Symmetry-resolved entanglement is a useful tool for characterizing symmetry-protected topological states. In two dimensions, their entanglement spectra are described by conformal field theories but the symmetry resolution is largely unexplored. However, addressing this problem numerically requires system sizes beyond the reach of exact diagonalization. Here, we develop tensor-network methods that can access much larger systems and determine universal and nonuniversal features in their entanglement. Specifically, we construct one-dimensional matrix product operators that encapsulate all the entanglement data of two-dimensional symmetry-protected topological states. We first demonstrate our approach for the Levin-Gu model. Next, we use the cohomology formalism to deform the phase away from the fine-tuned point and track the evolution of its entanglement features and their symmetry resolution. The entanglement spectra are always described by the same conformal field theory. However, the levels undergo a spectral flow in accordance with an insertion of a many-body Aharonov-Bohm flux.

The electronic structure of CeNiSn, which is a potential topological Kondo insulator and a Dirac nodal-loop semimetal, has been investigated by employing temperature $\left(T\right)$ dependent angle-resolved photoemission spectroscopy (ARPES). The Fermi surfaces (FSs) and the band structures of CeNiSn for three orthogonal crystallographic planes are measured, in which both the very dispersive bands and the flat bands are observed, having mainly the Ni $3d$ character and the Ce $4f$ character, respectively. The measured FSs and ARPES bands agree reasonably well with the density functional theory (DFT) calculations. The Fermi-edge $\left(E_F\right)$ photon energy $\left(h\nu \right)$ map along $k_b (=k_{\left(010\right)})$ shows that the metallic $E_F$-crossing states on the (010) surface have the three-dimensional character, suggesting that the observed $E_F$-crossing metallic states do not correspond to the topological surface states of the two-dimensional character. On the other hand, albeit weak, the features of the hourglass-type bulk band crossings are observed along $SXS$, with the energies and the slopes being similar to those predicted by the DFT calculations, supporting the Dirac semimetallic nature of CeNiSn. In $T$-dependent ARPES, the Ce $4f$ Kondo resonance states are clearly revealed at low $T$, which become much suppressed above $\sim 80$ K. This feature is consistent with the Kondo temperature of CeNiSn, estimated from its $\rho \left(T\right)$ data. This work demonstrates the importance of the coherent Kondo states in determining the topological properties of CeNiSn.

Motivated by the recent discoveries of superconductivity in bilayer and trilayer graphene, we theoretically investigate superconductivity and other interaction-driven phases in multilayer graphene stacks. To this end, we study the density of states of multilayer graphene with up to four layers at the single-particle band structure level in the presence of a transverse electric field. Among the considered structures, tetralayer graphene with rhombohedral (ABCA) stacking reaches the highest density of states. We study the phases that can arise in ABCA graphene by tuning the carrier density and transverse electric field. For a broad region of the tuning parameters, the presence of strong Coulomb repulsion leads to a spontaneous spin and valley symmetry breaking via Stoner transitions. Using a model that incorporates the spontaneous spin and valley polarization, we explore the Kohn-Luttinger mechanism for superconductivity driven by repulsive Coulomb interactions. We find that the strongest superconducting instability is in the $p$-wave channel, and occurs in proximity to the onset of Stoner transitions. Interestingly, we find a range of densities and transverse electric fields where superconductivity develops out of a strongly corrugated, singly connected Fermi surface in each valley, leading to a topologically nontrivial chiral $p+ip$ superconducting state with an even number of copropagating chiral Majorana edge modes. Our work establishes ABCA-stacked tetralayer graphene as a promising platform for observing strongly correlated physics and topological superconductivity.

We present a study of the superconducting properties of the candidate topological superconductor ${\mathrm{Ti}}_3\mathrm{Sb}$. Electrical transport measurements show zero resistance with a $T_{c,\mathrm{onset}}$ of $\approx 5.9$ K with a transition width $\mathrm{\Delta }{T}_c\approx 0.6$ K. The superconducting phase boundaries as derived from magnetotransport and magnetic susceptibility measurements agree well. We estimate an upper critical field $B_{c2}\left(0\right)\approx 4.5$ T. A Ginzburg-Landau (GL) analysis yields values of the coherence length and penetration depth of $\xi =6.2$ nm and $\lambda =340$ nm, respectively, and a GL parameter $\kappa \approx 55$, indicating extreme type-II behavior. Furthermore, we observe a step height in the specific heat $\frac{\mathrm{\Delta }{\mathrm{C}}_{\mathrm{e}}}{\gamma T_c}\approx 1.61\pm 0.24$ (with $T_c=4.8\pm 0.4$ K), a value larger than the Bardeen-Cooper-Schrieffer value of 1.43, suggesting modest coupling. Measurements of the temperature dependence of the London penetration depth via the tunnel-diode oscillator technique down to $\approx 450$ mK show a full superconducting gap, consistent with a conventional $s$-wave gap structure.

