The electronic states of a single Bi(111) bilayer and its edges, suggested as a two-dimensional topological insulator, are investigated by scanning tunneling spectroscopy (STS) and first-principles calculations. Well-ordered bilayer films and islands with zigzag edges are grown epitaxially on a cleaved ${\mathrm{Bi}}_2{\mathrm{Te}}_2\mathrm{Se}$ crystal. The calculation shows that the band gap of the Bi bilayer closes with a formation of a new but small hybridization gap due to the strong interaction between Bi and ${\mathrm{Bi}}_2{\mathrm{Te}}_2\mathrm{Se}$. Nevertheless, the topological nature of the Bi bilayer and the topological edge state are preserved only with an energy shift. The edge-enhanced local density of states are identified and visualized unambiguously by STS in good agreement with the calculation. This is a clear sign of the topological edge state, which corresponds to the quantum spin Hall state. The interfacial state between Bi and ${\mathrm{Bi}}_2{\mathrm{Te}}_2\mathrm{Se}$ is also identified inside the band gap region. This state exhibits a subtle edge modulation, which was previously interpreted as the evidence of the topological edge state [Yang et al., Phys. Rev. Lett. 109, 016801 (2012)].

The presence of topological zero modes in dislocations is usually thought to be independent of local details and determined by topological invariants. We demonstrate that in insulators with particle-hole symmetry and an odd number of orbitals per site, changes in the microscopic details of the dislocation core can affect the electronic structure drastically without changing the topological charge of the defect (the Burgers vector), creating or annihilating nontrivial bound states with an associated fractional charge. We show that this observation is related to the behavior of end modes of a dimerized chain and discuss how the end or defect states are predicted from topological invariants in these more complicated cases. Furthermore, using explicit examples on the honeycomb lattice, we explain how bound states in vacancies, dislocations, and disclinations are related to each other and to edge modes and how similar features arise in nodal semimetals such as graphene.

In this Rapid Communication, we present a comprehensive study of the Hubbard model on the isotropic triangular lattice by using the recently developed ladder dual-fermion approach. This method is a nonlocal extension of the dynamical mean-field theory and is free of finite-size effect. In addition to confirming the much-discussed phase diagram at half-filling, our work provides insights into both hole- and electron-doped regimes and, in particular, the finite-temperature phase diagrams. We find the triangular system to be short-range correlated with an associated magnetic phase diagram, which is asymmetric with respect to hole and electron doping. In contrast to the unfrustrated lattice, it can adiabatically be cooled by increasing the interactions. Strikingly, at the electron-doped side, the entropy displays a maximum. This latter example, as well as other results of our work, may provide insights for a variety of correlated triangular materials, such as the water-intercalated sodium-doped cobaltates.

We obtain the spin-orbit interaction and spin-charge coupled transport equations of a two-dimensional heavy hole gas under the influence of strain and anisotropy. We show that a simple two-band Hamiltonian can be used to describe the holes. In addition to the well-known cubic hole spin-orbit interaction, anisotropy causes a Dresselhaus-like term, and strain causes a Rashba term. We discover that strain can cause a shifting symmetry of the Fermi surfaces for spin up and down holes. We predict an enhanced spin lifetime associated with a spin helix standing wave similar to the Persistent Spin Helix which exists in the two-dimensional electron gas with equal Rashba and Dresselhaus spin-orbit interactions. These results may be useful both for spin-based experimental determination of the Luttinger parameters of the valence-band Hamiltonian and for creating long-lived spin excitations.

We experimentally quantify the contribution of magnetic dipole (MD) transitions to the near-infrared light emission from trivalent erbium-doped yttrium oxide (Er${}^{3+}$:Y${}_2$O${}_3$). Using energy-momentum spectroscopy, we demonstrate that the ${}^4$I${}_{13/2}{\to }^4$I${}_{15/2}$ emission near 1.5 $\mu$m originates from nearly equal contributions of electric dipole (ED) and MD transitions that exhibit distinct emission spectra. We then show how these distinct spectra, together with the differing local density of optical states for ED and MD transitions, can be leveraged to control Er${}^{3+}$ emission in structured environments. We demonstrate that far-field emission spectra can be tuned to resemble almost pure emission from either ED or MD transitions and show that the observed spectral modifications can be accurately predicted from the measured ED and MD intrinsic emission rates.

The fractional quantum Hall effect (FQHE), observed in two-dimensional (2D) charged particles at high magnetic fields, is one of the most fascinating, macroscopic manifestations of a many-body state stabilized by the strong Coulomb interaction. It occurs when the filling factor ($\nu$) of the quantized Landau levels (LLs) is a fraction, which, with very few exceptions, has an odd denominator. In 2D systems with additional degrees of freedom it is possible to cause a crossing of the LLs at the Fermi level. At and near these crossings, the FQHE states are often weakened or destroyed. Here we report the observation of an unusual crossing of the two lowest-energy LLs in high-mobility GaAs 2D hole systems, which brings to life a new even-denominator FQHE at $\nu =1/2$.

