The crossover from localized to itinerant electron regimes in the geometrically frustrated spinel system ${\mathrm{Mn}}_{1-x}{\mathrm{Co}}_x{\mathrm{V}}_2{\mathrm{O}}_4$ is explored by neutron-scattering measurements, first-principles calculations, and spin models. At low Co doping, the orbital ordering (OO) of the localized ${\mathrm{V}}^{3+}$ spins suppresses magnetic frustration by triggering a tetragonal distortion. At high Co doping levels, however, electronic itinerancy melts the OO and lessens the structural and magnetic anisotropies, thus increasing the amount of geometric frustration for the V-site pyrochlore lattice. Contrary to the predicted paramagentism induced by chemical pressure, the measured noncollinear spin states in the Co-rich region of the phase diagram provide a unique platform where localized spins and electronic itinerancy compete in a geometrically frustrated spinel.

The surface of a magnetite single crystal with (001) orientation has been prepared by sputtering/annealing cycles providing the $\sqrt{2}\times \sqrt{2}R{45}^{\circ }$ reconstruction. The distribution of magnetic domains on the surface has been imaged by x-ray magnetic dichroism in a photoemission microscope. The easy axes are along the surface in-plane $\langle 110\rangle$ directions. The near-surface magnetic moment was determined by applying the sum rules to XMCD spectra obtained with different kinetic energies of the secondary electrons. A reduced total moment of $3.3 {\mu }_B$ and a ratio of about 0.10 between orbital and spin moment was found, which we attribute to the surface reconstruction.

We have used scanning micro x-ray diffraction to characterize different phases in superconducting ${\mathrm{K}}_x{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_2$ as a function of temperature, unveiling the thermal evolution across the superconducting transition temperature ($T_c\sim 32$ K), phase separation temperature ($T_{ps}\sim 520$ K), and iron-vacancy order temperature ($T_{vo}\sim 580$ K). In addition to the iron-vacancy ordered tetragonal magnetic phase and orthorhombic metallic minority filamentary phase, we have found clear evidence of the interface phase with tetragonal symmetry. The metallic phase is surrounded by this interface phase below $\sim 300$ K, and is embedded in the insulating texture. The spatial distribution of coexisting phases as a function of temperature provides clear evidence of the formation of protected metallic percolative paths in the majority texture with large magnetic moment, required for the electronic coherence for the superconductivity. Furthermore, a clear reorganization of iron-vacancy order around the $T_{ps}$ and $T_c$ is found with the interface phase being mostly associated with a different iron-vacancy configuration, that may be important for protecting the percolative superconductivity in ${\mathrm{K}}_x{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_2$.

A monolayer FeSe thin film grown on ${\mathrm{SrTiO}}_3$(001) (STO) shows the sign of $T_c>77\mathrm{K}$, which is higher than the $T_c$ record of 56 K for bulk FeAs-based superconductors. However, little is known about the magnetic ground state of FeSe, which should be closely related to its unusual superconductivity. Previous studies presume the collinear stripe antiferromagnetic (AFM) state as the ground state of FeSe, the same as that in FeAs superconductors. Here we find a magnetic order named the “pair-checkerboard AFM” as the magnetic ground state of tetragonal FeSe. The pair-checkerboard order results from the interplay between the nearest-, next-nearest, and unnegligible next-next-nearest neighbor magnetic exchange couplings of Fe atoms. The monolayer FeSe in pair-checkerboard order shows an unexpected insulating behavior with a Dirac-cone-like band structure related to the specific orbital order of the $d_{xz}$ and $d_{yz}$ characters of Fe atoms, which could explain the recently observed insulator-superconductor transition. The present results cast insights on the magnetic ordering in FeSe monolayer and its derived superconductors.

By using renormalization-group (RG) methods, we study a non-mean-field model of a spin glass built on a hierarchical lattice, the hierarchical Edwards-Anderson model in a magnetic field. We investigate the spin-glass transition in a field by studying the existence of a stable critical RG fixed point (FP) with perturbation theory. In the parameter region where the model has a mean-field behavior—corresponding to $d\ge 4$ for a $d$-dimensional Ising model—we find a stable FP that corresponds to a spin-glass transition in a field. In the non-mean-field parameter region the FP above is unstable, and we determine exactly all other FPs: to our knowledge, this is the first time that all perturbative FPs for the full set of RG equations of a spin glass in a field have been characterized in the non-mean-field region. We find that all potentially stable FPs in the non-mean-field region have a nonzero imaginary part: this constitutes, to the best of our knowledge, the first demonstration for a spin glass in a field that there is no perturbative FP corresponding to a spin-glass transition in the non-mean-field region. Finally, we discuss the possible interpretations of this result, such as the absence of a phase transition in a field or the existence of a transition associated with a nonperturbative FP.

