We study the generalized mutual information ${\tilde{I}}_n$ of the ground state of different critical quantum chains. The generalized mutual information definition that we use is based on the well established concept of the Rényi divergence. We calculate this quantity numerically for several distinct quantum chains having either discrete $Z\left(Q\right)$ symmetries ($Q$-state Potts model with $Q=2,3,4$ and $Z\left(Q\right)$ parafermionic models with $Q=5,6,7,8$ and also Ashkin-Teller model with different anisotropies) or the $U\left(1\right)$ continuous symmetries (Klein-Gordon field theory, $XXZ$ and spin-1 Fateev-Zamolodchikov quantum chains with different anisotropies). For the spin chains these calculations were done by expressing the ground-state wave functions in two special bases. Our results indicate some general behavior for particular ranges of values of the parameter $n$ that defines ${\tilde{I}}_n$. For a system, with total size $L$ and subsystem sizes $\ell$ and $L-\ell$, the ${\tilde{I}}_n$ has a logarithmic leading behavior given by $\frac{{\tilde{c}}_n}{4}log[\frac{L}{\pi }sin\left(\frac{\pi \ell }{L}\right)]$ where the coefficient ${\tilde{c}}_n$ is linearly dependent on the central charge $c$ of the underlying conformal field theory describing the system's critical properties.

For elucidation of the adsorption effects on the vibration properties of single-walled carbon nanotubes (SWNTs), photoluminescence and Raman scattering spectra from SWNTs at different vapor pressure of water were simultaneously measured and a molecular dynamics (MD) simulation was performed. The water vapor pressure dependence and its tube diameter $\left(d_{\mathrm{tube}}\right)$ dependence of the frequency of the radial breathing mode (RBM) peaks $\left({\omega }_{\mathrm{RBM}}\right)$ and the optical transition energy $\left(E_{ii}\right)$ indicate that the physical adsorption is quite important, and both ${\omega }_{\mathrm{RBM}}$ and $E_{ii}$ clearly depend on the number density of adsorption molecules on the SWNT surface. A simple adsorption model, where the vibrational coupling between the surrounding adsorption layer and SWNTs via van der Waals interaction is considered for RBM, reproduces the experimental and MD simulation results of ${\omega }_{\mathrm{RBM}}$ in a wide $d_{\mathrm{tube}}$ range for various SWNTs, such as isolated SWNTs in vacuum, SWNTs with adsorption water layer, and even bundled SWNTs. On the basis of the model, the variation of the relationship between ${\omega }_{\mathrm{RBM}}$ and $E_{ii}$ in a Kataura plot for various SWNT samples can also be understood generally as the “environmental effects.”

We theoretically predict two new classes of three-dimensional topological crystalline insulators (TCIs), which have an odd number of unpinned surface Dirac cones protected by crystal symmetries. The first class is protected by a single nonsymmorphic glide plane symmetry; the second class is protected by a composition of a twofold rotation and time-reversal symmetry (a magnetic group symmetry). Both classes of TCIs are characterized by a quantized $\pi$-Berry phase associated with surface states and a $Z_2$ topological invariant associated with the bulk bands. In the presence of disorder, these TCI surface states are protected against localization by the average crystal symmetries, and exhibit critical conductivity in the universality class of the quantum Hall plateau transition. These new TCIs exist in time-reversal-breaking systems with or without spin-orbital coupling, and their material realizations are discussed.

We calculate the local density of states (LDOS) for an infinite graphene sheet with a single centrosymmetric out-of-plane deformation, in order to investigate measurable strain signatures on graphene. We focus on the regime of small deformations and show that the strain-induced pseudomagnetic field induces an imbalance of the LDOS between the two triangular graphene sublattices in the region of the deformation. Real-space imaging reveals a characteristic sixfold symmetry pattern where the sublattice symmetry is broken within each fold, consistent with experimental and tight-binding observations. The open geometry we study allows us to make use of the usual continuum model of graphene and to obtain results independent of boundary conditions. We provide an analytic perturbative expression for the contrast between the LDOS of each sublattice, showing a scaling law as a function of the amplitude and width of the deformation. We confirm our results by a numerically exact iterative scattering matrix method.