We present a surface x-ray diffraction study in combination with stress experiments and ab initio calculations to investigate the structure and magnetic properties of 1.6 and 2.0 bilayer thick CoO(111) films grown on Ir(001). The CoO films grow in a wurtzite-like structure characterized by reduced distances between cobalt and oxygen atoms within one bilayer. The double-bilayer film is under tensile stress of +2.1 N/m which can be quantitatively attributed to epitaxial misfit and excludes the presence of significant Coulomb interactions. First-principles calculations reveal that the CoO films are metallic and that the magnetic order is noncollinear.

We present a rigorous full-wave electromagnetic approach to analyze the modes and resonances of dielectric and plasmonic nanoparticles of practically any geometry. Using boundary integral operators, we identify the resonances as inherent properties of the particles and propose a modal expansion for their optical response. We show that the resonance frequencies are isolated points on the complex plane. The approach allows the particles to be analyzed without specifying an incident field, which can be separately tailored for the desired interaction with the modes. We also connect the general theory to the Mie theory in spherical geometry and provide a connection to the quasistatic theory. In comparison to earlier work on modes and resonances of scatterers, our approach has the benefit that modes are defined entirely over a compact boundary surface of the scatterer. Furthermore, the boundary integral operator is of second-kind Fredholm type, enabling the rigorous characterization of the resonances.

We compare the classification of the electron bands in graphene, obtained by group theory algebra in the framework of a tight-binding model (TBM), with that calculated in a density-functional-theory (DFT) framework. Identification in the DFT band structure of all eight energy bands (four valence and four conduction bands) corresponding to the TBM-derived energy bands is performed and the corresponding analysis is presented. The four occupied (three $\sigma$-like and one $\pi$-like) and three unoccupied (two $\sigma$-like and one $\pi$-like) bands given by the DFT closely correspond to those predicted by the TBM, both by their symmetry and their dispersion law. However, the two lowest lying at the $\Gamma$-point unoccupied bands (one of them of a $\sigma$-like type and the other of a $\pi$-like one), are not of the TBM type. According to both their symmetry and the electron density these bands are plane waves orthogonal to the TBM valence bands; dispersion of these states can be determined unambiguously up to the Brillouin zone borders. On the other hand, the fourth unoccupied band given by the TBM can be identified among those given by the DFT band calculations; it is situated rather high with respect to energy. The interaction of this band with the free-electron states is so strong that it exists only in part of the $k$ space.

We study phononic heat transport in nanoscale devices. In the nonequilibrium Green's function formalism, an analytical small-frequency expansion of the phonon current transmission is derived for an arbitrary oscillator chain with typical contact-device-contact structure. Applying this expansion in a Landauer formula, it is possible to construct a systematic low-temperature expansion of the thermal conductance. It follows that quantized thermal conductance occurs as a plateau of the thermal conductance divided by the temperature within second order of the temperature expansion for completely heterogeneous systems as long as the product of force constant and oscillator mass is identical in both contacts, independent of the scattering area. Beyond this plateau, the higher-order terms of the low-temperature expansion yield a finite-temperature correction exhibiting the form of a cubic power law depending on the details of the scattering area. These findings are in agreement with experiments and numerical calculations. Our general results are applied to a double junction chain, where we find as the first phenomenon beyond our low-temperature expansion a second plateau. This plateau is associated with a thermal phase averaging of the phonon transmission, which leads for increasing temperatures to an independence of the thermal conductance from the device length.

We study the spin 1/2 triangular-lattice $J_1$-$J_2$-$J_3$ antiferromagnet close to the saturation field using the dilute Bose gas theory, where the magnetic structure is determined by the condensation of magnons. We focus on the case of ferromagnetic $J_1$ and antiferromagnetic $J_2,J_3$, which is particularly rich because frustration effects allow the single-magnon energy dispersion to have sixfold degenerate minima at incommensurate momenta. Our calculation also includes an interlayer coupling $J_0$, which covers both antiferromagnetic and ferromagnetic cases including negligibly small regime (two-dimensional case). Besides the spiral and fan phases, we find a new double-$q$ phase (superposition of two modes), dubbed “${\mathbf{Q}}_0$-${\mathbf{Q}}_1$” (or simply “01”) phase, that enjoys a new type of multiferroic character. Certain phase boundaries have a singular $J_0$ dependence for $J_0\to 0$, implying that even a very small interlayer coupling drastically changes the ground state. A mechanism for this singularity is presented. Moreover, in some regions of the parameter space, we show that a dilute gas of magnons can not be stable, and phase separation (corresponding to a magnetization jump) is expected. In the $J_1$-$J_2$ model ($J_3=0$), formation of two-magnon bound states is observed, which can lead to a quadrupolar (spin-nematic) ordered phase. Exact diagonalization analysis is also applied to the search of bound states.

