The photoelectron spectrum of the (0001) surface of single-crystalline yttrium bulk samples is rich in structure from the surface state near the Fermi energy to a series of spectral features between 2 and $10\mathrm{eV}$ binding energies. Many of them appear on other rare-earth surfaces, e.g., Gd, Ho, Pr, and Er, as well. However, it is an unsolved puzzle that none of the observed features, except for the surface state at the Fermi energy, can be found in data from clean rare-earth thin films. While some of the additional features in the results from single-crystal surfaces were already attributed to impurities such as chlorine, oxygen, and hydrogen, the peak at $-9.6\mathrm{eV}$ remains a source of speculation for more than $20\text{years}$ now. In this Rapid Communication, we provide a consistent picture of the surface electronic structure of Y(0001), which explains all differences between the data obtained from single-crystal surfaces and thin films. We show that the peak at $-9.6\mathrm{eV}$, which was previously assigned to a well-ordered clean surface, is in fact due to the formation of ordered carbon compounds originating from impurities in the bulk material.

We consider a defect in a strongly correlated host metal and discuss, within a slave-boson mean field formalism for the $t\text{−}{t}^{\prime }\text{−}J$ model, the formation of an induced paramagnetic moment which is extended over nearby sites. We study in particular an impurity in a metallic band, suitable for modeling the optimally doped cuprates, in a regime where the impurity moment is paramagnetic. The form of the local susceptibility as a function of temperature and doping is found to agree well with recent NMR experiments, without including screening processes leading to the Kondo effect.

We consider relativistic U(1) gauge theories in $2+1$ dimensions, with $N_b$ species of complex bosons and $N_f$ species of Dirac fermions at finite temperature. The quantum phase transition between the Higgs and Coulomb phases is described by a conformal field theory (CFT). At large $N_b$ and $N_f$, but for arbitrary values of the ratio $N_b∕N_f$, we present computations of various critical exponents and universal amplitudes for these CFTs. We make contact with the different spin liquids, charge liquids, and deconfined critical points of quantum magnets that these field theories describe. We compute physical observables that may be measured in experiments or numerical simulations of insulating and doped quantum magnets.

Spin-polarized electron transport driven by inhomogeneous magnetic dynamics is discussed in the limit of a large exchange coupling. Electron spins rigidly following the time-dependent magnetic profile experience spin-dependent fictitious electric and magnetic fields. We show that the electric field acquires important corrections due to spin dephasing, when one relaxes the spin-projection approximation. Furthermore, spin-flip scattering between the spin bands needs to be taken into account in order to calculate voltages and spin accumulations induced by the magnetic dynamics. A phenomenological approach based on the Onsager reciprocity principle is developed, which allows us to capture the effect of spin dephasing and make a connection to the well studied problem of current-driven magnetic dynamics. A number of results that recently appeared in the literature are related and generalized.

Singlet pairing in a Fermi superfluid is frustrated when the amounts of fermions of each pairing partner are unequal. The resulting “imbalanced superfluid” has been realized experimentally for ultracold atomic gases with $s$-wave interactions. Inspired by high-temperature superconductivity, we investigate the case of $d$-wave interactions and find marked differences from the $s$-wave superfluid. Whereas $s$-wave imbalanced Fermi gases tend to phase separate in real space, in a balanced condensate and an imbalanced normal halo, we show that the $d$-wave gas can phase separate in reciprocal space so that imbalance and superfluidity can coexist spatially. We show that the mechanism explaining this property is the creation of polarized excitations in the nodes of the gap. The Sarma mechanism, present only at nonzero temperatures for the $s$-wave case, is still applicable in the temperature zero limit for the $d$-wave case. As a result, the $d$-wave BCS superfluid is more robust with respect to imbalance and a region of the phase diagram can be identified where the $s$-wave BCS superfluidity is suppressed whereas the $d$-wave superfluidity is not. When these results are extended into the Bose–Einstein condensate limit of strongly bound molecules, the symmetry of the order parameter matters less. The effects of fluctuations beyond mean field is taken into account in the calculation of the structure factor and the critical temperature. The poles of the structure factor (corresponding to bound molecular states) are less damped in the $d$-wave case as compared to that in $s$ wave. On the BCS side of the unitarity limit, the critical temperature $T_c$ follows the temperature $T^{*}$ corresponding to the pair binding energy and as such will also be more robust against imbalance. Possible routes for the experimental observation of the $d$-wave superfluidity have been discussed.

