We present the appearance of nearly flat-band states with nonzero Chern numbers in a two-dimensional “diamond-octagon” lattice model comprising two kinds of elementary plaquette geometries, diamond and octagon, respectively. We show that the origin of such nontrivial topological nearly flat bands can be described by a short-ranged tight-binding Hamiltonian. By considering an additional diagonal hopping parameter in the diamond plaquettes along with an externally fine-tuned magnetic flux, it leads to the emergence of such nearly flat-band states with nonzero Chern numbers for our simple lattice model. Such topologically nontrivial nearly flat bands can be very useful to realize the fractional topological phenomena in lattice models when the interaction is taken into consideration. In addition, we also show that perfect band flattening for certain energy bands, leading to compact localized states can be accomplished by fine-tuning the parameters of the Hamiltonian of the system. We compute the density of states and the wave-function amplitude distribution at different lattice sites to corroborate the formation of such perfectly flat-band states in the energy spectrum. Considering the structural homology between a diamond-octagon lattice and a kagome lattice, we strongly believe that one can experimentally realize a diamond-octagon lattice using ultracold quantum gases in an optical lattice setting. A possible application of our lattice model could be to design a photonic lattice using single-mode laser-induced photonic waveguides and study the corresponding photonic flat bands.

At the microscopic level, individual spins in ferromagnets with random anisotropy tip transversely with distinct local angles relative to the magnetization $\vec{M}$. When driven by an rf field along the equilibrium ${\vec{M}}_0$, which changes $dM={\widehat{M}}_0·d\vec{M}$, the transverse tippings rotate about ${\vec{M}}_0$, corresponding to a new macroscopic collective angle $\varphi$ about ${\vec{M}}_0$. The coupling of $dM$ and $\varphi$ leads to a new longitudinal mode that in bulk has a frequency that is largely independent of field $H$. A longitudinal mode has been observed in thin films of ferromagnets with random anisotropy, but its frequency is $H$ dependent; for $H$ at angle $\theta$ to the film normal and fixed resonator frequency $f$, $Hcos\theta$ was constant to angles of ${80}^{\circ }$, with $H$ saturating for larger angles. When the demagnetization field is included the theory yields such an $H$ vs $\theta$ for $\theta <{80}^{\circ }$, thus providing evidence for the predicted angle $\varphi$. However, lower frequency resonators are needed to manifest the predicted macroscopic anisotropy energy.

We introduce a construction of symmetry-enriched topological orders on bipartite lattices in which two ${\mathbb{Z}}_2$ spin liquids defined on each sublattice are combined, and then anyons are condensed to reduce the topological order. By choosing different anyon condensate structures, one can vary the fractionalization pattern of the resulting spin liquid, some of which cannot be readily constructed from parton-based approaches. We demonstrate the construction for (i) a spin-1/2 honeycomb lattice where we construct a featureless state as well as intermediate states with topological order, (ii) a nonsymmorphic lattice, and (iii) lattices with magnetic translation symmetry. Finally, we discuss constraints on nonchiral topological orders in a bosonic system under magnetic field.

Results are presented on analytic and computational analyses of the spin states associated with a three-dimensional (3D) fcc lattice composed of ABC stacked kagome planes of magnetic ions with only long-range dipole-dipole interactions. Extending previous work on the 2D kagome system, where a discrete six-fold degeneracy of the ground state was revealed [Holden et al. Phys. Rev. B 91, 224425 (2015)], we show that the 3D lattice exhibits a continuous degeneracy characterized by just two spherical angles involving six sublattice spin vectors. Application of a heat bath Monte Carlo algorithm shows that thermal fluctuations reduce this degeneracy at very low temperature in an order-by-disorder process. A magnetic field applied along directions of high symmetry also results in lifting the continuous degeneracy to a subset of states from the original set of ground states. Metropolis Monte Carlo simulation results are also presented on the temperature and system size dependence of the energy, specific heat, and magnetization, providing evidence for a phase transition at $T\simeq 0.38$ (in units of the dipole strength). The results can be relevant to a class of magnetic compounds having the ${\mathrm{AuCu}}_3$ crystal structure.