Spin semimetals are a recently discovered new class of spintronic materials, which exhibit a band gap in one spin channel while exhibiting a semimetallic feature in the other, thus allowing for tunable spin transport. Here, we present experimental verification of spin semimetallic behavior in FeRhCrSi, a quaternary Heusler alloy with saturation moment 2 ${\mu }_B$ and Curie temperature $>400$ K. It crystallizes in the ${\mathrm{L}2}_1$ structure with $50\%$ antisite disorder between Fe and Rh. Below 300 K, it shows a weakly temperature-dependent electrical resistivity with a negative temperature coefficient, indicating normal semimetal or spin semimetal behavior. Anomalous magnetoresistance data reveal the dominant contribution from the asymmetric part, a clear signature of the spin-valve nature, which is retained even at room temperature. The asymmetric part of the magnetoresistance shows an unusual increase with increasing temperature. Hall measurements confirm the anomalous nature of the conductivity originating from the intrinsic Berry curvature, with holes being the majority carriers. Ab initio simulation confirms a unique long-range ferrimagnetic ordering to be the ground state, explaining the origin behind the unexpected low saturation moment. The ferrimagnetic disordered structure confirms the spin semimetallic feature of FeRhCrSi, as observed experimentally.

We consider quantum condensed matter systems without particle-number conservation. Since the particle number is not a good quantum number, states belonging to different particle-number sectors can hybridize, which causes topological anticrossings in the spectrum. The resulting spectral gaps support chiral edge excitations whose wavefunction is a superposition of states in the two hybridized sectors. This situation is realized in fully saturated spin-anisotropic quantum magnets without spin conservation, in which single magnons hybridize with magnon bound pairs, i.e., two-magnon bound states. The resulting chiral edge excitations are exotic composites that carry mixed spin-multipolar character, inheriting spin-dipolar and spin-quadrupolar character from their single-particleness and two-particleness, respectively. In contrast to established topological magnons, the topological effects discussed here are of genuine quantum mechanical origin and vanish in the classical limit. We discuss implications for intrinsic anomalous Hall-type transport and estimate that the thermal Hall conductivity brought about by the hybridization of magnons and magnon bound pairs can be as large as that of magnons with other magnons. We conclude that fully polarized quantum magnets are a promising platform for topology caused by hybridizations between particle-number sectors, complementing the field of ultracold atoms working with a conserved number of particles.

The spin waves in single crystals of the layered van der Waals antiferromagnet ${\mathrm{CoPS}}_3$ have been measured using inelastic neutron scattering. The data show four distinct spin wave branches with large ($\gtrsim 14$ meV) energy gaps at the Brillouin zone center indicating significant anisotropy. The data were modeled using linear spin wave theory derived from a Heisenberg Hamiltonian. Exchange interactions up to the third nearest-neighbor in the layered planes were required to fit the data with ferromagnetic $J_1=-1.37$ meV between first neighbors, antiferromagnetic $J_3=3.0$ meV between third neighbors, and a very small $J_2=0.09$ meV between second neighbors. A biaxial single-ion anisotropy was required, with a collinear term $D^x=-0.77$ meV for the axis parallel to the aligned moment direction and a coplanar term $D^z=6.07$ meV for an axis approximately normal to the layered crystal planes.