We report on an inelastic light scattering study in the two-dimensional electron system at filling factor $\nu =1$. The energy and the inelastic cross section of the cyclotron spin-flip mode are analyzed. The exchange enhanced electronic $g$ factor in the quantum Hall ferromagnet is measured. In addition to the magnetoplasmon and cyclotron spin-flip modes, inelastic scattering lines associated with spin-singlet and spin-triplet $D^{-}$ complexes are observed. The inelastic light scattering is shown to probe the thermodynamics of the quantum Hall ferromagnet and gives insight into the formation of ferromagnetic order in two dimensions. It is established that at temperatures above the bare Zeeman energy, the ferromagnet breaks up into domains, whose size and number change with temperature. The experimental data allow us to construct a stability diagram of the $\nu =1$ quantum Hall ferromagnet in the temperature versus magnetic field plane.

As a step toward analyzing second-harmonic generation (SHG) from crystalline Si nanospheres in glass, we develop an anisotropic bond model (ABM) that expresses SHG in terms of physically meaningful parameters and provide a detailed understanding of the basic physics of SHG on the atomic scale. Nonlinear-optical (NLO) responses are calculated classically via the four fundamental steps of optics: evaluate the local field at a given bond site, solve the force equation for the acceleration of the charge, calculate the resulting radiation, then superpose the radiation from all charges. Because the emerging NLO signals are orders of magnitude weaker and occur at wavelengths different from that of the pump beam, these steps are independent. Paradoxically, the treatment of NLO is therefore simpler than that of linear optics (LO), where these calculations must be done self-consistently. The ABM goes beyond previous bond models by including the complete set of underlying contributions: retardation (RD), spatial-dispersion (SD), and magnetic (MG) effects, in addition to the anharmonic restoring force acting on the bond charge. Transverse as well as longitudinal motion is also considered. We apply the ABM to obtain analytic expressions for SHG from amorphous materials under Gaussian-beam excitation. These materials represent an interesting test case not only because they are ubiquitous but also because the anharmonic-force contribution that dominates the SHG response of crystalline materials and ordered interfaces vanishes by symmetry. The remaining contributions, and hence the SHG signals, are entirely functions of the LO response and beam geometry, so the only new information available is the anisotropy of the LO response at the bond level. The RD, SD, and MG contributions are all of the same order of magnitude, so none can be ignored. Diffraction is important in determining not only the pattern of the emerging beam but also the phases and amplitudes of the different terms. The plane-wave expansion that gives rise to electric quadrupole magnetic dipole effects in LO appears here as retardation. Using the paraxial-ray approximation, we reduce the results to the isotropic case in two limits, that where the linear restoring force dominates (glasses) and that where it is absent (metals). Both forward- and backscattering geometries are discussed. Estimated signal strengths and conversion efficiencies for fused silica appear to be in general agreement with data where available. Predictions that allow additional critical tests of these results are made.

In ferromagnets, the spontaneous magnetization bears the Hall effect through the relativistic spin-orbit interaction. Similar effects also occur in thermoelectric and thermal transport phenomena. Their mechanism, if it is of the intrinsic or extrinsic origin, has been controversial for many decades. We present a unified theory of these Hall transport phenomena in ferromagnetic metals with dilute impurities at the zero temperature, in terms of a fully quantum-mechanical transport theory for multiband systems with the self-consistent $T$-matrix approximation. This theory becomes exact with a single impurity and is appropriate for treating the dilute limit of the impurity concentration $n_{\mathrm{imp}}$. With the Fermi energy $E_F$ and the spin-orbit interaction energy $E_{\mathrm{SO}}$ being fixed $(E_F>E_{\mathrm{SO}})$, three regimes and the associated two crossovers are found in the anomalous Hall conductivity ${\sigma }_{xy}$ as a function of $n_{\mathrm{imp}}$ that controls the longitudinal conductivity ${\sigma }_{xx}$. (i) In the superclean case with the relaxation rate $\hslash ∕\tau \lesssim u_{\mathrm{imp}}{E}_{\mathrm{SO}}D$, the skew scattering arising from the vertex correction yields a dominant contribution that is inversely proportional to $n_{\mathrm{imp}}$, where $u_{\mathrm{imp}}$ is the impurity potential strength and $D$ is the density of states. With increasing $\hslash ∕\tau$, this extrinsic skew-scattering contribution rapidly decays. (ii) In the moderately dirty regime $u_{\mathrm{imp}}{E}_{\mathrm{SO}}D\lesssim \hslash ∕\tau \lesssim E_F$, ${\sigma }_{xy}$ becomes insensitive to the scattering strength because of the intrinsic dissipationless topological Berry-phase contribution. It is resonantly enhanced to the order of the quantization unit of conductance when an accidental degeneracy of band dispersions around the Fermi level is lifted by the spin-orbit interaction. Further increasing $\hslash ∕\tau$, another crossover occurs to (iii) the scaling regime of ${\sigma }_{xy}\propto {\sigma }_{xx}^{\phi }$ with $\phi \sim 1.6$, which has recently been verified by experiments on a wide class of ferromagnets. Similar behaviors also appear in the temperature-linear coefficient of the thermal Hall conductivity ${\kappa }_{xy}$. The thermoelectric Hall conductivity ${\alpha }_{xy}$ strongly diverges in the clean limit when the Fermi level crosses edges of the avoided crossing, which may be observed by careful experiments. With increasing $\hslash ∕\tau$, there occurs an interference between positive and negative contributions to ${\alpha }_{xy}$, which often leads to a sign change and obscures similar crossovers in the anomalous Nernst effect.