We study the effect of site dilution in the Kitaev model. We derive an analytical solution of the dynamical spin correlation functions for arbitrary configurations of $Z_2$ fluxes. By incorporating this solution into a classical Monte Carlo scheme, we address how a site vacancy affects the experimental observables, such as the static spin susceptibility and the spin-lattice relaxation rate, $1/T_1$. As a result, we found an enhancement of dynamical magnetic response in the vicinity of vacancy, which leads to Friedel-like oscillation in local $1/T_1$, in contrast to limited influences on the static susceptibility. Furthermore, we found a sharp zero-energy peak in the magnetic excitation spectrum, which is attributed to the Vison-Majorana zero mode trapped near the site vacancy. This zero mode can be interpreted as a fractionalized spin hole into an Ising triplet with differentiated magnetic axes, which leads to the characteristic temperature and field-orientational dependence of $1/T_1$.

We recently proposed a high-pressure and high-temperature $P\overline{6}2m$-symmetry polymorph for ${\mathrm{CaF}}_2$ on the basis of ab initio random structure searching and density-functional theory calculations [J. R. Nelson et al., Phys. Rev. B 95, 054118 (2017)]. We revisit this polymorph using both ab initio and classical molecular dynamics simulations. The structure undergoes a phase transition to a superionic phase in which calcium ions lie on a bcc-symmetry lattice (space group $Im\overline{3}m$), a phase not previously discussed for the group-II difluorides. We demonstrate that modeling this phase transition is surprisingly difficult and requires very large simulation cells (at least 864 atoms) in order to observe correct qualitative and quantitative behavior. The prediction of superionic behavior in $P\overline{6}2m$ ${\mathrm{CaF}}_2$ was originally made through the observation of a lattice instability at the harmonic level in DFT calculations. Using superionic $\alpha -{\mathrm{CaF}}_2$, ${\mathrm{CeO}}_2$, $\beta -{\mathrm{PbF}}_2$, and ${\mathrm{Li}}_2\mathrm{O}$ as examples, we examine the potential of using phonons as a means to search for superionic materials and propose that this offers an affordable way to do so.

We used temperature dependent high-resolution x-ray powder diffraction and magnetization measurements to investigate structural, magnetic and electronic degrees of freedom across the ferromagnetic magnetoelastic phase transition in $\mathrm{M}{\mathrm{n}}_1\mathrm{F}{\mathrm{e}}_1{\mathrm{P}}_{0.6-\mathrm{w}}\mathrm{S}{\mathrm{i}}_{0.4}{\mathrm{B}}_{\mathrm{w}}$ ($w=0$, 0.02, 0.04, 0.06, 0.08). The magnetic transition was gradually tuned from a strong first-order ($w=0$) towards a second-order magnetic transition by substituting P by B. Increasing the B content leads to a systematic increase in the magnetic transition temperature and a decrease in thermal hysteresis, which is below 1 K for $w=0.08$. Furthermore, the largest changes in lattice parameter across the magnetic transition occur for $w=0$, which systematically becomes smaller approaching the samples with $w=0.08$. Electron density plots show a strong directional preference of the electronic distribution around Fe, which indicates the forming of bonds between Fe atoms and Fe and P/Si in the paramagnetic phase. On the other hand, Mn shows no preferred directions. Due to the low B concentrations ($w<0.08$), distortions of the lattice are limited. However, even small amounts of B strongly disturb the overall distribution of the electron density across the unit cell. Samples containing B show a strongly reduced change in the electron density compared to the parent compound without B. The magnetoelastic coupling shows a continuous weakening with the B content.

A preponderance of evidence suggests that the ground state of the nearest-neighbor $S=1/2$ antiferromagnetic Heisenberg model on the kagome lattice is a gapless spin liquid. Many candidate materials for the realization of this model possess in addition a Dzyaloshinskii-Moriya (DM) interaction. We study this system by tensor-network methods and deduce that a weak but finite DM interaction is required to destabilize the gapless spin-liquid state. The critical magnitude, $D_c/J\simeq 0.012\left(2\right)$, lies well below the DM strength proposed in the kagome material herbertsmithite, indicating a need to reassess the apparent spin-liquid behavior reported in this system.

