We present Raman scattering results on phonon polaritons in single crystals of $\alpha$-GaN. A detailed theoretical treatment of their dispersion and Raman scattering efficiency in wurtzite-type crystals is given. Pure symmetry polaritons (ordinary and extraordinary) are accessible in near-forward scattering geometry according to the theory. For this purpose, the experimental setup uses rectangular aperture windows in front of the entrance lens. Thus measurements with well defined wave-vector transfer can be realized. The observed dispersion curves and scattering efficiency results are compared with theoretical ones and are found to be in excellent agreement.

A number of recent articles have reported the existence of topologically nontrivial states and associated end states in one-dimensional incommensurate lattice models that would usually only be expected in higher dimensions. Using an explicit construction, we here argue that the end states have precisely the same origin as their counterparts in commensurate models and that incommensurability does not in fact provide a meaningful connection to the topological classification of systems in higher dimensions. In particular, we show that it is possible to smoothly interpolate between states with commensurate and incommensurate modulation parameters without closing the band gap and without states crossing the band gap.

Recent theoretical calculations and experimental results suggest that the strongly correlated material SmB${}_6$ may be a realization of a topological Kondo insulator. We have performed an angle-resolved photoemission spectroscopy study on SmB${}_6$ in order to elucidate elements of the electronic structure relevant to the possible occurrence of a topological Kondo insulator state. The obtained electronic structure in the whole three-dimensional momentum space reveals one electron-like $5d$ bulk band centered at the $X$ point of the bulk Brillouin zone that is hybridized with strongly correlated $f$ electrons, as well as the opening of a Kondo band gap ($\Delta$${}_B$ $\sim$ 20 meV) at low temperature. In addition, we observe electron-like bands forming three Fermi surfaces at the center $\overline{\Gamma }$ point and boundary $\overline{X}$ point of the surface Brillouin zone. These bands are not expected from calculations of the bulk electronic structure, and their observed dispersion characteristics are consistent with surface states. Our results suggest that the unusual low-temperature transport behavior of SmB${}_6$ is likely to be related to the pronounced surface states sitting inside the band hybridization gap and/or the presence of a topological Kondo insulating state.

We study the problem of disorder-free metals near a continuous quantum critical point. We depart from the standard paradigm [Hertz, Phys. Rev. B 14, 1165 (1976) and Millis, Phys. Rev. B 48, 7183 (1993)] and treat both fermions and bosons (i.e., order parameter fields) on equal footing. We construct a Wilsonian effective field theory that integrates out only high-energy boson and fermion modes. Below the upper critical dimension of the theory ($d=3$ spatial dimensions), we find new fixed points in which the bosons are described by the Wilson-Fisher fixed point and are coupled to a non-Fermi-liquid metal. We describe subtleties with the renormalization group flow of four-Fermi interactions, which can be surmounted in a controlled large-$N$ limit. In this limit, we find that the theory has no superconducting instability.

We investigate the ground-state properties of the highly degenerate noncoplanar phase of the classical bilinear-biquadratic Heisenberg model on the triangular lattice with Monte Carlo simulations. For that purpose, we introduce an Ising pseudospin representation of the ground states, and we use a simple Metropolis algorithm with local updates, as well as a powerful cluster algorithm. At sizes that can be sampled with local updates, the presence of long-range order is surprisingly combined with an algebraic decay of correlations and the complete disordering of the chirality. It is only thanks to the investigation of unusually large systems (containing $\sim$${10}^8$ spins) with cluster updates that the true asymptotic regime can be reached and that the system can be proven to consist of equivalent (i.e., equally ordered) sublattices. These large-scale simulations also demonstrate that the scalar chirality exhibits long-range order at zero temperature, implying that the system has to undergo a finite-temperature phase transition. Finally, we show that the average distance in the order parameter space, which has the structure of an infinite Cayley tree, remains remarkably small between any pair of points, even in the limit when the real space distance between them tends to infinity.