High-resolution synchrotron x-ray diffraction measurements were performed on single crystalline and powder samples of $\mathrm{Bi}{\mathrm{Mn}}_2{\mathrm{O}}_5$. A linear temperature dependence of the unit cell volume was found between $T_N=38$ and $100\mathrm{K}$, suggesting that a low-energy lattice excitation may be responsible for the lattice expansion in this temperature range. Between $T^{*}\sim 65\mathrm{K}$ and $T_N$, all lattice parameters showed incipient magnetoelastic effects, due to short-range spin correlations. An anisotropic strain along the $\mathbf{a}$ direction was also observed below $T^{*}$. Below $T_N$, a relatively large contraction of the $a$ parameter following the square of the average sublattice magnetization of Mn was found, indicating that a second-order spin Hamiltonian accounts for the magnetic interactions along this direction. On the other hand, the more complex behaviors found for $b$ and $c$ suggest additional magnetic transitions below $T_N$ and perhaps higher-order terms in the spin Hamiltonian. Polycrystalline samples grown by distinct routes and with nearly homogeneous crystal structure above $T_N$ presented structural phase coexistence below $T_N$, indicating a close competition amongst distinct magnetostructural states in this compound.

The effect of sample size and surface roughness on the phonon thermal conductivity ${\kappa }_p$ of ${\mathrm{Nd}}_2\mathrm{Cu}{\mathrm{O}}_4$ single crystals was studied down to $50\mathrm{mK}$. At $0.5\mathrm{K}$, ${\kappa }_p$ is proportional to $\sqrt{A}$, where $A$ is the cross-sectional area of the sample. This demonstrates that ${\kappa }_p$ is dominated by boundary scattering below $0.5\mathrm{K}$ or so. However, the expected $T^3$ dependence of ${\kappa }_p$ is not observed down to $50\mathrm{mK}$. Upon roughing the surfaces, the $T^3$ dependence is restored, showing that departures from $T^3$ are due to specular reflection of phonons off the mirrorlike sample surfaces. We propose an empirical power law fit to ${\kappa }_p\sim T^{\alpha }$ (where $\alpha <3$) in cuprate single crystals. Using this method, we show that recent thermal conductivity studies of Zn doping in $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ reaffirm the universal heat conductivity of $d$-wave quasiparticles at $T\to 0$.

The formation dynamics of stable gold (Au) wires of single-atom width during tensile deformation of the nanometer-sized Au contacts was observed in situ at room temperature by transmission electron microscopy. Simultaneously, force and conductance were measured using functions of scanning probe microscopy. The wires were extended to $2.7\pm 0.1\mathrm{nm}$ and the number of atoms was increased to 10; the average interatomic distance was $0.30\pm 0.02\mathrm{nm}$. The duration of the observation of the wires exceeded $10\mathrm{s}$. The results of the simultaneous observation of the atomic configuration, force, and conductance led to the conclusion that the stable Au wires observed in this study are complexed with light-element atoms. The constants of the mechanical properties of the individual wires, i.e., elastic limit, Young’s modulus, and strength, were analyzed on the basis of stress-strain curves experimentally measured on an atomic scale. During elastic elongation, a force of $1.6\pm 0.7\mathrm{nN}$ acted on the Au wires with an elastic limit of 0.15–0.20. Young’s modulus of single-atom-width Au wires was $47–116\mathrm{GPa}$ and strength was $8–17\mathrm{GPa}$, estimated using a cross-sectional area of $0.118{\mathrm{nm}}^2$, which is that of a single atom in bulk along ⟨110⟩. Using these mechanical constants, the average interatomic distance in stress-free wires was estimated to be $0.26\pm 0.02\mathrm{nm}$. The histogram of conductances for the single-atom-width Au wires showed a peak at approximately $1G_0$ (where $G_0=2e^2∕h$, $e$ being the charge of an electron and $h$ Planck’s constant) until the total number of atoms exceeds 5. For longer wires constructed of more than six atoms, the conductance decreased to less than $0.1G_0$.

