Topological spin liquids can be described by topological gauge theories with global symmetry. Due to the presence of both nontrivial bulk deconfined gauge fluxes and global symmetry, topological spin liquids are examples of the so-called “symmetry enriched topological phases” (SETs). In this paper, we find that, in some twisted versions of topological gauge theories (with discrete Abelian gauge group $G_g$), implementing a global symmetry (denoted by $G_s$) is anomalous although symmetry charge carried by topological pointlike excitations is normally fractionalized and classified by the second cohomology group. To demonstrate the anomaly, we fully gauge the global symmetry, rendering a new gauge theory that is not gauge invariant. Therefore, the SET order of the ground state is anomalous, which cannot exist in the three-dimensional system alone. Such an anomalous state construction generalizes the “2D surface topological order” to three dimensions. A concrete example with $G_g={\mathbb{Z}}_2\times {\mathbb{Z}}_4$ and $G_s={\mathbb{Z}}_2$ is calculated.

In a cubic ferromagnet, small spontaneous lattice distortions are expected below the Curie temperature, but the phenomenon is usually neglected. This study focuses on such an effect in the ${\mathrm{U}}_4{\mathrm{Ru}}_7{\mathrm{Ge}}_6$ compound. Based on DFT calculations, we propose a lattice distortion from the cubic $Im\text{−}3m$ space group to a lower, rhombohedral, symmetry described by the $R\text{−}3m$ space group. The strong spin-orbit coupling of the uranium ions plays an essential role in lowering the symmetry, giving rise to two different U sites (U1 and U2). Using polarized neutron diffraction in applied magnetic fields of 1 and $9\mathrm{T}$ in the ordered state ($1.9\mathrm{K}$) and in the paramagnetic state ($20\mathrm{K}$), we bring convincing experimental evidence of this splitting of the U sites, with different magnetic moments. The data have been analyzed both by maximum entropy calculations and by a direct fit in the dipolar approximation. In the ordered phase, the ${\mu }_{\mathrm{L}}/{\mu }_{\mathrm{S}}$ ratio of the orbital and spin moments on the U2 site is remarkably lower than for the free ${\mathrm{U}}^{3+}$ or ${\mathrm{U}}^{4+}$ ion, which points to a strong hybridization of the U $5f$ wave functions with the $4d$ wave functions of the surrounding Ru. On the U1 site, the ${\mu }_{\mathrm{L}}/{\mu }_{\mathrm{S}}$ ratio exhibits an unexpectedly low value: the orbital moment is almost quenched, like in metallic $\alpha$-uranium. As a further evidence of the $5f\text{−}4d$ hybridization in the ${\mathrm{U}}_4{\mathrm{Ru}}_7{\mathrm{Ge}}_6$ system, we observe the absence of a magnetic moment on the Ru1 site, but a rather large induced moment on the Ru2 site, which is in closer coordination with both U positions. Very similar results are obtained at $20\mathrm{K}$ in the ferromagnetic regime induced by the magnetic field of $9\mathrm{T}$. This shows that applying a strong magnetic field above the Curie temperature also leads to the splitting of the uranium sites, which further demonstrates the intimate coupling of the magnetic ordering and structural distortion. We propose that the difference between the magnetic moment on the U1 and U2 sites results from the strong spin-orbit interaction with different local point symmetries.

We report on the optical response of a nonreciprocal bianisotropic metamaterial, consisting of spherical, metal-coated magnetic nanoparticles embedded in an optically active medium, thus combining gyrotropy, plasmonic resonances, and chirality in a versatile design. The corresponding effective medium is deduced by an appropriate two-step generalized Maxwell-Garnett homogenization scheme. The associated photonic band structure and transmission spectra are obtained through a six-vector formulation of Maxwell equations, which provides an efficient framework for general bianisotropic structures going beyond existing approaches that involve cumbersome nonlinear eigenvalue problems. Our results, analyzed and discussed in the light of group theory, provide evidence that the proposed metamaterial exhibits some remarkable frequency-tunable properties, such as strong, plasmon-enhanced nonreciprocal polarization azimuth rotation and magnetochiral dichroism.