We have investigated the Co-doping dependence of the structural, transport, and magnetic properties of $\epsilon$-${\mathrm{Fe}}_{1-x}$${\mathrm{Co}}_x$Si epilayers grown by molecular beam epitaxy on silicon (111) substrates. Low energy electron diffraction, atomic force microscopy, x-ray diffraction, and high-resolution transmission electron microscopy studies have confirmed the growth of phase-pure, defect-free $\epsilon$-${\mathrm{Fe}}_{1-x}$${\mathrm{Co}}_x$Si epitaxial films with a surface roughness of $\sim$1 nm. These epilayers are strained due to lattice mismatch with the substrate, deforming the cubic B20 lattice so that it becomes rhombohedral. The temperature dependence of the resistivity changes as the Co concentration is increased, being semiconducting for low $x$ and metallic for $x\gtrsim 0.3$. The films exhibit the positive linear magnetoresistance that is characteristic of $\epsilon$-${\mathrm{Fe}}_{1-x}$${\mathrm{Co}}_x$Si below their magnetic ordering temperatures $T_{\mathrm{ord}}$, as well as the huge anomalous Hall effect of order several $\mu \Omega$cm. The ordering temperatures are higher than those observed in bulk, up to 77 K for $x=0.4$. The saturation magnetic moment of the films varies as a function of Co doping, with a contribution of $\sim$$1{\mu }_{\mathrm{B}}$/ Co atom for $x\lesssim 0.25$. When taken in combination with the carrier density derived from the ordinary Hall effect, this signifies a highly spin-polarized electron gas in the low $x$, semiconducting regime.

We report measurements of ac magnetic susceptibility ${\chi }_{\text{ac}}$ and de Haas–van Alphen (dHvA) oscillations in ${\mathrm{KFe}}_2$${\mathrm{As}}_2$ under high pressure up to 24.7 kbar. The pressure dependence of the superconducting transition temperature $T_c$ changes from negative to positive across $P_c\sim 18$ kbar, as previously reported. The ratio of the upper critical field to $T_c$, i.e., $B_{c2}/T_c$, is enhanced above $P_c$, and the shape of the ${\chi }_{\text{ac}}$ versus field curves qualitatively changes across $P_c$. dHvA oscillations smoothly evolve across $P_c$, indicating no drastic change in the Fermi surface up to 24.7 kbar. Three dimensionality increases with pressure, while effective masses show decreasing trends. We suggest a crossover from a nodal to a full-gap $s$ wave as a possible explanation.

Several ${\mathrm{Cu}}^{2+}$ hydroxide minerals have been recently identified as candidate realizations of the $S=1/2$ kagome Heisenberg model. In this context, we have studied the distorted system ${\mathrm{KCu}}_3{\mathrm{As}}_2{\mathrm{O}}_7$(OD)${}_3$ using neutron scattering and bulk measurements. Although the distortion favors magnetic order over a spin liquid ground state, refinement of the magnetic diffraction pattern below $T_{N1}=7.05\left(5\right)$ K yields a complex helical structure with $\mathbf{k}=(0.77,0,0.11)$. This structure, as well as the spin excitation spectrum, are well described by a classical Heisenberg model with ferromagnetic nearest neighbor couplings. Multiferroicity is observed below $T_{N1}$, with an unusual crossover between improper and pseudoproper behavior occurring at $T_{N2}=5.5$ K. The polarization at $T=2$ K is $P=1.5\mu$Cm${}^{-2}$. The properties of ${\mathrm{KCu}}_3{\mathrm{As}}_2{\mathrm{O}}_7$(OD)${}_3$ highlight the variety of physics which arise from the interplay of spin and orbital degrees of freedom in ${\mathrm{Cu}}^{2+}$ kagome systems.

In the pyrochlore iridates R${}_2$Ir${}_2$O${}_7$ (R = lanthanide, Y) determination of the magnetic structure of the iridium moments remains an outstanding problem despite the role this is expected to play in the formation of novel band structures and topologies in these materials. In this work, an analysis of the experimentally measured spontaneous muon spin precession frequency is presented which incorporates both probabilistic and ab initio modeling techniques to determine the ground state magnetic structure. It is shown that the experimentally observed results are consistent only with a magnetically ordered Ir${}^{4+}$ sublattice with the so-called “all-in/all-out” magnetic structure, and that the electronic state of the Ir${}^{4+}$ is best described by the $J_{\mathrm{eff}}=\frac{1}{2}$ model in several member compounds. Through this approach it is also demonstrated that such a simple structure is not likely to be present on the rare-earth sublattice which contains much larger localized moments.