The rare earth $\left(R\right)$ tellurides $R_2{\mathrm{Te}}_5$ have a crystal structure intermediate between that of $R{\mathrm{Te}}_2$ and $R{\mathrm{Te}}_3$, consisting of alternating single and double Te planes sandwiched between $R\mathrm{Te}$ block layers. We have successfully grown single crystals of ${\mathrm{Nd}}_2{\mathrm{Te}}_5$, ${\mathrm{Sm}}_2{\mathrm{Te}}_5$, and ${\mathrm{Gd}}_2{\mathrm{Te}}_5$ from a self-flux and we describe here evidence for charge density wave formation in these materials. The superlattice patterns for all three compounds are relatively complex, consisting at room temperature of at least two independent wave vectors. Consideration of the electronic structure indicates that, to a large extent, these wave vectors are separately associated with sheets of the Fermi surface which are principally derived from the single and double Te layers.

We theoretically investigate the effects of interaction between an optical dipole (semiconductor quantum dot or molecule) and metal nanoparticles. The calculated absorption spectra of hybrid structures demonstrate strong effects of interference coming from the exciton-plasmon coupling. In particular, the absorption spectra acquire characteristic asymmetric line shapes and strong antiresonances. We present here an exact solution of the problem beyond the dipole approximation and find that the multipole treatment of the interaction is crucial for the understanding of strongly interacting exciton-plasmon nanosystems. Interestingly, the visibility of the exciton resonance becomes greatly enhanced for small interparticle distances due to the interference phenomenon, multipole effects, and electromagnetic enhancement. We find that the destructive interference is particularly strong. Using our exact theory, we show that the interference effects can be experimentally observed in the exciting systems even at room temperature.

We compute the tunneling current in a double point contact geometry of a quantum Hall system at filling fraction $\nu =\frac{5}{2}$, as a function of voltage and temperature, in the weak tunneling regime. We quantitatively compare two possible candidates for the state at $\nu =\frac{5}{2}$: the Moore-Read Pfaffian state, and its particle-hole conjugate, the anti-Pfaffian. We find that both possibilities exhibit the same qualitative behavior, and both have an even-odd effect that reflects their non-Abelian nature, but differ quantitatively in their voltage and temperature dependence.

In two dimensions, the laws of physics permit the existence of anyons, particles with fractional statistics which are neither Fermi nor Bose. That is, upon exchange of two such particles, the quantum state of a system acquires a phase which is neither 0 nor $\pi$, but can be any value. The elementary excitations (Laughlin quasiparticles) of a fractional quantum Hall fluid have a fractional electric charge and are expected to obey fractional statistics. In this paper we report experimental realization of a Laughlin quasiparticle interferometer, where quasiparticles of the $1∕3$ fluid execute a closed path around an island of the $2∕5$ fluid and thus acquire statistical phase. Interference fringes are observed as conductance oscillations as a function of magnetic flux, similar to the Aharonov-Bohm effect. We observe the interference shift by one fringe upon introduction of five magnetic flux quanta $(5h∕e)$ into the island. The corresponding $2e$ charge period is confirmed directly in calibrated gate experiments. These results constitute direct observation of fractional statistics of Laughlin quasiparticles.

