We examine the statics and dynamics of vortices in the presence of a periodic quasi-one-dimensional substrate, focusing on the limit where the vortex lattice constant is smaller than the substrate lattice period. As a function of the substrate strength and filling factor, within the pinned state, we observe a series of order-disorder transitions associated with buckling phenomena in which the number of vortex rows that fit between neighboring substrate maxima increases. These transitions coincide with steps in the depinning threshold, jumps in the density of topological defects, and changes in the structure factor. At the buckling transition, the vortices are disordered, while between the buckling transitions the vortices form a variety of crystalline and partially ordered states. In the weak substrate limit, the buckling transitions are absent and the vortices form an ordered hexagonal lattice that undergoes changes in its orientation with respect to the substrate as a function of vortex density. At intermediate substrate strength, certain ordered states appear that are correlated with peaks in the depinning force. Under an applied drive, the system exhibits a rich variety of distinct dynamical phases, including plastic flow, a density-modulated moving crystal, and moving floating solid phases. We also find a dynamic smectic-to-smectic transition in which the smectic ordering changes from being aligned with the substrate to being aligned with the external drive. The different dynamical phases can be characterized using velocity histograms and the structure factor. We discuss how these results are related to recent experiments on vortex ordering in thin films with periodic thickness modulations. Our results should also be relevant for other types of systems such as ions, colloids, or Wigner crystals interacting with periodic quasi-one-dimensional substrates.

Probing the ferroelectricity at the nanometer scale is of particular interest for a wide range of applications. In this Rapid Communication, the structural distortion of ${\mathrm{BaTiO}}_3$ (BTO) is studied in its ferroelectric (rhombohedral and tetragonal), and paraelectric phases from the O $K$ near edge structures in electron energy loss spectroscopy. Modifications of the electronic structure are detected in the lowest energy fine structure (FS) of the O $K$ edge in the ferroelectric phases, and are interpreted by core-hole valence-electron screening geometry. For the paraelectric phase, the lowest energy FS of the O $K$ edge is comparable to the one obtained at room temperature, which is inconsistent with an expected cubic structure. The variations observed in the O $K$ near edge structures, such as a broader and more asymmetric lowest energy FS at low temperature, suggest that the magnitude of the $\mathrm{Ti}^{4+}$ off-centering along $\langle 111\rangle$ increases in lower-temperature phases. These findings demonstrate the sensitivity of the O $K$ near edge structures to the structural distortions of BTO polymorphs, and form a basis for further investigations on defective or strained BTO at the nanoscale.

${\mathrm{CuAs}}_2{\mathrm{O}}_4$ is a $S=1/2$ quasi-one-dimensional ribbon chain compound which orders ferromagnetically at 7.4 K under ambient conditions. ${\mathrm{CuAs}}_2{\mathrm{O}}_4$ features nearest- and next-nearest-neighbor spin-exchange interactions along the spin chains with a ratio $\alpha =J_{\mathrm{nn}}/J_{\mathrm{nnn}}$ in close proximity to the quantum critical point at $\alpha =-4$. We apply hydrostatic pressure up to $\sim 11.5$ GPa and examine the structural and magnetic properties using Raman spectroscopy, single-crystal synchrotron x-ray diffraction, and magnetic susceptibility measurements. External pressure severely reduces the axial Jahn-Teller elongations of the oxygen octahedra surrounding the ${\mathrm{Cu}}^{2+}$ cations and stabilizes the ferromagnetic ground state. At 9.2(2) GPa, we detect a structural phase transition leading to an increased twisting of the ${\mathrm{CuO}}_2$ ribbon chains and a large drop of the magnetic ordering temperature. Ab initio density functional theory calculations of the spin-exchange parameters, using the structural parameters as a function of pressure, support the experimental findings.