Understanding the formation of Cooper pairs in iron-based superconductors is one of the most important topics in condensed matter physics. In conventional superconductors, the electron-phonon interaction leads to the formation of Cooper pairs. In conventional strong-coupling superconductors like lead (Pb), the features due to electron-phonon interaction are evident in the infrared absorption spectra. Here we investigate the infrared absorption spectra of the iron arsenide superconductor $\mathrm{BaF}{\mathrm{e}}_{1.9}\mathrm{P}{\mathrm{t}}_{0.1}\mathrm{A}{\mathrm{s}}_2$. We find that this superconductor has fully gapped (nodeless) Fermi surfaces, and we observe the strong-coupling electron-boson interaction features in the infrared absorption spectra. Through modeling with the Eliashberg function based on Eliashberg theory, we obtain a good quantitative description of the energy gaps and the strong-coupling features. The full Eliashberg equations are solved to check the self-consistency of the electron-boson coupling spectrum, the largest energy gap, and the transition temperature ($T_{\mathrm{c}}$). Our experimental data and analysis provide compelling evidence that superconductivity in $\mathrm{BaF}{\mathrm{e}}_{1.9}\mathrm{P}{\mathrm{t}}_{0.1}\mathrm{A}{\mathrm{s}}_2$ is induced by the coupling of electrons to a low-energy bosonic mode that does not originate solely from phonons.

Using group theoretic and topological concepts, together with tunneling phenomena, we geometrically design interfacial wave networks that contain splitters which partition energy in two, three, four, or five directions. This enriches the valleytronics literature that has, so far, been limited to two-directional splitters. Additionally, we describe a design paradigm that gives greater detail about the relative transmission along outgoing leads, away from a junction; previously, only the negligible transmission leads were predictable. We utilize semianalytic numerical simulations, as opposed to finite element methods, to clearly illustrate all of these features with highly resolved edge states. As a consequence of this theory, networks, with directionality tunable by geometry, ideal for applications such as beam-splitters, switches, and filters are created. Coupling these networks that contain multidirectional energy-splitters culminates in the realization of a topological supernetwork.

We describe square lattice spin liquids, which break time-reversal symmetry, while preserving translational symmetry. The states are distinguished by the manner in which they transform under mirror symmetries. All the states have nonzero scalar spin chirality, which implies the appearance of spontaneous orbital charge currents in the bulk (even in the insulator); but in some cases, orbital currents are nonzero only in a formulation with three orbitals per unit cell. The states are formulated using both the bosonic and fermionic spinon approaches. We describe states with ${\mathbb{Z}}_2$ and U(1) bulk topological order, and the chiral spin liquid with semionic excitations. The chiral spin liquid has no orbital currents in the one-band formulation, but does have orbital currents in the three-band formulation. We discuss application to the cuprate superconductors, after postulating that the broken time-reversal and mirror symmetries persist into confining phases, which may also break other symmetries. In particular, the broken symmetries of the chiral spin liquid could persist into the Néel state.

We demonstrate a general pole-zero method for the design of the scattering resonances of multilayered nanospheres, and we apply it to the relevant cases of strongly dispersive light scattering from metal-dielectric-metal and all-dielectric nanostructures. The pole-zero method is based on the full-wave iterative solution of the Mie scattering theory of multilayered spheres, which is valid beyond the conventional quasistatic limit. By investigating scattering resonances in the complex frequency plane, we show how to engineer anomalous Fano-like dipolar line shapes from complex pole-zero interactions controlled by the geometrical parameters of the structures. The pole-zero method is then applied to the design of the backscattering and forward-scattering efficiencies beyond the dipolar approximation. The engineering of scattering and absorption resonances with customized line shapes in metal-dielectric nanostructures provides unique opportunities for active devices including optical sensors, light emitters, and nonlinear elements.

