We construct and study relativistic anyons in $1+1$ dimensions generalizing well-known models of Dirac fermions. First, a model of free anyons is constructed and then extended in two ways: (i) by adding density-density interactions, as in the Luttinger model, and (ii) by coupling the free anyons to a U(1)-gauge field, as in the Schwinger model. Second, physical properties of these extensions are studied. By investigating off-diagonal long-range order (ODLRO) at zero temperature, we show that anyonic statistics allows one to get arbitrarily close to ODLRO but that this possibility is destroyed by the gauge coupling. The latter is due to a nonzero effective mass generated by gauge invariance, which we show also implies the presence of screening, independently of the anyonic statistics.

We report 10 ground states arising from strong correlations in the single-orbital Hubbard model on the decorated honeycomb lattice, including Dirac metals, flat-band ferromagnets, real-space Mott insulators, dimer and trimer Mott insulators, and a spin-1 Mott insulator. The rich phase diagram arises from structures within the unit cell. Hence, such states are absent on simpler lattices. We argue that such insulating phases are prevalent on decorated lattices. These are found in many materials and common in coordination polymers, providing a playground to explore this physics.

We investigate a photonic device consisting of two coupled optical cavities possessing Rashba-Dresselhaus spin-orbit coupling, TE-TM splitting, and linear polarization splitting that opens a tunable energy gap at the diabolic points of the photon dispersion; giving rise to an actively addressable local Berry curvature. The proposed architecture stems from recent advancements in the design of artificial photonic gauge fields in liquid crystal cavities [K. Rechcińska et al., Science 366, 727 (2019)]. Our study opens perspectives for topological photonics, room-temperature spinoptronics, and studies on the quantum geometrical structure of photonic bands in extreme settings.

Neutron diffraction and x-ray pair distribution function experiments were performed to investigate the magnetic and local crystal structures of ${\mathrm{Ba}}_2\mathrm{FeSb}{\mathrm{Se}}_5$ and to compare them with the average (i.e., long range) structural model previously obtained by single-crystal x-ray diffraction. Changes in the local crystal structure (i.e., in the second coordination sphere) are observed upon cooling from 295 to 95 K, resulting in deviations from the average (i.e., long range) crystal structure. In this paper, we demonstrate that these observations cannot be explained by local or long-range magnetoelastic effects involving Fe-Fe correlations. Instead, we found that the observed differences between local and average crystal structure can be explained by Sb-$5s$ lone pair dynamics. We also find that, below the Néel temperature $(T_N=58\mathrm{K})$, the two distinct magnetic ${\mathrm{Fe}}^{3+}$ sites order collinearly, such that a combination of antiparallel and parallel spin arrangements along the $b$ axis results. The nearest-neighbor arrangement $(J_1=6\AA )$ is fully antiferromagnetic, while next-nearest-neighbor interactions are ferromagnetic in nature.

The Aubry-André-Harper model provides a paradigmatic example of aperiodic order in a one-dimensional lattice displaying a delocalization-localization phase transition at a finite critical value $V_c$ of the quasiperiodic potential amplitude $V$. In terms of the dynamical behavior of the system, the phase transition is discontinuous when one measures the quantum diffusion exponent $\delta$ of wave-packet spreading, with $\delta =1$ in the delocalized phase $V<V_c$ (ballistic transport), $\delta \simeq 1/2$ at the critical point $V=V_c$ (diffusive transport), and $\delta =0$ in the localized phase $V>V_c$ (dynamical localization). However, the phase transition turns out to be smooth when one measures, as a dynamical variable, the speed $v\left(V\right)$ of excitation transport in the lattice, which is a continuous function of potential amplitude $V$ and vanishes as the localized phase is approached. Here we consider a non-Hermitian extension of the Aubry-André-Harper model, in which hopping along the lattice is asymmetric, and show that the dynamical localization-delocalization transition is discontinuous, not only in the diffusion exponent $\delta$, but also in the speed $v$ of ballistic transport. This means that even very close to the spectral phase transition point, rather counterintuitively, ballistic transport with a finite speed is allowed in the lattice. Also, we show that the ballistic velocity can increase as $V$ is increased above zero, i.e., surprisingly, disorder in the lattice can result in an enhancement of transport.