We implement the homodyne detection scheme for an increase in the polarimetric sensitivity in spin noise spectroscopy. Controlling the laser intensity of the local oscillator, which is guided around the sample and does not perturb the measured spin system, we are able to improve the signal-to-noise ratio. The opportunity for additional amplification of the measured signal strength allows us to reduce the probe laser intensity incident on the sample and therefore to approach the nonperturbative regime. The efficiency of this scheme with signal enhancement by more than a factor of 3 at low probe powers is demonstrated on bulk $n$-doped GaAs, where the reduced electron-spin relaxation rate is shown experimentally. Additionally, the control of the optical phase provides us with the possibility to switch between measuring Faraday rotation and ellipticity without changes in the optical setup.

Weyl semimetals are a new paradigmatic topological phase of matter featuring a gapless spectrum. One of its most distinctive features is the presence of Fermi arc surface states. Here, we report on atomistic simulations of the dc conductance and quantum Hall response of a minimal Weyl semimetal. By using scattering theory we show that a quantized Hall conductance with a nonvanishing longitudinal conductance emerges associated to the Fermi arc surface states with a remarkable robustness to high concentrations of defects in the system. Additionally, we predict that a slab of a Weyl semimetal with broken time-reversal symmetry bears persistent currents fully determined by the system size and the lattice parameters.

We show that, contrary to previous suggestions based on computer simulations or erroneous theoretical treatments, the critical points of the random-field Ising model out of equilibrium, when quasistatically changing the applied source at zero temperature, and in equilibrium are not in the same universality class below some critical dimension $d_{DR}\approx 5.1$. We demonstrate this by implementing a nonperturbative functional renormalization group for the associated dynamical field theory. Above $d_{DR}$, the avalanches, which characterize the evolution of the system at zero temperature, become irrelevant at large distance, and hysteresis and equilibrium critical points are then controlled by the same fixed point. We explain how to use computer simulation and finite-size scaling to check the correspondence between in and out of equilibrium criticality in a far less ambiguous way than done so far.

We have considered the model of the phase transition of the second order for the Coulomb frustrated 2D charged system. The coupling of the order parameter with the charge was considered as the local temperature. We have found that in such a system, an appearance of the phase-separated state is possible. By numerical simulation, we have obtained different types (“stripes,” “rings,” “snakes”) of phase-separated states and determined the parameter ranges for these states. Thus the system undergoes a series of phase transitions when the temperature decreases. First, the system moves from the homogeneous state with a zero order parameter to the phase-separated state with two phases in one of which the order parameter is zero and, in the other, it is nonzero $\left(\tau >0\right)$. Then a first-order transition occurs to another phase-separated state, in which both phases have different and nonzero values of the order parameter (for $\tau <0)$. Only a further decrease of temperature leads to a transition to a homogeneous ordered state.

We present muon spin relaxation ($\mu \mathrm{SR}$) measurements of the extended kagome systems ${\mathrm{YBaCo}}_4{\mathrm{O}}_{7+\delta }$ ($\delta =0,0.1$), comprising two interpenetrating kagome sublattice of $\mathrm{Co}{\left(\mathrm{I}\right)}^{3+}$ ($S=3/2$) and a triangle sublattice of $\mathrm{Co}{\left(\mathrm{II}\right)}^{2+}$ ($S=2$). The zero- and longitudinal-field $\mu \mathrm{SR}$ spectra of the stoichiometric compound ${\mathrm{YBaCo}}_4{\mathrm{O}}_7$ unveil that the triangular subsystem orders at $T_N=101$ K. In contrast, the muon spin relaxation rate pertaining to the kagome subsystem shows persistent spin dynamics down to $T=20$ K and then a sublinear decrease $\lambda \left(T\right)\sim T^{0.66\left(5\right)}$ on cooling towards $T=4$ K. In addition, the introduction of interstitial oxygen ($\delta =0.1$) is found to drastically affect the magnetism. For the fast-cooling experiment ($>10$ K/min), ${\mathrm{YBaCo}}_4{\mathrm{O}}_{7.1}$ enters a regime characterized by persistent spin dynamics below 90 K. For the slow-cooling experiment (1 K/min), evidence is obtained for the phase separation into interstitial oxygen-poor and oxygen-rich regions with distinct correlation times. The observed temperature, cooling rate, and oxygen content dependencies of spin dynamics are discussed in terms of a broad range of spin-spin correlation times, relying on a different degree of frustration between the kagome and triangle sublattices as well as of oxygen migration.