We studied the electronic, magnetic, and optical properties of $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ insulator within the density-functional theory using the generalized gradient approximation taking into account strong Coulomb correlations (GGA+$U$) in the framework of the fully relativistic spin-polarized Dirac linear muffin-tin orbital band-structure method. The x-ray absorption spectra and x-ray magnetic circular dichroism (XMCD) at the Ir $L_{2,3}$ edges were investigated theoretically from first principles. The calculated results are in good agreement with experimental data. We found that the GGA+$U$ approach with Hubbard $U_{\text{eff}}=1.5\mathrm{eV}$ well describes the optical spectra and XMCD spectra at the Ir $L_{2,3}$ edges. We investigated the electronic structure of $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ under pressure from first principles. The hyperhoneycomb iridate $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ is on the border of the magnetic ordering with relatively weak Coulomb electron-electron correlations. The $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ undergoes a pressure-induced structural and magnetic phase transitions at $P_c=4.4$ GPa with symmetry lowering to the monoclinic $C2/c$. The structural phase transition is accompanied by a dimerization of the previously equally long $x/y$ Ir-Ir bonds. We find remarkable nonmagnetic ground states of $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ at $P_c$, with a concomitant electronic phase transition from a Mott insulator to band insulators. We found that $J_{\text{eff}}=1/2$ states are still dominant in the low-energy region in high-pressure monoclinic $C2/c$ structure.

We study phases of interacting Dirac matter that host Berry signatures. We predict a topological Lifshitz phase transition caused by the changes of a Dirac cone intersection from a semimetallic phase to helical insulating or metallic phases. These helical phases provide examples of a gapless topological phase where the spectral gap is not required for a topological protection. To realize nodal helical phases one would need to consider isotropic infinite-range interparticle interaction. This interaction could emerge because of a momentum conserving scattering of electrons from a bosonic mode. For repulsive/attractive inter-particle interaction in density/pseudospin channel, the system undergoes a transition to the helical insulator phase. For an attractive density-density interaction, a metallic phase forms that hosts a nodal circle and a nodal sphere in two and three dimensions, respectively. A sheet singularity of Berry curvature is highlighted as a peculiar feature of the nodal sphere phase in three dimensions and represents the extension of the Berry monopole singularities into an inflated monopole. To illustrate the properties of these helical phases we investigate Landau levels in both metallic and insulating phases. Our study provides an extension of the paradigm in the interacting Dirac matter and makes an interesting connection to inflated topological singularities in cosmology.

We study the phase transitions induced by a lateral superlattice potential (a metallic grid) placed on top of a two-dimensional electron gas (2DEG) formed in a semiconductor quantum well. In a quantizing magnetic field and at filling factor $\nu =1,$ the ground state of the 2DEG depends on the strength $V_g$ of the superlattice potential as well as on the number of flux quanta piercing the unit cell of the external potential. It was recently shown that in the case of a square lateral superlattice, the potential modulates both the electronic and spin density and in some range of $V_g$, the ground state is a two-sublattice spin meron crystal where adjacent merons have the global phase of their spin texture shifted by $\pi ,$ i.e., they are “antiferromagnetically” ordered. In this paper, we evaluate the importance of Landau-level mixing on the phase diagram obtained previously for the square lattice and derive the phase diagram of the 2DEG modulated by a triangular superlattice. When Landau-level mixing is considered, we find in this case that, in some range of $V_g,$ the ground state is a three-sublattice spin meron crystal where adjacent merons of the same vorticity have the global phase of their spin texture rotated by ${120}^{\circ }$ with respect to one another. This meron crystal is preceded in the phase diagram by another meron lattice phase with a very different spin texture that does not appear, at first glance, to resolve the spin frustration inherent to an antiferromagnetic ordering on a triangular lattice.

Nitrogen vacancy (NV) centers in diamond have been identified over the past few years as promising systems for a variety of applications, ranging from quantum information science to magnetic sensing. This relies on the unique optical and spin properties of the negatively charged NV. Many of these applications require shallow NV centers, i.e., NVs that are close (a few nm) to the diamond surface. In recent years there has been increasing interest in understanding the spin and charge dynamics of NV centers under various illumination conditions, specifically under infrared (IR) excitation, which has been demonstrated to have significant impact on the NV centers' emission and charge state. Nevertheless, a full understanding of all experimental data is still lacking, with further complications arising from potential differences between the photodynamics of bulk and shallow NVs. Here we suggest a generalized quantitative model for NV center spin- and charge-state dynamics under both green and IR excitation. We experimentally extract the relevant transition rates, providing a comprehensive model which reconciles all existing experimental results in the literature, except for highly nonlinear regimes. Moreover, we identify key differences between the photodynamics of bulk and shallow NVs, and use them to significantly enhance the initialization fidelity of shallow NVs to the useful negatively charged state.