Precise positioning of magnetic solitons requires controllable artificial pinning, while the accurate determination of the pinning profile remains a challenge. Here, we propose a topological solution to this problem. Taking the domain wall (DW) as a representative example, we study the collective dynamics of interacting DWs in a magnetic racetrack with pinning sites of alternate distances. By mapping the governing equations of DW motion to the Su-Schrieffer-Heeger model and evaluating the quantized Zak phase, we predict two topologically distinct phases in the racetrack. A robust edge state emerges at either one or both ends depending on the parity of the DW number and the ratio of alternating intersite lengths. We show that the in-gap DW oscillation frequency has a fixed value which depends only on the geometrical shape of the pinning notch, and is insensitive to device imperfections and inhomogeneities. The spring coefficient of the pinning potential can be quantified as the square of the robust DW frequency multiplied by its constant mass. Our findings pave the way to determining the pinning potential with high accuracy for generic magnetic solitons and suggest as well that the magnetic soliton-based racetrack is a unique playground to study topological phase transitions.

Temperature-dependent Raman spectroscopic studies of spin-phonon (SP) coupling and magnon scattering in bulk and few-layer (FL) antiferromagnet (AFM) ${\text{FePS}}_3$ with Néel temperature ($T_N$) $\approx$ 120 K were performed. Bulk and FL (2–5 atomic layers) samples show four distinct modes at room temperature between 150 and $400 {\text{cm}}^{-1}$ and a broad peak at $\approx 105 {\text{cm}}^{-1}$. On lowering the temperature, three distinct phenomena are observed. First, we see the SP coupling, identified by the deviation from the usual two- or three-phonon anharmonic behavior of the higher wave number peaks ($\ge 150 {\text{cm}}^{-1}$) at or below $T_N$. The strength of SP coupling can be calculated for bulk and FL flakes considering mean-field approximations. Secondly, we see the spin ordering marked by the evolution of three peaks at lower wave numbers (around $105 {\text{cm}}^{-1}$) below $T_N$ due to incommensurate magnetic cells at low temperature. Thirdly, magnon excitation in FL pristine ${\text{FePS}}_3$ is detected by the emergence of a distinct peak at $120 {\text{cm}}^{-1}$ ($\sim 3.6$ THz) at a temperature much lower than $T_N$ ($\approx 60$ K). Tracking the magnon mode in the designed van der Waals heterostructures with ${\text{Bi}}_2{\text{Te}}_3$ and ${\text{Cr}}_2{\text{Ge}}_2{\text{Te}}_6$ reveal interfacial electron and hole transfer from ${\text{FePS}}_3$, respectively. Raman spectroscopy can thus predict the magnetic transition temperature of FL magnetic insulators via SP coupling, zone-boundary phonons, and magnons. Quasi-two-dimensional AFMs and their heterostructures involving different electronic and magnetic orders may be promising candidates for ultrafast magnon transport involving magnetoelastic waves.

For strongly anisotropic time-reversal invariant (TRI) insulators in two and three dimensions, the band inversion can occur, respectively, at all TRI momenta of a high symmetry axis and plane. Although these classes of materials are topologically trivial as their strong and weak $Z_2$ indices are all trivial, they can host an even number of helical gapless edge states or surface Dirac cones on some boundaries. We show in this paper that when the gapless boundary states are gapped by $s_{\pm }$-wave superconductivity, a boundary time-reversal invariant topological superconductor (BTRITSC) characterized by a $Z_2$ invariant can be realized on the corresponding boundary. Since the dimension of the BTRITSC is lower than the bulk by one, the whole system is a TRI second-order topological superconductor. When the boundary of the BTRITSC is further cut open, Majorana Kramers pairs and helical gapless Majorana modes will, respectively, appear at the corners and hinges of the considered sample in two and three dimensions. Furthermore, a magnetic field can gap the helical Majorana hinge modes of the three-dimensional TRI second-order topological superconductor and lead to the realization of a third-order topological superconductor with Majorana corner modes. Our proposal can potentially be realized in insulator-superconductor heterostructures and iron-based superconductors whose normal states take the desired inverted band structures.