The phase diagram and critical properties of the $N$-component London superconductor are studied both analytically and through large-scale Monte Carlo simulations in $d=2+1$ dimensions (components here refer to different replicas of the complex scalar field). Examples are given of physical systems to which this model is applicable. The model with different bare phase stiffnesses for each component is a model of superconductivity, which should arise out of metallic phases of light atoms under extreme pressure. A projected mixture of electronic and protonic condensates in liquid metallic hydrogen under extreme pressure is the simplest example, corresponding to $N=2$. These are such that Josephson coupling between different matter field components is precisely zero on symmetry grounds. The $N$-component London model is dualized to a theory involving $N$ vortex fields with highly nontrivial interactions. We compute critical exponents $\alpha$ and $\nu$ for $N=2$ and $N=3$. Direct and dual gauge field correlators for general $N$ are given and the $N=2$ case is studied in detail. The model with $N=2$ shows two anomalies in the specific heat when the bare phase stiffnesses of each matter field species are different. One anomaly corresponds to an inverted $3\mathrm{D}xy$ fixed point, while the other corresponds to a $3\mathrm{D}xy$ fixed point. Correspondingly, for $N=3$, we demonstrate the existence of two neutral $3\mathrm{D}xy$ fixed points and one inverted charged $3\mathrm{D}xy$ fixed point. For the general case, there are $N$ fixed points, namely one charged inverted $3\mathrm{D}xy$ fixed point, and $N-1$ neutral $3\mathrm{D}xy$ fixed points. We explicitly identify one charged vortex mode and $N-1$ neutral vortex modes. The model for $N=2$ and equal bare phase stiffnesses corresponds to a field theoretical description of an easy-plane quantum antiferromagnet. In this case, the critical exponents are computed and found to be non-$3\mathrm{D}xy$ values. The $N$-component London superconductor model in an external magnetic field, with no interspecies Josephson coupling, will be shown to have a different feature, namely $N-1$ superfluid phases arising out of $N$ charged condensates. In particular, for $N=2$ we point out the possibility of two different types of field-induced phase transitions in ordered quantum fluids: (i) A phase transition from a superconductor to a superfluid or vice versa, driven by tuning an external magnetic field. This sets the superconducting phase of liquid metallic hydrogen apart from other known quantum fluids. (ii) A phase transition corresponding to a quantum fluid analogue of sublattice melting, where a composite field-induced Abrikosov vortex lattice is decomposed and disorders the phases of the constituent condensate with lowest bare phase stiffness. Both transitions belong to the $3\mathrm{D}xy$ universality class. For $N⩾3$, there is a feature not present in the cases $N=1$ and $N=2$, namely a partial decomposition of composite field-induced vortices driven by thermal fluctuations. A “color electric charge” concept, useful for establishing the character of these phase transitions, is introduced.

We present transport critical current measurements on microfibers consisting of a $80\text{−}\mathrm{nm}$ thick layer of polycrystalline $\mathrm{Mg}\mathrm{C}{\mathrm{Ni}}_3$ synthesized directly onto $7\text{−}\mu \mathrm{m}$ diameter carbon fibers. Near the transition temperature $T_c$, the critical current density $J_c$ is well described by the power law form ${[1-{(T∕T_c)}^2]}^{\alpha }$, where $\alpha =2$ with no crossover to the Ginzburg-Landau exponent $\alpha =1.5$. We extrapolate $J_c\left(0\right)\approx 4\times {10}^7\mathrm{A}∕{\mathrm{cm}}^2$, which is an order of magnitude greater than estimates obtained from magnetization measurements of polycrystalline powders. The field dependence is purely exponential $J_c(T,H)=J_c\left(T\right)\exp (-H∕H_0)$ over the entire field range of $0\text{to}9\mathrm{T}$. The unconventional scaling behavior of the critical current may be rooted in an anomalous temperature dependence of the London penetration depth.

We have performed magnetization measurements on ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4.$ A hysteresis in the temperature dependence of low field magnetization is observed well above the superconducting transition temperature. The behavior of the hysteresis resembles fundamental properties of the superconducting state and is discussed in terms of superconducting correlations.

Surface modes are generally believed to be an undesirable feature of finite photonic crystals (PC), unlike point or line defect modes. However, it is possible to make the surface mode radiate by appropriate corrugation of the PC interface. In this paper we show theoretically that the coherent action of these surface indentations can be engineered to collimate within a few degrees the light exiting a PC waveguide, or to funnel light coming from free space into the waveguide.

We present an efficient scheme for calculating the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay’s DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrices will be discussed. Our approach is stable, reliable, and minimizes the number of order ${\mathit{N}}_{\mathrm{atoms}}^3$ operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay’s scheme. A special ‘‘metric’’ and a special ‘‘preconditioning’’ optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calculations. It will be shown that the number of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order ${\mathit{N}}_{\mathrm{atoms}}^2$ scaling is found for systems containing up to 1000 electrons. If we take into account that the number of k points can be decreased linearly with the system size, the overall scaling can approach ${\mathit{N}}_{\mathrm{atoms}}$. We have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable. © 1996 The American Physical Society.