The temperature evolution of the electronic structure of a Ni-Fe(Co)-Ga/MgO(100), Heusler-type, ferromagnetic shape-memory alloy thin film has been followed by a bulk-sensitive hard x-ray photoelectron spectroscopy, element-selective soft x-ray magnetic circular dichroism, and first-principles calculation. The reversible changes of the electronic states near the Fermi energy show a hysteresis associated with the martensitic phase transition (MPT), where the pseudogap opens on cooling and closes again on warming. In addition, the Ni $3d$ spin magnetic moment increases by approximately two times across the MPT, whereas the change of Fe $3d$ moment is moderate. By comparing the experimental results with the calculated spin-resolved density of states, we conclude that the band Jahn-Teller effect of Ni $3d$ and Fe $3d$ orbitals is responsible for MPT.

$XY$ and Heisenberg spins, subjected to strong random fields acting at a few points in space with a concentration $c_r\ll 1$, are studied numerically on three-dimensional lattices containing over $4\times {10}^6$ sites. Glassy behavior with a strong dependence on initial conditions is found. Beginning with a random initial orientation of spins, the system evolves into ferromagnetic domains inversely proportional to $c_r$ in size. The area of the hysteresis loop $m\left(H\right)$ scales as $c_r^2$. These findings are explained by mapping the effect of a strong dilute random field onto the effect of a weak continuous random field. Our theory applies directly to ferromagnets with magnetic impurities, and is conceptually relevant to strongly pinned vortex lattices in superconductors and pinned charge-density waves.

We study a minimal model for a relaxor ferroelectric including dipolar interactions and short-range harmonic and anharmonic forces for the critical modes as in the theory of pure ferroelectrics together with quenched disorder coupled linearly to the critical modes. We present the simplest approximate solution of the model necessary to obtain the principal features of the correlation functions. Specifically, we calculate and compare the structure factor measured by neutron scattering in different characteristic regimes of temperature in the relaxor $\mathrm{Pb}\left({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}\right){\mathrm{O}}_3$.

We investigate a ladder system with two inequivalent legs, namely, a Hubbard chain and a one-dimensional electron gas. Analytical approximations, the density-matrix renormalization group method, and continuous-time quantum Monte Carlo simulations are used to determine ground-state properties, gaps, and spectral functions of this system at half-filling. Evidence for the existence of four different phases as a function of the Hubbard interaction and the rung hopping is presented. First, a Luttinger liquid exists at very weak interchain hopping. Second, a Kondo-Mott insulator with spin and charge gaps induced by an effective rung exchange coupling is found at moderate interchain hopping or strong Hubbard interaction. Third, a spin-gapped paramagnetic Mott insulator with incommensurate excitations and pairing of doped charges is observed at intermediate values of the rung hopping and the interaction. Fourth, the usual correlated band insulator is recovered for large rung hopping. We show that the wave numbers of the lowest single-particle excitations are different in each insulating phase. In particular, the three gapped phases exhibit markedly different spectral functions. We discuss the relevance of asymmetric two-leg ladder systems as models for atomic wires deposited on a substrate.

Nearly identical Pd nanocubes yield an x-ray powder diffraction pattern with interference fringes affording access to unprecedented structural details of nanocrystal size, shape, and complex atomic displacement for a billion-sized population. The excellent agreement between diffraction data and molecular dynamics (MD) provides strong experimental validation of MD simulations and the proposed data-interpretation paradigm. These results show that individual atomic displacements within the nanocubes are not only a function of disrupted bonds and the crystallographic plane of the adjacent surface, but are complex strain gradients extending across all surfaces of the particle strongly influenced by atomic displacements. This observation of nonuniform surface strain and the manner in which it is affected by different sizes, shapes, and locations within each facet could be the key to understanding many surface related properties of shaped nanocrystals including those associated with important catalysis applications.