“Magic” is the degree to which a state cannot be approximated by Clifford gates. We study mana, a measure of magic, in the ground state of the ${\mathbb{Z}}_3$ Potts model, and argue that it is a broadly useful diagnostic for many-body physics. In particular we find that the $q=3$ ground state has large mana at the model's critical point, and that this mana resides in the system's correlations. We explain the form of the mana by a simple tensor-counting calculation based on a MERA representation of the state. Because mana is present at all length scales, we conclude that the conformal field theory describing the three-state Potts model critical point is magical. These results control the difficulty of preparing the Potts ground state on an error-corrected quantum computer and constrain tensor network models of AdS-CFT.

The Heusler compound ${\mathrm{Co}}_2{\mathrm{FeAl}}_{0.5}{\mathrm{Si}}_{0.5}$ is an interesting material for spintronic applications due to its predicted half-metal ferromagnetic character with a large band gap in the minority states. In this work, we present the optical and magneto-optical properties of a ${\mathrm{Co}}_2{\mathrm{FeAl}}_{0.5}{\mathrm{Si}}_{0.5}$ bulk sample at room temperature. The spectral permittivity is found to be dominated by an absorption peak at 1.4 eV, originating mostly from absorptions by minority electrons. The best agreement between the experimentally obtained spectral permittivity tensor and the ab initio calculated one is for the local density approximation potential, closely followed by the generalized gradient approximation potential. However, the half-metallic ferromagnet character with $100\%$ spin polarization is preserved only in calculations employing the Coulomb interaction correction (+U). This suggests that ${\mathrm{Co}}_2{\mathrm{FeAl}}_{0.5}{\mathrm{Si}}_{0.5}$ is probably not a half metal as a single minority $d$-band dips below the Fermi level.

Measuring the Majorana entropy $S_M=k_{B}log\left(2^{\frac{1}{2}}\right)$ (where $log$ is the natural logarithm) may uniquely reveal whether an initial equilibrium state of a nanoscale device has a Majorana nature, and subsequent operations deal with an essentially nonlocal pair of non-Abelian Majorana bound states and not with trivial or other accidental non-Abelian states. However, in realistic setups both Majorana modes are inevitably involved in tunneling processes. We show that even when the tunneling amplitude of one Majorana mode is significantly suppressed, the Majorana entropy is ruined, and straightforward experiments will, in general, detect entropy $S\ll S_M$. To avoid this general problem we present a mechanism of the Majorana entropy revival via the tunneling phases of the Majorana modes and demonstrate that to successfully observe the universal Majorana plateau $S=S_M$ one should intelligently tune the tunneling phases instead of leaving them uncontrolled. Practical feasibility of appropriate Majorana entropy measurements is supported by an example with parameters well achievable in modern labs.