Spin ices, frustrated magnetic materials analogous to common water ice, have emerged over the past 15 years as exemplars of high frustration in three dimensions. Recent experimental developments aimed at interrogating anew the low-temperature properties of these systems, in particular whether the predicted transition to long-range order occurs, behoove researchers to scrutinize our current dipolar spin ice model description of these materials. In this work, we do so by combining extensive Monte Carlo simulations and mean-field theory calculations to analyze data from previous magnetization, diffuse neutron scattering, and specific-heat measurements on the paradigmatic ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ spin ice material. In this work, we also reconsider the possible importance of the nuclear specific heat $C_{\mathrm{nuc}}$ in ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. We find that $C_{\mathrm{nuc}}$ is not entirely negligible below a temperature $\sim 0.5$ K and must therefore be taken into account in a quantitative analysis of the calorimetric data of this compound below that temperature. We find that in this material, small effective spin-spin exchange interactions compete with the magnetostatic dipolar interaction responsible for the main spin ice phenomenology. This causes an unexpected “refrustration” of the long-range order that would be expected from the incompletely self-screened dipolar interaction and which positions the material at the boundary between two competing classical long-range-ordered ground states. This allows for the manifestation of new physical low-temperature phenomena in ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, as exposed by recent specific-heat measurements. We show that among the four most likely causes for the observed upturn of the specific heat at low temperature [an exchange-induced transition to long-range order, quantum non-Ising (transverse) terms in the effective spin Hamiltonian, the nuclear hyperfine contribution, and random disorder], only the last appears to be reasonably able to explain the calorimetric data.

Recent experiments demonstrate that plasmonic resonators can enhance the four-wave mixing (FWM) process by several orders of magnitude, due to the localization of the incident fields. We show that, when the plasmonic resonator is coupled to two quantum emitters, a three orders of magnitude enhancement can be obtained on top of the enhancement due to the localization. We explicitly demonstrate—on an expression for the steady-state FWM amplitude—how the presence of a Fano resonance leads to the cancellation of nonresonant terms in a FWM process. A cancellation in the denominator gives rise to an enhancement in the nonlinearity. The explicit demonstration we present here guides one to a method for achieving even larger enhancement factors by introducing additional coupling terms. The method is also applicable to Fano resonances induced by all-plasmonic couplings, which are easier to control in experiments.

Surface-enhanced Raman scattering (SERS) from bipyridyl ethylene adsorbed on gold dumbbells shows Fano-like spectra at high incident light intensity. This is accompanied by an increased electronic temperature, while no vibrational anti-Stokes scattering is observed. Theory indicates that interference between vibrational and electronic Raman scattering can yield such asymmetric scattering lineshapes. The best fit to observations is however obtained by disregarding this coupling and accounting for the detailed lineshape of the continuous electronic component of the SERS.

Blinking dynamics of strain-engineered direct-band-gap Si nanocrystals is measured over a broad interval of time scales and excitation intensities. The measured data are at first described using the autocorrelation function approach. Then, the relationship between the shape of the autocorrelation function and the distributions of on and off times is discussed. An original numerical approach allowing us to deduce and quantify the corresponding on- and off-times distributions is proposed. Both the autocorrelation function and the distribution of on and off times are observed to follow a broken-power-law function, for which we introduce an analytical formula. The broken-power-law function signifies a change in the power-law dynamics at short time scales (the power-law exponent changes on the time scale of 1–20 ms). Under the lowest excitation intensities, both the autocorrelation function and the distribution of on times are flat, implying the existence of a nonblinking regime. In addition to the broken-power-law dynamics, the end of the on-times distribution is also cut off by an exponential tail. All these temporal regimes are observed to be independent of excitation intensity for the lowest excitation intensities, whereas at higher excitation intensities, excitation intensity dependence appears. The distribution of off times is observed to be more robust, with changes occurring at higher excitation intensity than in the case of the on-times distribution. The different observed regimes are discussed in detail and a qualitative model including the emission of a trion is proposed.

