We review some recently published methods to represent atomic neighborhood environments, and analyze their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces. The crucial properties that such representations (sometimes called descriptors) must have are differentiability with respect to moving the atoms and invariance to the basic symmetries of physics: rotation, reflection, translation, and permutation of atoms of the same species. We demonstrate that certain widely used descriptors that initially look quite different are specific cases of a general approach, in which a finite set of basis functions with increasing angular wave numbers are used to expand the atomic neighborhood density function. Using the example system of small clusters, we quantitatively show that this expansion needs to be carried to higher and higher wave numbers as the number of neighbors increases in order to obtain a faithful representation, and that variants of the descriptors converge at very different rates. We also propose an altogether different approach, called Smooth Overlap of Atomic Positions, that sidesteps these difficulties by directly defining the similarity between any two neighborhood environments, and show that it is still closely connected to the invariant descriptors. We test the performance of the various representations by fitting models to the potential energy surface of small silicon clusters and the bulk crystal.

The surface of a ferroelectric BaTiO${}_3$(001) single crystal was studied using synchrotron radiation induced x-ray photoelectron diffraction (XPD), x-ray photoelectron spectroscopy (XPS), atomic force microscopy (AFM), and low-energy electron diffraction (LEED). AFM, XPS, and LEED show that the surface is BaO terminated with a (1$\times$1) reconstruction. The Ba $4d$, Ti $2p$, and O $1s$ XPD results were compared with multiple scattering simulations for out-of- (${\mathrm{P}}^{+},{\mathrm{P}}^{-}$) and in-plane (${\mathrm{P}}^{in}$) polarizations using a genetic algorithm to determine atomic rumpling and interlayer relaxation. Linear combinations of the XPD simulations of the surface structure of each polarization state allow determination of the domain ordering. The best agreement with experiment is found for 55$\%$ ${\mathrm{P}}^{+}$, 38$\%$ ${\mathrm{P}}^{-}$, and 7$\%$ ${\mathrm{P}}^{in}$. The rumpling is smaller at the surface than in the bulk, suggesting that both domain ordering and surface structural changes contribute to screening of the polarization.

The universal behavior of two-dimensional loop models can change dramatically when loops are allowed to cross. We study models with crossings both analytically and with extensive Monte Carlo simulations. Our main focus (the “completely packed loop model with crossings”) is a simple generalization of well-known models that shows an interesting phase diagram with continuous phase transitions of a new kind. These separate the unusual “Goldstone” phase observed previously from phases with short loops. Using mappings to ${\mathbb{Z}}_2$ lattice gauge theory, we show that the continuum description of the model is a replica limit of the $\sigma$ model on real projective space (${\mathbb{RP}}^{n-1}$). This field theory sustains ${\mathbb{Z}}_2$ point defects, which proliferate at the transition. In addition to studying the new critical points, we characterize the universal properties of the Goldstone phase in detail, comparing renormalization group (RG) calculations with numerical data on systems of linear size up to $L={10}^6$ at loop fugacity $n=1$. (Very large sizes are necessary because of the logarithmic form of correlation functions and other observables.) The model is relevant to polymers on the verge of collapse, and a particular point in parameter space maps to self-avoiding trails at their $\Theta$ point; we use the RG treatment of a perturbed $\sigma$ model to resolve some perplexing features in the previous literature on trails. Finally, one of the phase transitions considered here is a close analog of those in disordered electronic systems—specifically, Anderson metal-insulator transitions—and provides a simpler context in which to study the properties of these poorly understood (central-charge-zero) critical points.

Nonlinear dynamics of Josephson vortices (fluxons) in artificial stacks of superconducting-normal-superconducting Josephson junctions under simultaneously applied time-periodic ac and constant biasing dc currents is studied using the time dependent Ginzburg-Landau formalism with a Lawrence-Doniach extension. At zero external magnetic field and dc biasing current the resistive state of the system is characterized by periodic nucleation and annihilation of fluxon-antifluxon pairs, relative positions of which are determined by the state of neighboring junctions. Due to the mutual repulsive interaction, fluxons in different junctions move out of phase. Their collective motion can be synchronized by adding a small ac component to the biasing dc current. Coherent motion of fluxons is observed for a broad frequency range of the applied drive. In the coherent state the maximal output voltage, which is proportional to the number of junctions in the stack, is observed near the characteristic frequency of the system determined by the crossing of the fluxons across the sample. However, in this frequency range the dynamically synchronized state has an alternative—a less ordered state with smaller amplitude of the output voltage. Collective behavior of the junctions is strongly affected by the sloped sidewalls of the stack. Synchronization is observed only for weakly trapezoidal cross sections, whereas irregular motion of fluxons is observed for larger slopes of the sample edge.