Recently, it was argued that the braiding and statistics of anyons in a two-dimensional topological phase can be extracted by studying the quantum entanglement of the degenerate ground states on the torus. This construction either required a lattice symmetry (such as $\pi /2$ rotation) or tacitly assumed that the minimum entanglement states (MESs) for two different bipartitions can be uniquely assigned quasiparticle labels. Here we describe a procedure to obtain the modular $\mathcal{S}$ matrix, which encodes the braiding statistics of anyons, which does not require making any of these assumptions. Our strategy is to coherently compare MESs of three independent entanglement bipartitions of the torus, which leads to a unique modular $\mathcal{S}$. This procedure also puts strong constraints on the modular $\mathcal{T}$ and $\mathcal{U}$ matrices without requiring any symmetries, and in certain special cases, completely determines it. Our method applies equally to Abelian and non-Abelian topological phases.

We experimentally investigate the symmetry in the hidden order (HO) phase of intermetallic ${\mathrm{URu}}_2{\mathrm{Si}}_2$ by mapping the lattice and magnetic excitations via inelastic neutron and x-ray scattering measurements in the HO and high-temperature paramagnetic phases. At all temperatures, the excitations respect the zone edges of the body-centered tetragonal paramagnetic phase, showing no signs of reduced spatial symmetry, even in the HO phase. The magnetic excitations originate from transitions between hybridized bands and track the Fermi surface, whose features are corroborated by the phonon measurements. Due to a large hybridization energy scale, a full uranium moment persists in the HO phase, consistent with a lack of observed crystal-field-split states. Our results are inconsistent with local order-parameter models and the behavior of typical density waves. We suggest that an order parameter that does not break spatial symmetry would naturally explain these characteristics.

We report a comprehensive investigation of the lattice dynamics of ${\mathrm{URu}}_2{\mathrm{Si}}_2$ as a function of temperature using Raman scattering, optical conductivity, and inelastic neutron scattering measurements as well as theoretical ab initio calculations. The main effects on the optical phonon modes are related to Kondo physics. The ${\mathrm{B}}_{1g}$ (${\Gamma }_3$ symmetry) phonon mode slightly softens below $\sim 100\mathrm{K}$, in connection with the previously reported softening of the elastic constant, $C_{11}-C_{12}$, of the same symmetry, both observations suggesting a ${\mathrm{B}}_{1g}$ symmetry-breaking instability in the Kondo regime. Through optical conductivity, we detect clear signatures of strong electron-phonon coupling, with temperature-dependent spectral weight and Fano line shape of some phonon modes. Surprisingly, the line shapes of two phonon modes, ${\mathrm{E}}_u$(1) and ${\mathrm{A}}_{2u}$(2), show opposite temperature dependencies. The ${\mathrm{A}}_{2u}$(2) mode loses its Fano shape below 150 K, whereas the ${\mathrm{E}}_u$(1) mode acquires it below 100 K, in the Kondo crossover regime. This may point to momentum-dependent Kondo physics. By inelastic neutron-scattering measurements we have drawn the full dispersion of the phonon modes between 300 and 2 K. No remarkable temperature dependence has been obtained, including through the hidden order transition. Ab initio calculations with the spin-orbit coupling are in good agreement with the data except for a few low-energy branches with propagation in the ($a,b$) plane.

CeRuPO is a rare example of a ferromagnetic (FM) Kondo-lattice system. External pressure suppresses the ordering temperature to zero at about $p_c\approx 3$ GPa. Our ac-susceptibility and electrical-resistivity investigations evidence that the type of magnetic ordering changes from FM to antiferromagnetic (AFM) at about $p^{*}\approx 0.87\text{GPa}$. Studies in applied magnetic fields suggest that ferromagnetic and antiferromagnetic correlations compete for the ground state at $p>p^{*}$, but finally the AFM correlations win. The change in the magnetic ground-state properties is closely related to the pressure evolution of the crystalline-electric-field level scheme and the magnetic Ruderman-Kittel-Kasuya-Yosida exchange interaction. The Néel temperature disappears abruptly in a first-order-like fashion at $p_c$, hinting at the absence of a quantum critical point. This is consistent with the low-temperature transport properties exhibiting Landau–Fermi-liquid behavior in the whole investigated pressure range up to 7.5 GPa.

