization, as the first-order change of the energy due to an homogeneous magnetic field, within the projector augmented-wave (PAW) formalism of density functional theory, for systems with periodic boundary conditions. To accomplish this, magnetic translation symmetry is invoked together with a perturbative treatment of the density operator, yielding well-posed expressions that account fully for all PAW terms. The terms may be computed in a standard PAW implementation using density functional perturbation theory to compute the necessary wave-function derivatives, rather than the finite-difference approach that has been used previously. In order to obtain nontrivial magnetization, we also impose nuclear magnetic dipole moments on atomic sites of interest, which gives direct access to the chemical shielding, as measured in nuclear magnetic resonance spectroscopy. The resulting expressions have been implemented and tested, and results are shown both for atoms and solids.

Recent observations of superconductivity in moire graphene have led to an intense interest in that system, with subsequent studies revealing a more complex phase diagram including correlated insulators and ferromagnetic phases. Here we propose an alternate system, electrostatically patterned bilayer graphene, in which a supermodulation is induced via metallic gates rather than the moire effect. We show that, by varying either the gap or the modulation strength, bilayer graphene can be tuned into the strongly correlated regime. Further calculations show that this is not possible in monolayer graphene. We present a general technique for addressing Coulomb screening of the periodic potential and demonstrate that this system is experimentally feasible.

We demonstrate the existence of a conceptually distinct topological pumping phenomenon in one-dimensional chains undergoing topological adiabatic cycles. Specifically, for a stack of two semi-infinite chains cycled in opposite directions and coupled at one edge by a gapping potential, we derive a higher-order bulk-boundary correspondence that relates the bulk Chern number associated with the adiabatic cycle of a single infinite chain and the number of electrons transferred between the semi-infinite chains. The relation is formulated using the relative index of two projections and proven using $K$-theoretic calculations. The phenomenon is exemplified using the Rice-Mele model and possible experimental implementations with classical and quantum degrees of freedom are discussed.

We manipulate the coupling effect between interdot tunneling and the external control field to study the optical diffractive property in a quantum dot molecule (QDM) system. Based on the density matrix approach, an analytical relation is obtained for the optical susceptibility, which shows tunneling-induced transparency (TIT) in the absorption spectra. We propose an innovative optoelectronic device called tunneling-induced grating, which operates based on the diffraction of the forward-transmitted probe laser light. The diffraction integrals for the far-field regime (i.e., Fraunhofer diffraction) are numerically solved, and the effect of interdot tunneling coupling strength on the diffraction patterns is studied. It is shown that the transmission is increased under tunneling-induced quantum coherence. The weak probe light can be diffracted into higher-order directions upon applying a standing-wave control field. The optimal parametric condition for maximum first- and second-order diffractions is obtained. The results find the potential applications in quantum information processing devices, such as all-optical grating and switches at low light levels.

Coated and multicoated cylinder systems constitute an appealing metamaterial category, as they allow a very rich and highly tunable response, resulting from the interplay of the many different geometrical and material parameters involved. Here we derive and propose an effective medium approach for the detailed description and analysis of the electromagnetic wave propagation in such systems. In particular, we investigate infinitely-long multilayered cylinders with additional electric and magnetic surface conductivities at each interface. Our effective medium approach is based on the well known in the solid state physics community coherent potential approximation (CPA) method, combined with a transfer matrix-based formulation for cylindrical waves. Employing this effective medium scheme, we investigate two realistic systems, one comprising of cylindrical tubes made of uniform tunable graphene sheets and one of cylinders/tubes formed of metasurfaces exhibiting both electric and magnetic sheet conductivities. Both systems show a rich palette of engineerable electromagnetic features, including tunable hyperbolic response, double negative response, and $\epsilon$-near-zero and $\mu$-near-zero response regions.

The recent discoveries of large anomalous Hall effect (AHE) in antiferromagnets (AFMs) have brought intense study in theories and experiments. Special attention has also been given to the topic of topological Hall effect (THE). Both of them provide a good platform for understanding the interplay between magnetism and transport characteristics. Here, we report the magnetic and electrical transport properties of a layered AFM ${\mathrm{V}}_{0.3}{\mathrm{NbS}}_2$ single crystal. It orders antiferromagnetically below $T_{N1}\sim 53\mathrm{K}$ and exhibits weak magnetic hysteresis loop with a tiny net magnetization ($\approx 16m{\mu }_B/\mathrm{V}$) along the $c$ axis as a result of canted antiferromagnetic configuration. Of particular interest is the realization of AHE in such AFMs with a near-perfect cancellation of moment, which probably originates from the contribution of nonzero Berry curvature. THE is detected at low temperatures, which acts as the probe of spin reorientation in the magnetization process induced by field. The magnetoresistance shows a weak irreversible behavior near zero field, consistent with the hysteresis loop in magnetization and Hall resistivity. It presents a negative value below 7 T, which is ascribed to the spin-dependent scattering. The observation of anomalous transport in ${\mathrm{V}}_{0.3}{\mathrm{NbS}}_2$ serves as a platform for studying AHE within AFMs.

${\mathrm{LaCrGe}}_3$ is an itinerant, metallic ferromagnet with a Curie temperature $\left(T_C\right)$ of $\sim$86 K. Whereas ${\mathrm{LaCrGe}}_3$ has been studied extensively as a function of pressure as an example of avoided ferromagnetic quantum criticality, questions about its ambient pressure-ordered state remain: specifically, whether there is a change in the nature of the ferromagnetically ordered state below $T_C\sim$ 86 K. We present anisotropic $M\left(H\right)$ isotherms, coupled with anisotropic AC susceptibility data, and demonstrate that ${\mathrm{LaCrGe}}_3$ has a remarkable, low temperature coercivity associated with exceptionally sharp, complete magnetization reversals to and from fully polarized states. This coercivity is temperature dependent; it drops to zero in the 40–55 K region and reappears in the 70–85 K regions. At low temperatures ${\mathrm{LaCrGe}}_3$ has magnetization loops and behavior that has been previously associated with micromagnetic/nanocrystalline materials, not bulk macroscopic samples.