We systematically investigate the influence of free-electron concentrations from $1.5\times {10}^{17}{\mathrm{cm}}^{-3}$ up to $1.6\times {10}^{21}{\mathrm{cm}}^{-3}$ on the optical properties of single-crystalline ${\mathrm{In}}_2{\mathrm{O}}_3$ in the cubic bixbyite structure. Dielectric functions of bulk crystals and epitaxial films on various substrates are determined by spectroscopic ellipsometry from the mid-infrared $\left(37\mathrm{meV}\approx 300{\mathrm{cm}}^{-1}\right)$ into the ultraviolet $\left(6.5\mathrm{eV}\right)$ spectral region. Eight transverse optical phonon modes are resolvable for low carrier-density material. The analysis of the plasma frequencies yields effective electron masses which increase from a zero-density mass of $m^{*}=0.18m_0$ to $0.4m_0$ at $n={10}^{21}{\mathrm{cm}}^{-3}$. This mirrors the nonparabolicity of the conduction band being described by an analytical expression. The onset of absorption due to dipole-allowed interband transitions is found at $3.8\mathrm{eV}$ for $n\le {10}^{19}{\mathrm{cm}}^{-3}$. It undergoes a blue-shift (effective Burstein-Moss shift) for higher electron densities as a result of the dominating phase-space filling compared to band gap renormalization. A comprehensive model describing the absorption onset is developed, taking nonparabolicity into account, yielding an accurate description and explanation of the observations. The agreement of modeled and measured absorption onset independently supports the effective electron masses derived from infrared data. The high-frequency dielectric constant of undoped ${\mathrm{In}}_2{\mathrm{O}}_3$ is found to be ${\varepsilon }_{\infty }=(4.08\pm 0.02)$.

We propose a simple analytical model to explain the possible appearance of the metallic conductivity in the two-dimensional (2D) ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface. Our model considers the interface within a macroscopic approach, which is usual for semiconductor heterojunctions and is based on drift-diffusion equations. The solution of these equations allows us to obtain the positions of band edges as a function of distances from the interface. We show that for the 2D metallic conductivity to appear at the interface, the constituting substances should have the same type (either electronic or hole) of conductivity; in the opposite case the possible transition to metallic phase has a three-dimensional character. The results of our model calculations are in agreement with available experimental data.

The electronic structure of ${\mathrm{SrTiO}}_3$ and ${\mathrm{SrHfO}}_3$ (001) surfaces with oxygen vacancies is studied by means of first-principles calculations. We reveal how oxygen vacancies within the first atomic layer of the ${\mathrm{SrTiO}}_3$ surface (i) induce a large antiferrodistortive motion of the oxygen octahedra at the surface, (ii) drive localized magnetic moments on the Ti $3d$ orbitals close to the vacancies, and (iii) form a two-dimensional electron gas localized within the first layers. The analysis of the spin texture of this system exhibits a splitting of the energy bands according to the Zeeman interaction, lowering of the Ti $3d_{xy}$ level in comparison with $d_{xz}$ and $d_{yz}$, and also an in-plane precession of the spins. No Rashba-like splitting for the ground state or for the ab initio molecular dynamics trajectory at 400 K is recognized as suggested recently by A. F. Santander-Syro et al. [Nat. Mater. 13, 1085 (2014)]. Instead, a sizable Rashba-like splitting is observed when the Ti atom is replaced by a heavier Hf atom with a much larger spin-orbit interaction. However, we observe the disappearance of the magnetism and the surface two-dimensional electron gas when full structural optimization of the ${\mathrm{SrHfO}}_3$ surface is performed. Our results uncover the sensitive interplay of spin-orbit coupling, atomic relaxations, and magnetism when tuning these Sr-based perovskites.

We report on spatial measurements of the superconducting proximity effect in epitaxial graphene induced by a graphene-superconductor interface. Superconducting aluminum films were grown on epitaxial multilayer graphene on SiC. The aluminum films were discontinuous, with networks of trenches in the film morphology reaching down to exposed graphene terraces. Scanning tunneling spectra measured on the graphene terraces show a clear decay of the superconducting energy gap with increasing separation from the graphene-aluminum edges. The spectra were well described by BCS theory. The decay length for the superconducting energy gap in graphene was determined to be greater than 400 nm. Deviations in the exponentially decaying energy gap were also observed on a much smaller length scale of tens of nanometers.

We present results on the radiative lifetimes of excitons and trions in a monolayer of metal dichalcogenide ${\mathrm{MoS}}_2$. The small exciton radius and the large exciton optical oscillator strength result in radiative lifetimes in the 0.18–0.30 ps range for excitons that have small in-plane momenta and couple to radiation. Average lifetimes of thermally distributed excitons depend linearly on the exciton temperature and can be in the few picoseconds range at small temperatures and more than a nanosecond near room temperature. Localized excitons exhibit lifetimes in the same range and the lifetime increases as the localization length decreases. The radiative lifetimes of trions are in the hundreds of picosecond range and increase with the increase in the trion momentum. Average lifetimes of thermally distributed trions increase with the trion temperature as the trions acquire thermal energy and larger momenta. We expect our theoretical results to be applicable to most other 2D transition metal dichalcogenides.