We use neutron scattering to study the effect of uniaxial pressure on the tetragonal-to-orthorhombic structural ($T_s$) and paramagnetic-to-antiferromagnetic ($T_N$) phase transitions in NaFeAs and compare the outcome with similar measurements on as-grown and annealed BaFe${}_2$As${}_2$. In previous work on as-grown BaFe${}_2$As${}_2$, uniaxial pressure necessary to detwin the sample was found to induce a significant increase in zero pressure $T_N$ and $T_s$. However, we find that similar uniaxial pressure used to detwin NaFeAs and annealed BaFe${}_2$As${}_2$ has a very small effect on their $T_N$ and $T_s$. Since transport measurements on these samples still reveal resistivity anisotropy above $T_N$ and $T_s$, we conclude that such anisotropy can not be due to uniaxial strain-induced $T_N$ and $T_s$ shifts, but must arise from intrinsic electronic anisotropy in these materials.

We present measurements of the vortex-state surface impedance, $Z_s=R_s+\mathrm{i}{X}_s$, of a high-quality, ortho-II-ordered single crystal of the cuprate high-temperature superconductor YBa${}_2$Cu${}_3$O${}_{6.52}$ ($T_c=59$ K). Measurements have been made at four microwave frequencies ($\omega /2\pi =2.64$, 4.51, 9.12, and 13.97 GHz) for magnetic fields ranging from 0 to 7 T. From these data we obtain the field, frequency, and temperature dependence of the vortex viscosity, pinning constant, depinning frequency, and flux-flow resistivity. The vortex viscosity, $\eta (\omega ,T)$, has a surprisingly strong frequency dependence and bears a striking resemblance to the zero-field quasiparticle conductivity, ${\sigma }_{\mathrm{qp}}(\omega ,T)$, suggesting that the dominant dissipative mechanism for the flux lines is induced electric fields coupling to bulk, long-lived $d$-wave quasiparticles outside the vortex cores. This is in sharp contrast to the conventional Bardeen-Stephen picture, in which dissipation takes place inside quasinormal vortex cores. The strong frequency dependence of the vortex viscosity in the microwave range requires us to treat it as a complex response function, with an imaginary part that is predicted to contribute to the apparent pinning force on the vortices. Measurements of the frequency dependence of the pinning force confirm that this term is present, and in a form consistent with the requirements of causality. At low temperatures the flux-flow resistivity, ${\rho }_{\mathrm{ff}}\propto 1/\eta$, has the form ${\rho }_{\mathrm{ff}}\left(T\right)={\rho }_0+{\rho }_1\ln (1/T)$, reminiscent of the dc resistivity of cuprates in the pseudogap regime.

We have observed hysteresis in superconducting resistive transition curves of Ba${}_{0.07}$K${}_{0.93}$Fe${}_2$As${}_2$ ($T_c\sim 8$ K) below about 1 K for in-plane fields. The hysteresis is not observed as the field is tilted away from the $ab$ plane by 20${}^{\circ }$ or more. The temperature and angle dependencies of the upper critical field indicate a strong paramagnetic effect for in-plane fields. We suggest that the hysteresis can be attributed to a first-order superconducting transition due to the paramagnetic effect. Magnetic torque data are also shown.

We observe the electron spin resonance of conduction electrons in boron-doped (6400 ppm) superconducting diamond ($T_{\text{c}}=3.8\text{K}$). We clearly identify the benchmarks of conduction electron spin resonance (CESR): the nearly temperature independent electron spin resonance signal intensity and its magnitude, which is in good agreement with that expected from the density of states through the Pauli spin susceptibility. The temperature dependent CESR linewidth weakly increases with increasing temperature, which can be understood in the framework of the Elliott-Yafet theory of spin relaxation. An anomalous and yet unexplained relation is observed between the $g$-factor, CESR linewidth, and the resistivity using the empirical Elliott-Yafet relation.