We perform a projective symmetry group (PSG) classification of symmetric quantum spin liquids with different gauge groups on the square-octagon lattice. Employing the Abrikosov fermion representation for spin $\frac{1}{2}$, we obtain $32\text{SU}\left(2\right), 1808\text{U}\left(1\right),$ and $384{\mathbb{Z}}_2$ algebraic PSGs. Constraining ourselves to mean-field parton ansätze with short-range amplitudes, the classification reduces to a limited number, with 4 $\text{SU}\left(2\right)$, 24 $\text{U}\left(1\right),$ and 36 ${\mathbb{Z}}_2$, distinct phases. We discuss their ground-state properties and spinon dispersions within a self-consistent treatment of the Heisenberg Hamiltonian with frustrating couplings.

Although substantial effort has been dedicated to analyzing the Higgs (amplitude) mode in superconducting systems, there are relatively few studies of the Higgs peak's dispersion and width, quantities which are observable in spectroscopic measurements. These properties can be obtained from the location of the pole of the amplitude (Higgs) susceptibility in the lower half plane of complex frequency. We analyze the behavior of the Higgs mode in a two-dimensional neutral fermionic superfluid at $T=0$ throughout the crossover from Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) behavior. This occurs when the dressed chemical potential $\mu$ changes sign from positive to negative. For $\mu >0$, we find a pole in the Higgs susceptibility in the lower half plane of frequency and demonstrate that it leads to a well-defined peak in spectroscopic probes. For $\mu <0$, the pole still exists but is “hidden,” not giving rise to a peak in spectroscopic probes. Extending this analysis to a charged superconductor, we find that the Higgs mode is unaffected by the long-range Coulomb interaction.

Elastic deformations (strain) couple to the electronic degrees of freedom in Weyl semimetals as an axial magnetic field (chiral gauge field), which in turn affects their impurity-dominated diffusive transport. Here we study the longitudinal magnetoconductance (LMC) in the presence of strain, Weyl cone tilt, and finite intervalley scattering, taking into account the momentum dependence of the scattering processes (both internode and intranode), as well as charge conservation. We show that strain-induced chiral gauge field results in “strong sign reversal” of the LMC, which is characterized by the reversal of orientation of the magnetoconductance parabola with respect to the magnetic field. On the other hand, external magnetic field results in “strong sign reversal,” only for sufficiently strong intervalley scattering. When both external and chiral gauge fields are present, we observe both strong and weak sign reversal, where in the case of weak sign reversal, the rise and fall of magnetoconductivity depends on the direction of the magnetic field and/or the chiral gauge field, and is not correlated with the orientation of the LMC parabola. The combination of the two fields is shown to generate striking features in the LMC phase diagram as a function of various parameters such as tilt, strain, and intervalley scattering. We also study the effect of strain-induced chiral gauge field on the planar Hall conductance and highlight its distinct features that can be probed experimentally.

We report on experimental studies that were performed with a microwave Dirac billiard (DB), that is, a flat resonator containing metallic cylinders arranged on a triangular grid, whose shape has a threefold rotational ($C_3$) symmetry. Its band structure exhibits two Dirac points (DPs) that are separated by a nearly flat band. We present a procedure that we employed to identify eigenfrequencies and to separate the eigenstates according to their transformation properties under rotation by $\frac{2\pi }{3}$ into the three $C_3$ subspaces. This allows us to verify previous numerical results of Zhang and Dietz [Phys. Rev. B 104, 064310 (2021)], thus confirming that the properties of the eigenmodes coincide with those of artificial graphene around the lower DP, and they are well described by a tight-binding model for a honeycomb-kagome lattice of corresponding shape. Above all, we investigate the properties of the wave-function components in terms of the fluctuation properties of the measured scattering matrix, which are numerically not accessible. They are compared to random-matrix theory predictions for quantum-chaotic scattering systems exhibiting extended or localized states in the interaction region, that is, the DB. Even in regions where the wave functions are localized, the spectral properties coincide with those of typical quantum systems with chaotic classical counterparts.

Exchange interactions determine the correlations between microscopic spins in magnetic materials. Probing the dynamics of these spin correlations on ultrashort length and time scales is, however, rather challenging, since it requires simultaneously high spatial and high temporal resolution. Recent experimental demonstrations of laser-driven two-magnon modes—zone-edge excitations in antiferromagnets governed by exchange coupling—posed questions about the microscopic nature of the observed spin dynamics, the mechanism underlying its excitation, and their macroscopic manifestation enabling detection. Here, on the basis of a simple microscopic model, we derive the selection rules for cubic systems that describe the polarization of pump and probe pulses required to excite and detect dynamics of nearest-neighbor spin correlations and can be employed to isolate such dynamics from other magnetic excitations and magneto-optical effects. We show that laser-driven spin correlations contribute to optical anisotropy of the antiferromagnet even in the absence of spin-orbit coupling. In addition, we highlight the role of subleading anisotropy in the spin system and demonstrate that the dynamics of the antiferromagnetic order parameter occurs only in next-to-leading order, determined by the smallness of the magnetic anisotropy as compared to the isotropic exchange interactions in the system. We expect that our results will stimulate and support further studies of magnetic correlations on the shortest length and time scales.