We describe the topological surface states of Bi${}_4$Se${}_3$, a compound in the infinitely adaptive Bi${}_2$-Bi${}_2$Se${}_3$ natural superlattice phase series, determined by a combination of experimental and theoretical methods. Two observable cleavage surfaces, terminating at Bi or Se, are characterized by angle-resolved photoelectron spectroscopy and scanning tunneling microscopy, and modeled by ab initio density functional theory calculations. Topological surface states are observed on both surfaces, but with markedly different dispersions and Kramers point energies. Bi${}_4$Se${}_3$ therefore represents the only known compound with different topological states on differently terminated, easily distinguished and stable surfaces.

A comparative study of the structure and magnetism of Fe/CoO(111) and Fe/CoO(001) epitaxial bilayers was performed to investigate the role of uncompensated spins in the exchange bias (EB) phenomenon. Low-energy electron diffraction, x-ray photoelectron spectroscopy, conversion electron Mössbauer spectroscopy (CEMS), and the magneto-optic Kerr effect were used to characterize the structural and magnetic properties of the bilayers. Magnetically compensated and uncompensated CoO films were prepared using molecular beam epitaxy through the evaporation of single Co atomic layers and their subsequent oxidation (layer-by-layer technique) on MgO crystals with (001) and (111) orientations. Two-monolayer-thick ${}^{57}$Fe probes located on top of the oxide films and covered with ${}^{56}$Fe allowed for an analysis of the interfacial chemical and magnetic structure using CEMS. For both structures, submonolayer oxidation of the iron detected at the Fe/CoO interface was found to be accompanied by the formation of a mixed FeCo region. The Fe layers showed fourfold magnetocrystalline anisotropy when grown on CoO(001) and weak uniaxial anisotropy when grown on CoO(111). Although the structural quality and composition of the two structures were comparable, they exhibited distinct EB properties. A hysteresis loop shift as high as 354 Oe at 80 K was obtained for the Fe/CoO(111) bilayer, compared to only 37 Oe for the magnetically compensated Fe/CoO(001).

Nanoscale magnets might form the building blocks of next generation memories. To explore their functionality, magnetic sensing at the nanoscale is key. We present a multifunctional combination of a nanometer-sized superconducting quantum interference device (nanoSQUID) and a Ni nanotube attached to an ultrasoft cantilever as a magnetic tip. By scanning the Nb nanoSQUID with respect to the Ni tube, we map out and analyze their magnetic coupling, demonstrate the imaging of an Abrikosov vortex trapped in the SQUID structure — which is important in ruling out spurious magnetic signals — and reveal the high potential of the nanoSQUID as an ultrasensitive displacement detector. Our results open a new avenue for fundamental studies of nanoscale magnetism and superconductivity.

Thin films of topological insulator Bi${}_2$Se${}_3$ were deposited directly on insulating ferromagnetic EuS. Unusual negative magnetoresistance was observed near the zero field below the Curie temperature $T_C$, resembling the weak localization effect; whereas the usual positive magnetoresistance was recovered above $T_C$. Such negative magnetoresistance was only observed for Bi${}_2$Se${}_3$ layers thinner than $t\sim 4$ nm, when its top and bottom surfaces are coupled. These results provide evidence for a proximity effect between a topological insulator and an insulating ferromagnet, laying the foundation for future realization of the half-integer quantized anomalous Hall effect in three-dimensional topological insulators.

We investigate the strain-induced coupling between a nitrogen-vacancy impurity and a resonant vibrational mode of a diamond nanoresonator. We show that under near-resonant laser excitation of the electronic states of the impurity, this coupling can modify the state of the resonator and either cool the resonator close to the vibrational ground state or drive it into a large-amplitude coherent state. We derive a semiclassical model to describe both effects and evaluate the stationary state of the resonator mode under various driving conditions. In particular, we find that by exploiting resonant single- and multiphonon transitions between near-degenerate electronic states, the coupling to high-frequency vibrational modes can be significantly enhanced and dominate over the intrinsic mechanical dissipation. Our results show that a single nitrogen-vacancy impurity can provide a versatile tool to manipulate and probe individual phonon modes in nanoscale diamond structures.