We theoretically study the quantum transport in a three-dimensional Weyl electron system in the presence of the charged impurity scattering using a self-consistent Born approximation. The scattering strength is characterized by the effective fine-structure constant $\alpha$, which depends on the dielectric constant and the Fermi velocity of the linear band. We find that the Boltzmann theory fails at the band touching point, where the conductivity takes a nearly constant value almost independent of $\alpha$, even though the density of states linearly increases with $\alpha$. There the magnitude of the conductivity only depends on the impurity density. The qualitative behavior is quite different from the case of the Gaussian impurities, where the minimum conductivity vanishes below a certain critical impurity strength.

Both $\alpha \text{-Sn}$ and HgTe are expected to have similar topological properties because of their inverted band structure and zero-gap character. We investigate how the different crystal symmetries and the bonding to barrier materials act to the quantum phase transition versus the thickness of the corresponding quantum well (QW) structures. They are simulated by ${\left(\text{SnSn}\right)}_N{\left(\text{CdTe}\right)}_M$ and ${\left(\text{HgTe}\right)}_N{\left(\text{CdTe}\right)}_M\left(110\right)$ superlattices. Their electronic structures and eigenstates are studied by means of first-principles calculations using the modified Becke-Johnson exchange-correlation functional and spin-orbit interaction. Significant differences are observed for the two QW materials. A topological transition between trivial insulator and quantum spin Hall phase together with the formation of topologically protected edge states are observed in the case of HgTe QWs, while these features are considerably modified for $\alpha \text{-Sn}$. The different behaviors are discussed in the light of the different symmetry, spin-orbit interaction, and interface bonding. For a better understanding of the influence of the interface electrostatics also results for ${\left(\text{HgTe}\right)}_N{\left(\text{InSb}\right)}_M\left(110\right)$ systems are discussed.

We study relevant perturbations at the spin quantum Hall critical point using a network model formulation. The model has been previously mapped to classical percolation on a square lattice, and we use the mapping to extract exact analytical values of the scaling dimensions of the relevant perturbations. We find that several perturbations that are distinct in the network model formulation correspond to the same operator in the percolation picture. We confirm our analytical results by comparing them with numerical simulations of the network model.

In this theoretical work, we propose a chemical route to creating stable benzene-transition metal-graphene sandwich structures. The binding energy of the transition metal to graphene is enhanced through adsorption at appropriate defects, immobilizing the metal onto the graphene web. Capping the metal with a benzene ring further stabilizes the structure. The stability and the magnetic properties of these composite structures vary for different defects such as vacancies and nitrogen substitutionals in graphene. The proposed complexes have high cohesive energies and are either metallic or are small-band-gap semiconductors. Several of the proposed structures also have large spin polarization energies that make them suitable for use as nanomagnets in ambient conditions. This work also sheds light on the experimental results in the field where the sandwich structures may have been successfully created. We show that defect engineering is a viable option for creating designer, graphene-based structures that may play an important role in fields as diverse as spintronics, nanoelectronics, hydrogen storage, and catalysis.

Recent analysis has confirmed earlier general arguments that the Kerr response vanishes in any time-reversal invariant system which satisfies the Onsager relations. Thus, the widely cited relation between natural optical activity (gyrotropy) and the Kerr response, employed in our original paper, is incorrect. However, there is increasingly clear experimental evidence that, as argued in our paper, the onset of an observable Kerr signal in the cuprates reflects point-group symmetry rather than time-reversal symmetry breaking.

The dynamics of quantum phase transitions are inevitably accompanied by the formation of defects when crossing a quantum critical point. For a generic class of quantum critical systems, we solve the problem of minimizing the production of defects through the use of a gradient-based deterministic optimal control algorithm. By considering a finite-size quantum Ising model with a tunable global transverse field, we show that an optimal power-law quench of the transverse field across the Ising critical point works well at minimizing the number of defects, in spite of being drawn from a subset of quench profiles. These power-law quenches are shown to be inherently robust against noise. The optimized defect density exhibits a transition at a critical ratio of the quench duration to the system size, which we argue coincides with the intrinsic speed limit for quantum evolution.