The interface between a topological insulator and a ferromagnetic insulator exhibits an interesting interplay of topological Dirac electrons and magnetism. As has been shown recently, the breaking of time-reversal invariance by magnetic order generates a Chern-Simons term in the action, that in turn leads to a Berry phase and a magnetoelectric effect of topological origin. Here, we consider the system in the presence of a long-range Coulomb interaction between the Dirac electrons, and find that the magnetoelectric effect of the fluctuating electric field becomes nonlocal. We derive a Landau-Lifshitz equation for the fluctuation-induced magnetization dynamics and the Euler-Lagrange equation of the Coulomb field by explicit one-loop calculations. Via the Coulomb interaction, divergences in the in-plane magnetization affect the magnetization dynamics over large distances in a topologically protected way.

We present a comprehensive computational and experimental examination of the $\mathrm{C}{\mathrm{r}}_{1-x}{\mathrm{V}}_x{\mathrm{O}}_2 \left(0\le x\le 0.5\right)$ system. The entire series crystallizes in the rutile structure, but the compounds exhibit significantly different magnetic properties depending on $x$. Lattice parameter $a$ increases linearly with $x$, but the $c$ parameter is slightly reduced due to vanadium-vanadium bonding. The V-for-Cr substitution creates $\mathrm{C}{\mathrm{r}}^{3+}\text{−}{\mathrm{V}}^{5+}$ pairs; this leads to competition between ferromagnetic $\left(\mathrm{C}{\mathrm{r}}^{4+}\text{−}\mathrm{C}{\mathrm{r}}^{4+}\right)$ and antiferromagnetic $\left(\mathrm{C}{\mathrm{r}}^{3+}\text{−}\mathrm{C}{\mathrm{r}}^{3+}\right)$ interactions such that the materials change from ferromagnetic to antiferromagnetic with increasing $x$. Weak ferromagnetic interactions arising from $\mathrm{C}{\mathrm{r}}^{4+}$ are observed even in the seemingly antiferromagnetic phases with the exception of $x=0.5$, which contains only $\mathrm{C}{\mathrm{r}}^{3+}$. Density functional theory calculations are performed, but they incorrectly predict the $x=0.5$ phase to be a half-metal. This is caused by an incorrect prediction of the oxidation states of chromium and vanadium.

We consider the superconducting state in a clean crystal with antiferromagnetic (AF) structure of localized magnetic moments taking into account the exchange interaction between magnetic moments and conduction electrons. We assume that the localized moments order at the Neel temperature $T_N$ due to the RKKY interaction predominantly. In such crystals, the periodic exchange field acting on conducting electrons results in the formation of an insulating gap on the Fermi surface for electrons moving in directions that depend on the orientation of the wave vector of AF ordering. We assume a scenario in which the Cooper pairing occurs in the open parts of the Fermi surface at the temperature $T_c$. We show that at high amplitudes of exchange field $h_e>T_c/{\mu }_B$, the structure of superconducting state just below the temperature $T_c$ depends on the relation between $T_c$ and $T_N$. At low ratio $T_c/T_N$, a nonuniform superconducting state, like the Fulde-Farrell-Larkin-Ovchinnikov high-field phase, should exist, while at bigger ratio superconducting order parameter is uniform. The nonuniform structure of superconducting state may be probed by tunneling measurements.

We use ab initio evolutionary algorithm and first-principles calculations to investigate structural, electronic, vibrational, and superconducting properties of two-dimensional ($2\mathrm{D}$) boron allotropes. Remarkably, we show that conventional BCS superconductivity in the stable $2\mathrm{D}$ boron structures is ubiquitous with the critical temperature $T_c$ above the liquid hydrogen temperature for certain configurations. Due to the electronic states of the Fermi surface originating from both $\sigma$ and $\pi$ electrons, the superconductivity of the $2\mathrm{D}$ structures arises from multiple phonon modes. Our results support that $2\mathrm{D}$ boron structure may be a pure single-element material with the highest $T_c$ on conditions without high pressure and external strain.