We study the effects of electron correlations on the topological phase transition in the Bernevig-Hughes-Zhang model using the variational cluster approach, in which the short-range spatial correlations are taken into account exactly. We calculate the spin Chern number and local magnetic moment to show that the topologically nontrivial antiferromagnetic order exists and that the magnetic transition is of the second order. We furthermore demonstrate that under the spin-quantized condition the topological phase transition is caused by the closing of the bulk band gap.

By developing a method to represent the Renyi entropies via a replica trick on classical statistical mechanical systems, we introduce a procedure to calculate the Renyi mutual information (RMI) in any Monte Carlo simulation. Through simulations on several classical models, we demonstrate that the RMI can detect finite-temperature critical points, and even identify their universality class, without knowledge of an order parameter or other thermodynamic estimators. Remarkably, in addition to critical points mediated by symmetry breaking, the RMI is able to detect topological vortex-unbinding transitions, as we explicitly demonstrate on simulations of the $XY$ model.

We calculate the nonequilibrium conductance through a molecule or a quantum dot in which the occupation of the relevant electronic level is coupled with intensity $\lambda$ to a phonon mode and also to two conducting leads. The system is described by the Anderson-Holstein Hamiltonian. We solve the problem using the Keldysh formalism and the noncrossing approximation for both the electron-electron and the electron-phonon interactions. We obtain a moderate decrease of the Kondo temperature $T_K$ with $\lambda$ for fixed renormalized energy of the localized level $\widetilde{E_d}$. The meaning and value of $\widetilde{E_d}$ are discussed. The spectral density of localized electrons shows, in addition to the Kondo peak of width $2T_K$, satellites of this peak shifted by multiples of the phonon frequency ${\omega }_0$. The nonequilibrium conductance as a function of bias voltage $V_b$ at small temperatures also displays peaks at multiples of ${\omega }_0$ in addition to the central dominant Kondo peak near $V_b=0$.

We discuss a model Kondo-type Hamiltonian representing an analytically tractable version of the model used by Yin et al. [Phys. Rev. B 86, 239904(E) (2012)] to explain the non-Fermi-liquid behavior of iron chalcogenides and ruthenates in an intermediate energy range. We consider a regime where a complete screening of the local degrees of freedom proceeds in two stages described by two characteristic energy scales $T_K^{\text{orb}}\gg E_0$. The first scale marks a screening of the orbital degrees of freedom and the second one marks a crossover to the regime with coherent propagation of quasiparticles. We present analytical results for the specific heat and magnetic susceptibility at $T\ll T_K^{\text{orb}}$.

We develop a local coupling theory to simultaneously treat the weak and strong interaction between a quantum emitter and photons in arbitrary nanostructures. The local coupling strength proportional to the projected local density of states (PLDOS) for photons is determined by a flexible and efficient method. The recent experimental observation for the photonic crystal (PC) slabs is very well interpreted by our ab initio PLDOS, while the scaling invariant law is found to be inapplicable for these PC slabs. More importantly, a bridge linking the PLDOS and cavity quantum electrodynamics is established by the local coupling strength to account for quality factor, $g$ factor, and vacuum Rabi splitting. Our work enriches the knowledge about the light-matter interaction in nanostructures.

We compare the merits of a hopping model and a mobility edge model in the description of the effect of charge-carrier concentration on the electrical conductivity, carrier mobility, and Fermi energy of organic semiconductors. We consider the case of a composite electronic density of states (DOS) that consists of a superposition of a Gaussian DOS and an exponential DOS. Using kinetic Monte Carlo simulations, we apply the two models in order to interpret the recent experimental data reported for n-doped C${}_{60}$ films. While both models are capable of reproducing the experimental data very well and yield qualitatively similar characteristic parameters for the density of states, some discrepancies are found at the quantitative level.