We present a theoretical study of the quantum critical behavior in heat transport via a two-state system with subohmic reservoirs. We calculate the temperature dependence of the thermal conductance near the quantum phase transition via the continuous-time quantum Monte Carlo method and discuss its critical exponents. We also propose a superconducting circuit to realize the subohmic spin-boson model that can be used to observe quantum critical phenomena.

Optical charge state switching was previously observed in photoluminescence experiments for the divacancy defect in $4H$-SiC. The participating dark charge state could not be identified with certainty. We use constrained density-functional theory to investigate the mechanism of charge state conversion from the bright neutral charge state of the divacancy defect to the positive and negative charge states including corresponding recovery of the neutral charge state. While we can confirm that the positive charge state is dark, we do not find evidence that the negative charge state is dark. We compute similar absorption energies required for conversion of the neutral defect to both charge states. However, the formation of the positive charge state requires a series of excitations involving a 2-photon excitation, while the creation of the negative charge state is achieved through a single 2-photon process. Calculated absorption energies for the recovery of the neutral defect from the positive charge state fit the experimental value better than those from the negative charge state. Defect formation energies as a function of the Fermi energy show a very small Fermi energy range in which the negative charge state is most stable, while the positive charge state exhibits a wide stability range. Overall, our computational results give more support to the identification of the dark charge state as the positive over the negative charge state in the mechanism of optical charge state switching.

Resonant inelastic x-ray scattering (RIXS) is a promising technique for obtaining electron-phonon coupling constants. However, the ability to extract these coupling constants throughout the Brillouin zone for crystalline materials remains limited. To address this need, we developed a Green's function formalism to capture electron-phonon contributions to core-level spectroscopies without explicitly solving the full vibronic problem. Our approach is based on the cumulant expansion of the Green's function combined with many-body theory calculated vibrational coupling constants. The methodology is applied to x-ray photoemission spectroscopy, x-ray absorption spectroscopy (XAS), and RIXS. In the case of the XAS and RIXS, we use a two-particle exciton Green's function, which accounts implicitly for particle-hole interference effects that have previously proved difficult. To demonstrate the methodology and gain a deeper understanding of the experimental technique, we apply our formalism to small molecules, for which unambiguous experimental data exist. This comparison reveals that the vibronic coupling constant probed by RIXS is in fact related to exciton-phonon coupling rather than electron-phonon coupling, challenging the conventional interpretation of the experiment.

The magnetic specific heat of $\mathrm{RbFeS}{\mathrm{e}}_2$ and the spin state of $\mathrm{F}{\mathrm{e}}^{3+}$ ions in the compound have been studied. Phonon dispersion and phonon density of states (PDOS), element specific and total, were evaluated from first-principles calculations. It is shown that iron atoms in quasi-one-dimensional chains have dramatically different vibrational properties against Rb and Se atoms: the Fe PDOS is mostly concentrated within two Einstein-like optical phonon peaks at high frequencies. Analysis of our Mössbauer data for $\mathrm{RbFeS}{\mathrm{e}}_2$, utilizing the calculated Fe PDOS as well as our optical absorption measurements, have shown full agreement with the location of the high-frequency optical-type lattice vibrations within the $\mathrm{FeS}{\mathrm{e}}_4$ tetrahedra. The calculated PDOS was utilized to evaluate the lattice contribution to the specific heat. The phonon heat capacity has been used to evaluate the magnetic specific heat of the quasi-one-dimensional antiferromagnetically correlated $\mathrm{F}{\mathrm{e}}^{3+}$ ion chains in $\mathrm{RbFeS}{\mathrm{e}}_2$. An intermediate spin state $S=3/2$ has been found most closely relevant to our magnetic entropy analysis for $\mathrm{F}{\mathrm{e}}^{3+}$ ions in $\mathrm{RbFeS}{\mathrm{e}}_2$.