The spin reorientation (SR) and magnetoelastic properties of pseudobinary ferromagnetic $\mathrm{T}{\mathrm{b}}_{1-x}\mathrm{N}{\mathrm{d}}_x\mathrm{C}{\mathrm{o}}_2$ ($0\le x\le 1.0$) systems involving a morphotropic phase boundary (MPB) were studied by high-resolution synchrotron x-ray diffraction (XRD), magnetization, and magnetostriction measurements. The easy magnetization direction of the Laves phase lies along the $\langle 111\rangle$ axis with $x<0.65$, whereas it lies along the $\langle 100\rangle$ axis for $x>0.65$ below Curie temperature ($T_{\mathrm{C}}$). The temperature-dependent magnetization curves showed SR; this can be explained by a two-sublattice model. Based on the synchrotron (XRD) and magnetization measurements, the SR phase diagram for a MPB composition of $\mathrm{T}{\mathrm{b}}_{0.35}\mathrm{N}{\mathrm{d}}_{0.65}\mathrm{C}{\mathrm{o}}_2$ was obtained. Contrary to previously reported ferromagnetic systems involving MPB, the MPB composition of $\mathrm{T}{\mathrm{b}}_{0.35}\mathrm{N}{\mathrm{d}}_{0.65}\mathrm{C}{\mathrm{o}}_2$ exhibits a low saturation magnetization ($M_{\mathrm{S}}$), indicating a compensation of the Tb and Nd magnetic moments at MPB. The anisotropic magnetostriction (${\lambda }_{\mathrm{S}}$) first decreased until $x=0.8$ and then continuously increased in the negative direction with further increase of Nd concentration. The decrease in magnetostriction can be attributed to the decrease of spontaneous magnetostriction ${\lambda }_{111}$ and increase of ${\lambda }_{100}$ with opposite sign to ${\lambda }_{111}$. This paper indicates an anomalous type of MPB in the ferromagnetic $\mathrm{T}{\mathrm{b}}_{1-x}\mathrm{N}{\mathrm{d}}_x\mathrm{C}{\mathrm{o}}_2$ system and provides an active way to design novel functional materials with exotic properties.

Ambient-pressure-grown ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$ with a superconducting transition temperature $T_c\sim 3$ K possesses a highly anisotropic normal state. By a series of electrical resistivity measurements with a magnetic-field direction varying between the crystalline $c$ axis and the $ab$ plane, we present datasets displaying the temperature dependence of the out-of-plane upper critical field $H_{c2}^{\perp }\left(T\right)$, the in-plane upper critical field $H_{c2}^{\parallel }\left(T\right)$, as well as the angular dependence of $H_{c2}$ at fixed temperatures for ambient-pressure-grown ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$ single crystals. The anisotropy of the superconductivity, $H_{c2}^{\parallel }/H_{c2}^{\perp }$, reaches $\sim 16$ on approaching 0 K, but it decreases significantly near $T_c$. A pronounced upward curvature of $H_{c2}^{\parallel }\left(T\right)$ is observed near $T_c$, which we analyze using a two-gap model. Moreover, $H_{c2}^{\parallel }\left(0\right)$ is found to exceed the Pauli paramagnetic limit, which can be understood by considering the strong spin-orbit coupling associated with Bi as well as the breaking of the local inversion symmetry at the electronically active ${\mathrm{BiS}}_2$ bilayers. Hence, ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$ with a centrosymmetric lattice structure is a unique platform to explore the physics associated with local parity violation in the bulk crystal.

We report the experimental realization of a Dirac semimetal state in NdSb, a material with antiferromagnetic ground state. The occurrence of a topological semimetal state has been well supported by our band structure calculations and the experimental observation of chiral-anomaly-induced negative magnetoresistance. A field-induced Fermi surface reconstruction is observed in response to the change of spin polarization. The observation of a topological semimetal state in a magnetic material provides an opportunity to investigate the magnetotopological phenomena.

We obtain a controlled description of a strongly correlated regime of electronic behavior. We begin by arguing that there are two ways to characterize the electronic degree of freedom, either by the canonical fermion algebra or the graded Lie algebra $\mathfrak{su}\left(2\right|2)$. The first underlies the Fermi liquid description of correlated matter, and we identify a regime governed by the latter. We exploit an exceptional central extension of $\mathfrak{su}\left(2\right|2)$ to employ a perturbative scheme recently developed by Shastry and obtain a series of successive approximations for the electronic Green's function. We then focus on the leading approximation, which reveals a splitting in two of the electronic dispersion. The Luttinger sum rule is violated, and a Mott metal-insulator transition is exhibited. We offer a perspective.