Several families of layered perovskite oxide ferroelectrics exhibit a coupling between polarization and structural order parameters, such as octahedral rotation distortions. This coupling provides opportunities for novel electric field-based manipulation of material properties, and it also stabilizes complex domain patterns and domain-wall vortices. Among layered perovskites with such coupled orders, the Aurivillius-phase oxides ${\mathrm{SrBi}}_2{B}_2{\mathrm{O}}_9$ ($B=\text{Ta,}\text{Nb}$) are well-known for their excellent room-temperature ferroelectric performance. This work combines group theoretic analysis with density functional theory calculations to examine the ferroelectric switching processes of ${\mathrm{SrBi}}_2{B}_2{\mathrm{O}}_9$. Low-energy two-step ferroelectric switching paths are identified, with polarization reversal facilitated by structural order-parameter rotations. Analysis of the domain structure reveals how the relative energetics of the coupled order parameters translates into a network of several distinct domain-wall types linked by domain-wall vortex structures. Comparisons are made between the ferroelectric switching and domain structure of ${\mathrm{SrBi}}_2{B}_2{\mathrm{O}}_9$ and those of the layered $n=2$ Ruddlesden-Popper hybrid improper ferroelectrics. The results provide insight into how ferroelectric properties may be optimized by engineering the complex crystal structures of Aurivillius-phase oxides.

We report thermal conductivity measurements on single crystals of herbertsmithite, over a wide range of temperatures ($0.05–120$ K) in magnetic fields up to 15 T. We also report measurements of the thermal Hall effect, found to be vanishingly small. At high temperatures, in the paramagnetic regime, the thermal conductivity has a negligible field dependence. Upon cooling and the development of correlations, the onset of a clear monotonic field dependence below about 20 K signals a new characteristic temperature scale that may reflect the subtle crossover towards the quantum spin liquid regime. Deconfined spinons, if present, are not detected and phonons, as the main carriers of heat, are strongly scattered by the intrinsic spin excitations and the magnetic defects. In view of the colossal fields required to affect the intrinsic spins, most of the field-induced evolution is attributed to the progressive polarization of some magnetic defects. By elaborating a phenomenological model, we extract the magnetization of these main scattering centers which does not resemble the Brillouin function for free spins $\frac{1}{2}$, requiring to go beyond the paradigm of isolated paramagnetic spins. Besides, the onset of a nonmonotonic field dependence below about 2 K underlines the existence of another characteristic temperature scale, previously highlighted with other measurements, and sheds new light on the phase diagram of herbertsmithite down to the lowest temperatures.

Using time- and angle-resolved photoemission spectroscopy, we study the surface exciton formed on $\mathrm{InP}\left(110\right)\text{−}\left(1\times 1\right)$ surface at 90 K under ultrahigh vacuum conditions. The surface exciton shows a characteristic photoemission peak with a long lifetime of 9.5 ns at 90 K. The exciton binding energy is 28 meV, about 5.5 times larger than the energy of bulk excitons. The radial probability density at the lowest state of the exciton is spheroidal, confined within $\sim 6\AA$ from the surface along the surface-normal direction with a radial spread of $\sim 44\AA$ in the plane parallel to the surface, being a quasi–two-dimensional excitonic state. These features are consistently described in terms of the exciton theory based on the Wannier equation. Both the reduced screening effects and the two-dimensional confinement at the surface region play important roles in charactering the surface exciton on $\mathrm{InP}\left(110\right)\text{−}\left(1\times 1\right)$ surfaces.

We describe scanning tunneling spectroscopic signatures of Majorana zero modes (MZMs) in Kitaev spin liquids. The tunnel conductance is determined by the dynamical spin correlations of the spin liquid, which we compute exactly, and by spin-anisotropic cotunneling form factors. Near a ${\mathbb{Z}}_2$ vortex, the tunnel conductance has a staircase voltage dependence, where conductance steps arise from MZMs and (at higher voltages) from additional vortex configurations. By scanning the probe tip position, one can detect the vortex locations. Our analysis suggests that topological magnon bound states near defects or magnetic impurities generate spectroscopic signatures that are qualitatively different from those of MZMs.

We examine the physical implications of the viscous redundancy of two-dimensional anisotropic fluids, where different components of the viscosity tensor lead to identical effects in the bulk of a system [Rao and Bradlyn, Phys. Rev. X 10, 021005 (2020)]. We first reintroduce the redundancy, show how it reflects a lack of knowledge of microscopic information of a system, and give microscopic examples. Next, we show that fluid flow in systems with a boundary can distinguish between otherwise redundant viscosity coefficients. In particular, we show how the dispersion and damping of gravity-dominated surface waves can be used to resolve the redundancies between both dissipative and Hall viscosities, and discuss how these results apply to recent experiments in chiral active fluids with nonvanishing Hall viscosity. Our results highlight the importance of divergenceless, magnetizationlike contributions to the stress (which we dub contact terms). Finally, we apply our results to the hydrodynamics of quantum Hall fluids and show that the extra contribution to the action that renders the bulk Wen-Zee action gauge invariant in systems with a boundary can be reinterpreted in terms of the bulk viscous redundancy.