The crystallographic and physical properties of the recently discovered filled skutterudite superconductor ${\mathrm{SrOs}}_4{\mathrm{P}}_{12}$, synthesized by a high-pressure and -temperature technique, are studied by measuring electrical resistivity, specific heat, and magnetization, and by performing electronic band calculations. X-ray powder diffraction with Rietveld refinement indicates that the lattice parameter of ${\mathrm{SrOs}}_4{\mathrm{P}}_{12}$ is 8.093(2) Å and that fractional coordinates of the P site are [0, 0.3607(9), 0.1450(9)], which is also confirmed by calculations based on density functional theory. The electrical resistivity indicates a metallic nature of ${\mathrm{SrOs}}_4{\mathrm{P}}_{12}$, which is consistent with the density of states at Fermi energy with 7.5 (states/eV)/f.u. deduced from the electronic band calculations. The Sommerfeld coefficient $\gamma$ and Einstein temperature $\theta {}_{\mathrm{E}}$ of ${\mathrm{SrOs}}_4{\mathrm{P}}_{12}$ are deduced as $\gamma \sim 26\mathrm{mJ}/{\mathrm{mol}\mathrm{K}}^2$ and $\theta {}_{\mathrm{E}}\sim 150$ K, respectively. A larger isotropic atomic displacement parameter $U_{\mathrm{eq}}$ of Sr compared to other atomic species as obtained from a Rietveld analysis and a specific heat anomaly around 30 K refers to anharmonic lattice vibrations of Sr in ${\mathrm{SrOs}}_4{\mathrm{P}}_{12}$. ${\mathrm{SrOs}}_4{\mathrm{P}}_{12}$ exhibits two superconducting transitions at $T_{\mathrm{c}1}=1.6$ K and $T_{\mathrm{c}2}=1.0$ K. Specific-heat data indicate that the observed superconductivity is of bulk nature with approximate volume fractions of $27\%$ and $38\%$ for superconductivity at $T_{\mathrm{c}1}$ and $T_{\mathrm{c}2}$, respectively. The electrical resistivity under field and pressure as well as the specific heat under field indicate that $T_{\mathrm{c}1}$ is sensitive to the magnetic field and $T_{\mathrm{c}2}$ is sensitive to pressure. The results show that ${\mathrm{SrOs}}_4{\mathrm{P}}_{12}$ is an $s$-wave weakly coupled superconductor with an electron-phonon mass enhancement ${\lambda }_{\text{ep}}\sim 0.47$.

Raman scattering experiments on isotopically enriched hexagonal boron nitride have been performed under pressure up to 11 GPa at room temperature. The sublinear increase of the Raman-active $E_{2g}$ mode frequencies has been characterized. The pressure behavior has been analyzed by means of a bond-stiffness–bond-length scaling parameter $\gamma$ which takes into consideration the vast differences in $a$- and $c$-axis compressibilities. The interlayer shear mode exhibits a $\gamma$ parameter similar to that of graphite, and the mode frequency in isotopically pure samples separates faster at low pressures as a result of van der Waals interactions. Because of the extremely low $a$-axis compressibility, the intralayer mode exhibits a rather large scaling parameter. Within experimental uncertainties, no systematic departures related to isotopic mass have been observed.

Optical spin pumping of color centers in diamond is presently attracting broad interest as a platform for dynamic nuclear polarization at room temperature, but the mechanisms involved in the generation and transport of polarization within the host crystal are still partly understood. Here we investigate the impact of continuous radio-frequency (RF) excitation on the generation of nuclear magnetization produced by optical illumination. In the presence of RF excitation far removed from the nuclear Larmor frequency, we witness a magnetic-field-dependent sign reversal of the measured nuclear spin signal when the drive is sufficiently strong, a counterintuitive finding that immediately points to nontrivial spin dynamics. With the help of analytical and numerical modeling, we show our observations indicate a modified form of solid effect, down-converted from the microwave to the radio-frequency range through the driving of hybrid transitions involving one (or more) nuclei and two (or more) electron spins. Our results open intriguing opportunities for the manipulation of many-electron spin systems by exploiting hyperfine couplings as a means to access otherwise forbidden intraband transitions.

Self-trapping of photocarriers due to the strong carrier-phonon interaction is ubiquitous in metal oxides, which exerts detrimental influence on the performance of the oxide-based optoelectronic devices. The self-trapped species could be isolated self-trapped charges (i.e., isolated polarons) or bound self-trapped electron-hole pairs (i.e., polaron-pairs, self-trapped excitons), and they may show distinct dynamic behaviors. Here, we find that the self-trapping in hematite ($\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$) primarily results in self-trapped excitons rather than spatially separated polaronic charges or electron-hole polaron-pairs based on both dynamic and spectral evidence. The formation and recombination of self-trapped excitons are found to be substantially independent of defect concentration varying from monocrystalline to polycrystalline $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ films. The spectral feature attributed to small electron polarons can only be resolved above the noise floor by raising excitation intensity so that the Auger process dominates the recombination. Based on the comparison of monocrystalline and polycrystalline sample data, we suggest that the isolated electron polaron formation is likely facilitated by defects. Our finding invokes reconsideration of the photocurrent generation mechanism in $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ photoanodes.