We show that the spectral weights $W_{m\vec{K}}\left(\vec{k}\right)$ used for the unfolding of two-component spinor eigenstates $|{\psi }_{m\vec{K}}^{\mathrm{SC}}\rangle =|\alpha \rangle |{\psi }_{m\vec{K}}^{\mathrm{SC}},\alpha \rangle +|\beta \rangle |{\psi }_{m\vec{K}}^{\mathrm{SC}},\beta \rangle$ can be decomposed as the sum of the partial spectral weights $W_{m\vec{K}}^{\mu }\left(\vec{k}\right)$ calculated for each component $\mu =\alpha ,\beta$ independently, effortlessly turning a possibly complicated problem involving two coupled quantities into two independent problems of easy solution. Furthermore, we define the unfolding-density operator ${\widehat{\rho }}_{\vec{K}}(\vec{k};\varepsilon )$, which unfolds the primitive cell expectation values ${\phi }^{\mathrm{pc}}(\vec{k};\varepsilon )$ of any arbitrary operator $\widehat{\phi }$ according to ${\phi }^{\mathrm{pc}}(\vec{k};\varepsilon )=\text{Tr}({\widehat{\rho }}_{\vec{K}}(\vec{k};\varepsilon )\widehat{\phi })$. As a proof of concept, we apply the method to obtain the unfolded band structures, as well as the expectation values of the Pauli spin matrices, for prototypical physical systems described by two-component spinor eigenfunctions.

We study the effect of disorder in strongly interacting small atomic chains. Using the Kotliar-Ruckenstein slave-boson approach, we diagonalize the Hamiltonian via scattering matrix theory. We numerically solve the Kondo transmission and the slave-boson parameters that allow us to calculate the Kondo temperature. We demonstrate that in the weak disorder regime, disorder in the energy levels of the dopants induces a nonscreened disorder in the Kondo couplings of the atoms. We show that disorder increases the Kondo temperature of a perfect chain. We find that this disorder in the couplings comes from a local distribution of Kondo temperatures along the chain. We propose two experimental setups where the impact of local Kondo temperatures can be observed.

We construct generalized Hofstadter models that possess “color-entangled” flat bands and study interacting many-body states in such bands. For a system with periodic boundary conditions and appropriate interactions, there exist gapped states at certain filling factors for which the ground-state degeneracy depends on the number of unit cells along one particular direction. This puzzling observation can be understood intuitively by mapping our model to a single-layer or a multilayer system for a given lattice configuration. We discuss the relation between these results and the previously proposed “topological nematic states,” in which lattice dislocations have non-Abelian braiding statistics. Our study also provides a systematic way of stabilizing various fractional topological states in $C>1$ flat bands and provides some hints on how to realize such states in experiments.

The double perovskite ${\mathrm{Ba}}_2{\mathrm{NaOsO}}_6$ (BNOO), an exotic example of a very high oxidation state (heptavalent) osmium $d^1$ compound and also uncommon by being a ferromagnetic open $d$-shell (Mott) insulator without Jahn-Teller (JT) distortion, is modeled using a density functional theory based hybrid functional incorporating exact exchange for correlated electronic orbitals and including the large spin-orbit coupling (SOC). The experimentally observed narrow-gap ferromagnetic insulating ground state is obtained, but only when including spin-orbit coupling, making this a Dirac-Mott insulator. The calculated easy axis along [110] is in accord with experiment, providing additional support that this approach provides a realistic method for studying this system. The predicted spin density for [110] spin orientation is nearly cubic (unlike for other directions), providing an explanation for the absence of JT distortion. An orbital moment of $-0.4{\mu }_B$ strongly compensates the $+0.5{\mu }_B$ spin moment on Os, leaving a strongly compensated moment more in line with experiment. Remarkably, the net moment lies primarily on the oxygen ions. An insulator-metal transition, by rotating the magnetization direction with an external field under moderate pressure, is predicted as one consequence of strong SOC, and metallization under moderate pressure is predicted. Comparison is made with the isostructural, isovalent insulator ${\mathrm{Ba}}_2{\mathrm{LiOsO}}_6$, which, however, orders antiferromagnetically.