We present the theory and numerical evaluations of the backscattering rate determined by acceptor holes or Mn spins in HgTe and (Hg,Mn)Te quantum wells in the quantum spin Hall regime. The role of anisotropic $s\text{−}p$ and $sp\text{−}d$ exchange interactions, Kondo coupling, Luttinger liquid effects, precessional dephasing, and bound magnetic polarons is quantified. The determined magnitude and temperature dependence of conductance are in accord with experimental results for HgTe and (Hg,Mn)Te quantum wells.

Multipartite entanglement refers to the simultaneous entanglement between multiple subsystems of a many-body quantum system. While multipartite entanglement can be difficult to quantify analytically, it is known that it can be witnessed through the quantum Fisher information (QFI), a quantity that can also be related to dynamical Kubo response functions. In this work, we first show that the finite temperature QFI can generally be expressed in terms of a static structure factor of the system, plus a correction that vanishes as $T\to 0$. This implies that the static structure factor witnesses multipartite entanglement near quantum critical points at temperatures below a characteristic energy scale of the system. Therefore, in systems with a known static structure factor, we can deduce finite temperature scaling of multipartite entanglement and low temperature entanglement depth without knowledge of the full dynamical response function of the system. This is particularly useful to study 1D quantum critical systems in which sub-power-law divergences can dominate entanglement growth, where the conventional scaling theory of the QFI breaks down. The 1D spin-$\frac{1}{2}$ antiferromagnetic Heisenberg model is an important example of such a system, and we show that multipartite entanglement in the Heisenberg chain diverges nontrivially as $\sim ln{(1/T)}^{3/2}$. We verify these predictions with calculations of the QFI using conformal field theory and matrix product state simulations. Finally we discuss the implications of our results for experiments to probe entanglement in quantum materials, comparing to neutron scattering data in ${\mathrm{KCuF}}_3$, a material well described by the Heisenberg chain.

In a magnetic metal, the Hall resistance is generally taken to be the sum of the ordinary Hall resistance and the anomalous Hall resistance. Here it is shown that this empirical relation is no longer valid when either the ordinary Hall angle or the anomalous Hall angle is not small. Using the proper conductivity relation, we reveal an unexpected magnetoresistance (MR) induced by the anomalous Hall effect (AHE). A $B$-linear MR arises and the sign of the slope depends on the sign of the anomalous Hall angle, giving rise to a characteristic bowtie shape. The Hall resistance in a single-band system can exhibit a nonlinearity which is usually considered as a characteristic of a two-band system. A $B$-symmetric component appears in the Hall. These effects reflect the fundamental difference between the ordinary Hall effect and the AHE. Furthermore, we experimentally reproduce the unusual MR and Hall reported before in ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ and show that these observations can be well explained by the proposed mechanism. MR often observed in quantum anomalous Hall insulators provides further confirmation of the picture. The effect may also account for the large MR observed in nonmagnetic three-dimensional topological Dirac semimetals.

X-ray beams with orbital angular momentum (OAM) are a promising tool for x-ray characterization techniques. Beams with OAM have a helicity—an azimuthally varying phase—which leads to a gradient of the light field. New material properties can be probed by utilizing the helicity of an OAM beam. Here, we demonstrate a dichroic effect in resonant diffraction from an artificial antiferromagnet with a topological defect. We found that the scattered OAM beam has circular dichroism at the antiferromagnetic Bragg peak whose sign is coupled to its helicity, which reveals the real-space configuration of the antiferromagnetic ground state. Thermal cycling of the artificial antiferromagnet can change the ground state, as indicated by reversal of the sign of circular dichroism. This result is one of the first demonstrations of a soft x-ray spectroscopy characterization technique utilizing the OAM of x rays. This helicity-dependent circular dichroism exemplifies the potential to utilize OAM beams to probe matter in a way that is inaccessible using currently available x-ray techniques.