The lack of useful and cost-efficient group-IV direct band gap light emitters still presents the main bottleneck for complementary metal-oxide semiconductor-compatible short-distance data transmission, single-photon emission, and sensing based on silicon photonics. Germanium, a group-IV element like Si, is already widely used in silicon fabs. While the energy band gap of Ge is intrinsically indirect, we predict that the insertion of Ge-Ge split-[110] interstitials into crystalline Ge can open up a direct band gap transmission path. Here, we calculate from first principles the band structure and optical emission properties of Ge, Sb, and Sn split-[110] interstitials in bulk and low-dimensional Ge at different doping concentrations. Two types of electronic states provide the light-emission enhancement below the direct band gap of Ge: a hybridized L-$\mathrm{\Gamma }$ state at the Brillouin zone center and a conduction band of $\mathrm{\Delta }$ band character that couples to a raised valence band along the $\mathrm{\Gamma }$-X direction. Majority carrier introduced to the system through doping can enhance light emission by saturation of nonradiative paths. Ge-Sn split interstitials in Ge shift the top of the valence band towards the $\mathrm{\Gamma }$-X direction and increase the $\mathrm{\Gamma }$ character of the L-$\mathrm{\Gamma }$ state, which results in a shift to longer emission wavelengths. Key spectral regions for datacom and sensing applications can be covered by applying quantum confinement in defect-enhanced Ge quantum dots for an emission wavelength shift from the midinfrared to the telecom regime.

Magnetic-field-angle-resolved heat capacity of dimer-Mott organic superconductors $\kappa \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_{2}X$ is reported (BEDT-TTF and $X$ represent bis(ethylenedithio)tetrathiafulvalene and a monovalent anion, respectively). Temperature and field dependence of heat capacity indicates that the superconductivity has line nodes on the Fermi surface, which is a typical feature of $d$-wave superconductivity. In-plane field-angle dependence exhibits fourfold oscillations as well as twofold oscillations due to anisotropy of superconducting gap functions. From analyses of the fourfold term, the gap symmetry is determined as $d_{x^2-y^2}+s_{\pm }$ for $X=\mathrm{Cu}\left[\mathrm{N}{\left(\mathrm{CN}\right)}_2\right]\mathrm{Br}$ and $d_{xy}$ for $X=\mathrm{Ag}{\left(\mathrm{CN}\right)}_2{\mathrm{H}}_2\mathrm{O}$. We suggest that the symmetry difference comes from the competition of $d_{xy}$ and $d_{x^2-y^2}$ antiferromagnetic fluctuations depending on lattice geometry.

Dynamical topology in ferroelectrics such as polarization rotation begins to attract interest because it brings new opportunities to generate properties that the static states cannot achieve. However, polarization behavior cannot be complicated under the spatially homogeneous electric fields that ferroelectrics are typically subjected to. Here, we demonstrate that a ferroelectric nanostructure with polarization rotation under cyclic electric fields is induced by a $\frac{1}{2}\left[1\overline{1}0\right]\left(110\right)$ dislocation in $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$. Phase-field simulations show that an elastic field specific to the dislocation causes an L-shaped ferroelectric nanoregion in paraelectric $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ while a trajectory of polarization exhibits clockwise rotation under one cyclic electric field. Furthermore, we demonstrate that the trajectory exhibits a clockwise-oscillation-anticlockwise transition, depending on the angle of the one cyclic electric field, which leads to functionalities such as binary addition. This work provides a strategy to engineer polarization dynamics and expands the knowledge of topology and the application of ferroelectrics.

We present a theory of the nonlinear spin Seebeck effect (SSE) in a ferromagnetic nanowire at cryogenic temperatures. We adopt a microscopic quantum noise model based on a collection of two-level systems. At certain positions of Pt detectors to the wire, the transverse SSE changes sign as a function of temperature and/or temperature gradient. On the other hand, the longitudinal SSE does not show significant nonlinearities even far outside the regime of validity of linear response theory.