A series of density functional theory (DFT) simulations was performed to investigate the approach, contact, and subsequent separation of two atomically flat surfaces consisting of different materials. Aluminum (Al) and titanium nitride (TiN) slabs were chosen as a model system representing a metal-ceramic interface and the interaction between soft and hard materials. The approach and separation were simulated by moving one slab in discrete steps normal to the surfaces allowing for electronic and atomic relaxations after each step. Various configurations were analyzed by considering (001), (011), and (111) surfaces as well as several lateral arrangements of these surfaces at the interface. Several tests were conducted on the computational setup, for example, by changing the system size or using different approximations for the exchange correlation functional. The performed simulations revealed the influences of these aspects on adhesion, equilibrium distance, and material transfer. These interfacial properties depend sensitively on the chosen configuration due to distinct bond situations. Material transfer, in particular, was observed if the absolute value of the adhesion energy for a given configuration is larger than the energy cost to remove surface layers. This result was found to be independent of the employed exchange correlation functional. Furthermore, it was shown that a simple comparison of the surface energies of the slabs is not sufficient to predict the occurrence of material transfer.

We report the specific heat of graphite, highly oriented pyrolytic graphite (HOPG), graphene oxide (GO), and reduced graphene oxide (RGO) from 300 K to 50 mK. Graphite and HOPG exhibits transition from three dimensions $(C_v\propto T^3)$ to two dimensions $(C_v\propto T^2)$ as the temperature increases above 4 K and approaching linearity in temperature for both around room temperature is observed. We observe a Schottky-like peak in specific heat of graphene oxide and reduced graphene oxide near 0.1 K, whose intensity and peak position varies with external magnetic field. We find that the random Heisenberg superexchange interaction between the Anderson (disorder) localized $\pi$ electrons of GO/RGO is responsible for the specific-heat peak. The exchange interaction strength between the localized spins falls off with distance as a weak power law $(\propto \frac{1}{r^{2.5}})$, rather than the usual exponential fall in insulating magnets.

We analyze the bound-state spectra of mass-profile quantum dots in graphene, a system at current experimental reach. Homogeneous perpendicular magnetic fields are also considered which result in breaking the valley degeneracy. The spectra show rich features, arising from the chiral band structure of graphene and its Landau levels and we identify three different regimes depending on the ratio between the radius of the dot and the magnetic length. We further carry out a comparison with potential-well quantum dots discussed in Recher et al. [Phys. Rev. B 79, 085407 (2009)] and conclude that mass confinement may offer significant advantages for optical applications in the THz and infrared regime. Also due to experimental advances, we additionally analyze the band structure of a linear chain of mass-profile quantum dots, where overlap-assisted hopping processes play a major role for closely packed arrays. The inclusion of Coulomb interactions between electron-hole pairs of adjacent sites leads to a new regime where Förster transfer processes become dominant.

Using first-principles computational techniques, we have investigated the structural, vibrational, and dielectric properties of a Ruddlesden-Popper-type layered oxide ${\mathrm{Ba}}_2{\mathrm{ZrO}}_4$ subjected to a wide range of biaxial strains emulating epitaxial thin-film environment. Under compressive strains, this compound experiences an incommensurate distortion characterized by planar displacements of individual perovskite slabs away from their high symmetry positions. On the other hand, under increasing epitaxial tension, the original centrosymmetric structure becomes unstable—first, with respect to antiferrodistortive oxygen cage rotations and then also with respect to in-plane polar distortions. Both the incommensurate-to-commensurate and the nonpolar-to-polar phase transformations are accompanied by anomalies of the static dielectric response, however, only in the latter case a divergence of the in-plane dielectric constant is observed. Remarkably, even after the transition into the ferroelectric state (with polarization of up to 0.12 ${\mathrm{C}/\mathrm{m}}^2$ at 3.5% tension) dielectric permittivity of ${\mathrm{Ba}}_2{\mathrm{ZrO}}_4$ remains unusually high, which is explained by an emergence of a Goldstone-like excitation in the system manifested through an in-plane libration of the polarization vector. Since ${\mathrm{Ba}}_2{\mathrm{ZrO}}_4$ displays a yet poorly understood tendency to absorb small molecules, such as water and ${\mathrm{CO}}_2$, acquiring better insights into the physical underpinnings of its behavior can produce more efficient functional materials for applications in advanced technologies for carbon sequestration.