The superconductor ThIrSi, with $T_c=6.5\mathrm{K}$, is expected to show unusual features in view of its noncentrosymmetric structure and the presence of heavy elements featuring a sizable spin-orbit coupling. Here, we report a comprehensive study of its electronic properties by means of magnetization, muon-spin rotation and relaxation ($\mu \mathrm{SR}$) and nuclear magnetic resonance (NMR) measurements. Both the superfluid density ${\rho }_{\mathrm{sc}}\left(T\right)$ (determined via transverse-field $\mu \mathrm{SR}$) and the spin-lattice relaxation rate $T_1^{-1}\left(T\right)$ (determined via NMR) suggest a nodeless superconductivity. Furthermore, the absence of spontaneous magnetic fields below $T_c$, as evinced from zero-field $\mu \mathrm{SR}$ measurements, indicates a preserved time-reversal symmetry in the superconducting state of ThIrSi. Temperature-dependent upper critical fields as well as field-dependent superconducting muon-spin relaxations suggest the presence of multiple superconducting gaps in ThIrSi.

We study the dynamical properties of pointlike defects, represented by monoatomic chalcogen vacancies, in ${\mathrm{WS}}_2$–graphene and ${\mathrm{MoS}}_2$–graphene heterobilayers. Employing a multidisciplinary approach based on the combination of ab initio, model Hamiltonian and density matrix techniques, we propose a minimal interacting model that allows for the calculation of electronic transition times associated to population and depopulation of the vacancy by an additional electron. We obtain the “coarse-grained” semiclassical dynamics by means of a quantum master equation approach and discuss the potential role of virtual charge fluctuations in the internal dynamics of impurity quasidegenerate states. The interplay between the symmetry of the lattice and the spin degree of freedom through the spin-orbit interaction and its impact on charge quenching is studied in detail.

We present low-temperature Raman measurements on gate-tunable graphene encapsulated in hexagonal boron nitride, which allows us to study in detail the Raman $G$ and 2D mode frequencies and linewidths as a function of the charge carrier density. We observe a clear softening of the Raman $G$ mode (of up to 2.5 ${\mathrm{cm}}^{-1}$) at low carrier density due to the phonon anomaly and a residual $G$ mode linewidth of $\approx 3.5{\mathrm{cm}}^{-1}$ at high doping. By analyzing the $G$ mode dependence on doping and laser power we extract an electron-phonon-coupling constant of $\approx 4.4\times {10}^{-3}$ (for the $G$ mode phonon). The ultraflat nature of encapsulated graphene results in a minimum Raman 2D peak linewidth of 14.5 ${\mathrm{cm}}^{-1}$ and allows us to observe intrinsic electron-electron scattering-induced broadening of the 2D peak of up to 18 ${\mathrm{cm}}^{-1}$ for an electron density of $5\times {10}^{12}{\mathrm{cm}}^{-2}$ (laser excitation energy of 2.33 eV). Our findings not only provide insights into electron-phonon coupling and the role of electron-electron scattering in the broadening of the 2D peak but also crucially show the limitations when it comes to the use of Raman spectroscopy (i.e., the use of the frequencies and the linewidths of the $G$ and 2D modes) to benchmark graphene in terms of charge carrier density, strain, and strain inhomogeneities. This is particularly relevant when utilizing spatially resolved 2D Raman linewidth maps to assess substrate-induced nanometer-scale strain variations.

Time-resolved near-edge x-ray absorption with Auger-electron detection is employed as a surface-sensitive probe to study the dynamics of surface atomic motion in graphite upon laser excitation. To this end, ultrafast changes in photoelectron spectra with a focus on carbon KVV-Auger intensities are used as probe in a pump-probe scheme with pulsed femtosecond near-infrared laser excitation of a highly oriented pyrolytic graphite (HOPG) sample. The dynamics of the HOPG surface excitation at the $K$ edge appears as transient change in Auger yield. Since the directional bond character of carbon is reflected in linear dichroism of x-ray absorption, the transient angular variation of the $1s\to \pi$ transitions can be used to uncover the laser-induced dynamics of the atomic surface structure which shows a huge anisotropy upon usage of s- or $p$-polarized x-ray probe pulses, respectively.