Determining the magnetic order of solids in high magnetic fields is technologically challenging. Here we probe the cascade of magnetic phase transitions in frustrated multiferroic CuFeO${}_2$ using nuclear forward scattering (NFS) in pulsed magnetic fields up to 30 T. Our results are in excellent agreement with detailed neutron diffraction experiments, currently limited to 15 T, while providing experimental confirmation of the proposed higher field phases for both $H\parallel c$ and $H\perp c$. We thus establish NFS as a valuable tool for spin structure studies in very high fields, both complementing and expanding on the applicability of existing techniques.

We report the observation of coherent oscillations associated with charge-density-wave (CDW) order in the underdoped cuprate superconductor YBa${}_2$Cu${}_3$O${}_{6+x}$ by time-resolved optical reflectivity. Oscillations with frequency $1.87$ THz onset at approximately 105 and 130 K for dopings of $x=0.67$ (ortho-VIII) and $x=0.75$ (ortho-III), respectively. Upon cooling below the superconducting critical temperature ($T_c$), the oscillation amplitude is enhanced, the phase shifts by $\pi$, and the frequency softens by $\delta \nu /\nu \approx 7\%$. A biquadratically coupled Landau-Ginzburg model qualitatively describes this behavior as arising from competition between superconducting and CDW orders.

The dynamics of BCS (Bardeen-Cooper-Schrieffer) superconductors is fairly well understood due to the availability of a mean-field solution for the pairing Hamiltonian, a solution which gives the quantum state of a superconductor as a state of almost-free fermions interacting only with a condensate. As a result, transition probabilities may be computed, and expressed in terms of matrix elements of electron creation and annihilation operators between approximate eigenstates. These matrix elements are also called “coherence factors.” Mean-field theory is however not sufficient to describe all eigenstates of a superconductor, a deficiency which is hardly important in (or very close to) equilibrium, but one that becomes relevant in certain out-of-equilibrium situations. We report here on a computation of matrix elements (coherence factors) for the pairing Hamiltonian between any “two-arc” eigenstates in the thermodynamic limit.

We consider spaces of trial wave functions for ground states and edge excitations in the fractional quantum Hall effect that can be obtained in various ways. In one way, functions are obtained by analyzing the entanglement of the ground-state wave function, partitioned into two parts. In another, functions are defined by the way in which they vanish as several coordinates approach the same value, or by a projection-operator Hamiltonian that enforces those conditions. In a third way, functions are given by conformal blocks from a conformal field theory (CFT). These different spaces of functions are closely related. The use of CFT methods permits an algebraic formulation to be given for all of them. In some cases, we can prove that there is a ground state, a Hamiltonian, and a CFT such that, for any number of particles, all of these spaces are the same. For such cases, this resolves several questions and conjectures: it gives a finite-size bulk-edge correspondence, and we can use the analysis of functions to construct a projection-operator Hamiltonian that produces those functions as zero-energy states. For a model related to the $\mathcal{N}=1$ superconformal algebra, the corresponding Hamiltonian imposes vanishing properties involving only three particles; for this we determine all the wave functions explicitly. We do the same for a sequence of models involving the $M(3,p)$ Virasoro minimal models that has been considered previously, using results from the literature. We exhibit the Hamiltonians for the first few cases of these. The techniques we introduce can be applied in numerous examples other than those considered here.

Phase slips in a one-dimensional closed array of Josephson junctions hybridize the persistent current states and plasmon branches of excitations. The interference between phase slips passing through different junctions of the array makes the hybridization sensitive to the charges of the superconducting islands comprising the array. This in turn results in the Aharonov-Casher effect for plasmons, which in the absence of phase slips are insensitive to island charges.