We study theoretically a recently proposed hole spin initialization scheme for $p$-doped quantum well or dot systems via coupling to trion states with subpicosecond circularly polarized laser pulses. We analyze the efficiency of spin initialization and predict the intrinsic spin coherence loss due to the pulse excitation itself as well as the phonon-induced spin dephasing, both taking place on the time scale of the driving laser pulse. We show that the ratio of the degree of dephasing to the achieved orientation effect does not depend on the pulse area but is sensitive to the temperature and detuning. The optimal excitation parameters are identified.

Molybdenum disulfide (MoS${}_2$) is a promising material for making two-dimensional crystals and flexible electronic and optoelectronic devices at the nanoscale. MoS${}_2$ flakes can show high mobilities and have even been integrated in nanocircuits. A fundamental requirement for such use is efficient thermal transport. Electronic transport generates heat which needs to be evacuated, more crucially so in nanostructures. Anharmonic phonon-phonon scattering is the dominant intrinsic limitation to thermal transport in insulators. Here, using appropriate samples, ultralow energy Raman spectroscopy and first-principles calculations, we provide a full experimental and theoretical description of compression and shear modes of few-layer (FL) MoS${}_2$. We demonstrate that the compression modes are strongly anharmonic with a marked enhancement of phonon-phonon scattering as the number of layers is reduced, most likely a general feature of nanolayered materials with weak interlayer coupling.

We present a specially designed evolutionary algorithm for the prediction of surface reconstructions. This technique allows one to automatically explore stable and low-energy metastable configurations with variable surface atoms and variable surface unit cells through the whole chemical potential range. The power of evolutionary search is demonstrated by the efficient identification of diamond $2\times 1$ (100) and $2\times 1$ (111) surface reconstructions with a fixed number of surface atoms and a fixed cell size. With further variation of surface unit cells, we study the reconstructions of the polar surface MgO (111). Experiment has detected an oxygen trimer (ozone) motif [Plass et al., Phys. Rev. Lett. 81, 4891 (1998)]. We predict another version of this motif which can be thermodynamically stable in extreme oxygen-rich conditions. Finally, we perform a variable stoichiometry search for a complex ternary system: semipolar GaN $\left(10\overline{1}1\right)$ with and without adsorbed oxygen. The search yields a counterintuitive reconstruction based on N${}_3$ trimers. These examples demonstrate that an automated scheme to explore the energy landscape of surfaces will improve our understanding of surface reconstructions. The method presented in this paper can be generally applied to binary and multicomponent systems.

An exciton-polariton condensate (EPC) confined in a parabolic two-dimensional trap is considered theoretically. In the realistic limit of weakly interacting polaritons, the nonlinear term in the Gross-Pitaevskii equation describing the properties of the condensate can be considered as a perturbation with respect to the trapping potential, which allows for a convenient analytical description of the EPC ground state and Bogolyubov-type elementary excitations around it. The excitation modes with the energies and wave functions depending on the polariton-polariton coupling strength are derived for the condensate, neglecting interaction with uncondensed polaritons can be neglected. The energies of these modes are shown to be almost equidistant, even for a rather strong polariton-polariton interaction inside the condensate. This makes lateral parabolic traps promising candidates for realization of bosonic cascade lasers based on exciton polaritons. Another physical scenario is also considered where the interaction with a reservoir of uncondensed polaritons is more important than that inside the EPC. In this case, it is shown that the condensate is “reshaped” by the repulsive interaction with the reservoir, namely, pushed out from the center of the trap in real space and blue-shifted in energy, in agreement with the results obtained in a number of recent experiments.

Ultrafast transitions between opposite-spin states of multicomponent bosonic condensates, proceeding on the timescale comparable to the lifetime of the particles the condensate consists of, are demonstrated in a resonantly excited system of cavity polaritons in a magnetic field. Spin-sensitive pair interactions enable fast and massive spin flips occurring at critical amplitudes due to the interplay between amplitude-dependent shifts of eigenstates and the Zeeman splitting. Dominant spin of a condensate can be toggled back and forth by tuning of the pump intensity only, which was impossible in spin-degenerate cavity-polariton systems, cavities with weak exciton-photon coupling, and other previously known photonic systems and devices.