We have performed systematic angle-resolved photoemission spectroscopy (ARPES) of iron-chalcogenide superconductor ${\mathrm{FeTe}}_{1-x}$${\mathrm{Se}}_x$ ($0\le x\le 0.45$) to elucidate the electronic states relevant to the superconductivity. While the Fermi-surface shape is nearly independent of $x$, we found that the ARPES spectral line shape shows prominent $x$ dependence. A broad ARPES spectrum characterized by a small quasiparticle weight at $x=0$, indicative of incoherent electronic states, becomes progressively sharper with increasing $x$, and a well-defined quasiparticle peak appears around $x=0.45$ where bulk superconductivity is realized. The present result suggests the evolution from incoherent to coherent electronic states and its close relationship to the emergence of superconductivity.

We demonstrate how the nontrivial interplay between spin-orbit coupling and nodeless $s$-wave superconductivity can drive a fully gapped two-band topological insulator into a time-reversal invariant gapless topological superconductor supporting symmetry-protected Majorana flat bands. We characterize topological phase diagrams by a ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ partial Berry-phase invariant, and show that, despite the trivial crystal geometry, no unique bulk-boundary correspondence exists. We trace this behavior to the anisotropic quasiparticle bulk gap closing, linear vs quadratic, and argue that this provides a unifying principle for gapless topological superconductivity. Experimental implications for tunneling conductance measurements are addressed, relevant for lead chalcogenide materials.

A microscopic, or Hamiltonian-based, theory is developed to study the spin-wave instability thresholds for the parametric processes occurring in ultrathin ferromagnetic films under conditions of parallel pumping with a microwave field. Most previous work has focused on spheres or films with dimensions of order several microns or more, and the theoretical interpretation has been in terms of macroscopic (continuum) methods. At smaller size scales, as in ultrathin films with thickness less than about 100 nm, the discreteness of the quantized spin waves and their spatial distributions become modified, making it more appropriate (particularly for the nonlinear dynamics) to employ a microscopic or Hamiltonian-based approach with a lattice of effective spins interacting with one another through the magnetic dipole-dipole and exchange interactions. This work utilizes a similar microscopic approach, but with the effects of microwave pumping included, to calculate the spin-wave instability thresholds for the bands of quantized spin waves in ultrathin films with the saturation magnetization parallel to their surface. Magnetic materials with different ratios of the exchange to dipole-dipole strengths are considered, taking examples for relatively strong, intermediate, and weak exchange. In the case of parallel pumping it is found that the shape of the typical “butterfly curve,” as conventionally obtained with macroscopic samples of YIG, becomes modified in these ultrathin films due to the occurrence of several quantized spin-wave bands and their spatial properties.

Recently, interest has increased in the hyperbolic family of integrable Richardson-Gaudin (RG) models. It was pointed out that a particular linear combination of the integrals of motion of the hyperbolic RG model leads to a Hamiltonian that describes $p$-wave pairing in a two-dimensional system. Such an interaction is found to be present in fermionic superfluids (${}^3\text{He}$), ultracold atomic gases, and $p$-wave superconductivity. Furthermore the phase diagram is intriguing, with the presence of the Moore-Read and Read-Green lines. At the Read-Green line a rare third-order quantum phase transition occurs. The present paper makes a connection between collective bosonic states and the exact solutions of the $p_x+i{p}_y$ pairing Hamiltonian. This makes it possible to investigate the effects of the Pauli principle on the energy spectrum, by gradually reintroducing the Pauli principle. It also introduces an efficient and stable numerical method to probe all the eigenstates of this class of Hamiltonians. We extend the phase diagram to repulsive interactions, an area that was not previously explored due to the lack of a proper mean-field solution in this region. We found a connection between the point in the phase diagram where the ground state connects to the bosonic state with the highest collectivity, and the Moore-Read line where all the Richardson-Gaudin (RG) variables collapse to zero. In contrast with the reduced BCS case, the overlap between the ground state and the highest collective state at the Moore-Read line is not the largest. In fact it shows a minimum when most other bosonic states show a maximum of the overlap. We found remnants of the Read-Green line for finite systems, by investigating the total spectrum. A symmetry was found between the Hamiltonian with and without single-particle part. When the interaction was repulsive we found four different classes of trajectories of the RG variables.