Using time-resolved photoluminescence spectroscopy, we explore the transient behavior of bound and free excitons in GaN nanowire ensembles. We investigate samples with distinct diameter distributions and show that the pronounced biexponential decay of the donor-bound exciton observed in each case is not caused by the nanowire surface. At long times, the individual exciton transitions decay with a common lifetime, which suggests a strong coupling between the corresponding exciton states. A system of nonlinear rate equations taking into account this coupling directly reproduces the experimentally observed biexponential decay.

How magnetoelectric coupling actually occurs on a microscopic level in multiferroic BiFeO${}_3$ is not well known. By using high-resolution single crystal neutron diffraction techniques, we have determined the electric polarization of each individual element of BiFeO${}_3$, and concluded that magnetostrictive coupling suppresses the electric polarization at the Fe site below $T_N$. This negative magnetoelectric coupling appears to outweigh the spin current contributions arising from the cycloid spin structure, which should produce positive magnetoelectric coupling.

We discuss various properties of the variational class of continuous matrix product states, a class of Ansatz states for one-dimensional quantum fields that was recently introduced as the direct continuum limit of the highly successful class of matrix product states. We discuss both attributes of the physical states, e.g., by showing in detail how to compute expectation values, as well as properties intrinsic to the representation itself, such as the gauge freedom. We consider general translation noninvariant systems made of several particle species and derive certain regularity properties that need to be satisfied by the variational parameters. We also devote a section to the translation invariant setting in the thermodynamic limit and show how continuous matrix product states possess an intrinsic ultraviolet cutoff. Finally, we introduce a new set of states, which are tangent to the original set of continuous matrix product states. For the case of matrix product states, this construction has recently proven relevant in the development of new algorithms for studying time evolution and elementary excitations of quantum spin chains. We thus lay the foundation for similar developments for one-dimensional quantum fields.

High pressure electrical resistivity and x-ray diffraction experiments have been performed on Fe single crystals. The crystallographic investigation provides direct evidence that in the martensitic $\text{bcc}\to \text{hcp}$ transition at 14 GPa the ${\left\{110\right\}}_{\text{bcc}}$ become the ${\left\{002\right\}}_{\text{hcp}}$ directions. During a pressure cycle, resistivity shows a broad hysteresis of 6.5 GPa, whereas superconductivity, observed between 13 and 31 GPa, remains unaffected. Upon increasing pressure an electronic instability, probably a quantum critical point, is observed at around 19 GPa and, close to this pressure, the superconducting $T_c$ and the isothermal resistivity ($0<T<300$ K) attain maximum values. In the superconducting pressure domain, the exponent $n=5/3$ of the temperature power law of resistivity and its prefactor, which mimics $T_c$, indicate that ferromagnetic fluctuations may provide the glue for the Cooper pairs, yielding unconventional superconductivity.

Using Gaussian integral transform techniques borrowed from functional-integral field theory and the replica trick we derive a version of the coherent potential approximation (CPA) suited for describing (i) the diffusive (hopping) motion of classical particles in a random environment, and (ii) the vibrational properties of materials with spatially fluctuating elastic coefficients in topologically disordered materials. The effective medium in the present version of the CPA is not a lattice but a homogeneous and isotropic medium, representing an amorphous material on a mesoscopic scale. The transition from a frequency-independent to a frequency-dependent diffusivity (conductivity) is shown to correspond to the boson peak in the vibrational model. The anomalous regimes above the crossover are governed by a complex, frequency-dependent self-energy. The boson peak is shown to be stronger for non-Gaussian disorder than for Gaussian disorder. We demonstrate that the low-frequency nonanalyticity of the off-lattice version of the CPA leads to the correct long-time tails of the velocity autocorrelation function in the hopping problem and to low-frequency Rayleigh scattering in the wave problem. Furthermore we show that the present version of the CPA is capable of treating the percolative aspects of hopping transport adequately.