Traditionally, quantum oscillations were interpreted as the hallmark of a Fermi surface. Recently, it was understood that in order to have well defined de Haas–van Alphen oscillations the presence of a Fermi surface is not required. Following the Luttinger approach, we investigate the oscillations of an inverted insulator. Clear quantum oscillations are found and we provide a formula for the Lifshitz-Kosevich amplitude both in the clean as well as weakly disordered regime. We find that the LK formula is strongly modified compared to systems with a Fermi surface.

Recently, constructing van der Waals (vdW) heterojunctions by stacking different two-dimensional (2D) materials has been considered to be effective strategy to obtain the desired properties. Here, through first-principles calculations, we find theoretically that the 2D $n$-InSe/$p$-GeSe(SnS) vdW heterojunctions are the direct-band-gap semiconductor with typical type-II band alignment, facilitating the effective separation of photogenerated electron and hole pairs. Moreover, they possess the high optical absorption strength ($\sim {10}^5$), broad spectrum width, and excellent carrier mobility ($\sim {10}^3\mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$). Interestingly, under the influences of the interlayer coupling and external electric field, the characteristics of type-II band alignment is robust, while the band-gap values and band offset are tunable. These results indicate that 2D $n$-InSe/$p$-GeSe(SnS) heterojunctions possess excellent optoelectronic and transport properties, and thus can become good candidates for next-generation optoelectronic nanodevices.

We investigate theoretically magnetism and magnetic phase transitions induced by electrostatic gating of two-dimensional square metal-organic framework compounds. We find that electrostatic gating can induce phase transitions between homogeneous ferromagnetic and various spin-textured antiferromagnetic states. Electronic structure and Wannier function analysis can reveal hybridizations between transition-metal $d$ orbitals and conjugated $\pi$ orbitals in the organic framework. Mn-containing compounds exhibit a strong $d-\pi$ hybridization that leads to partially occupied spin-minority bands, in contrast to compounds containing transition-metal ions other than Mn, for which electronic structure around the Fermi energy is only slightly spin split due to weak $d-\pi$ hybridization and the magnetic interaction is of the Ruderman-Kittel-Kasuya-Yosida type. We use a ferromagnetic Kondo lattice model to understand the phase transition in Mn-containing compounds in terms of carrier density and illuminate the complexity and the potential to control two-dimensional magnetization.

Thin topological insulator (TI) films support optical and acoustic plasmonic modes characterized by effective net charge or net spin density, respectively. We combine many-body and electromagnetic calculations to study how these modes can be selectively excited at films and nanodisks at infrared and THz frequencies. We first discuss the excitation of propagating plasmons in a thin film by a point dipolar source. We emphasize how changing the distance between the dipolar source and the film allows us to control the relative strength of the acoustic and optical plasmons and thus to excite net-spin or net-charge waves on demand. The acoustic and optical modes in a nanodisk structure can be efficiently tuned by changing the size of the disk or by applying electrostatic gating. Furthermore, these modes can be confined to regions of dimensions much smaller than the wavelength. The control of the excitation of acoustic and optical modes indicates that thin topological insulators are a promising system to manipulate the spin and charge properties of the plasmonic response, with potential applications in fast, compact, and electrically-controlled spintronic devices.

The successful realization of metamaterials and metasurfaces requires the judicious choice of constituent elements. In this paper, we demonstrate the implementation of time-varying metamaterials in the terahertz frequency regime by utilizing graphene-wrapped microwires as building blocks and modulation of graphene conductivity through exterior electrical gating. These elements enable enhancement of light-graphene interaction by utilizing optical resonances associated with Mie scattering, yielding a large tunability and modulation depth. We develop a semianalytical framework based on transition-matrix formulation for modeling and analysis of periodic and aperiodic arrays of such time-varying building blocks. The proposed method is validated against full-wave numerical results obtained using the finite-difference time-domain method. It provides an ideal tool for mathematical synthesis and analysis of space-time gradient metamaterials, eliminating the need for computationally expensive numerical models. Moreover, it allows for a wider exploration of exotic space-time scattering phenomena in time-modulated metamaterials. We apply the method to explore the role of modulation parameters in the generation of frequency harmonics and their emerging wavefronts. Several potential applications of such platforms are demonstrated, including frequency conversion, holographic generation of frequency harmonics, and spatiotemporal manipulation of light. The presented results provide key physical insights to design time-modulated functional metadevices using various building blocks and open up new directions in the emerging paradigm of time-modulated metamaterials.