The effect of octahedral tilting on the acentric structural transitions in $A\mathrm{Ga}{\mathrm{O}}_3/A^{\prime }\mathrm{Ga}{\mathrm{O}}_3$ [001], [110], and [111] superlattices $(A,A^{\prime }=\mathrm{La},\mathrm{Pr},\mathrm{Nd})$ is studied using density functional theory. We find the displacive transitions are driven by two octahedral rotations modes ($a^{-}{a}^{-}{c}^0$ and $a^0{a}^0{c}^{+}$ tilting) with amplitudes that depend on the $A$ and $A^{\prime }$ chemistry and cation ordering directions. We find the ground-state structures of the [001] and [111] ordered superlattices are polar. The coupling of octahedral tilting modes through a hybrid improper ferroelectric mechanism induces the polar displacements and produces the macroscopic electric polarizations. Our layer decomposed polarization analysis explains the magnitude of the polarization values along the ordering directions.

Motivated by experiments on ultracold atoms which have realized the Haldane model for a Chern insulator, we consider its strongly correlated Mott limit with spin-$\frac{1}{2}$ fermions. We find that slave rotor mean-field theory yields gapped or gapless chiral spin liquid Mott insulators. To study competing magnetic orders, we consider the strong coupling effective spin Hamiltonian which includes chiral three-spin exchange. We obtain its classical phase diagram, uncovering various chiral magnetic orders including tetrahedral, cone, and noncoplanar spiral states which can compete with putative chiral quantum spin liquids. We study the effect of thermal fluctuations on these states, identifying crossovers in the spin chirality, and phase transitions associated with lattice symmetry breaking. We also discuss analogous effective spin Hamiltonians for correlated spin-$\frac{1}{2}$ bosons. Finally, we point out possible experimental implications of our results for cold atom experiments.

We present a detailed experimental study of bulk and powder samples of the ferromagnetic Heusler shape-memory alloy ${\mathrm{Ni}}_2\mathrm{MnGa}$, including zero-field static and dynamic ${}^{55}\mathrm{Mn}$ NMR experiments, x-ray powder diffraction and magnetization experiments. The NMR spectra give direct access to the sequence of structural phase transitions in this compound, from the $\text{high}-T$ austenitic phase down to the $\text{low}-T$ martensitic phase. In addition, a detailed investigation of the so-called $rf-\text{enhancement}$ factor delivers the local magnetic stiffness and restoring fields for each separate structural environment, thus, differentiating signals coming from austenitic and martensitic components. In this way we can also resolve differences in the local spin moments of the two phases of the order of 0.08 Bohr magnetons, and reveal precursor phenomena of the martensitic transformation well inside the parent austenitic phase.

The magnetic structure of the mixed rare-earth system $\mathrm{P}{\mathrm{r}}_x{\mathrm{Y}}_{1-x}\mathrm{F}{\mathrm{e}}_3{\left(\mathrm{B}{\mathrm{O}}_3\right)}_4$ has been studied by elastic neutron powder diffraction and magnetic measurements. A spin reorientation from easy axis to easy plane occurs in the concentration range $x=0.67–0.45$ through the formation of inclined magnetic structures. The inclination of the Fe moments from the basal plane depends on the Pr content and ranges from 67(2)° for $x=0.67$ to $16{\left(4\right)}^{\circ }$ for $x=0.45$ at $T=3\mathrm{K}$. A nonmonotonic change of the inclination angle with temperature is found for all compounds but there is no sign of a spontaneous spin reorientation in the temperature range of magnetic order.

An approach based on a crystal-field model for the $\mathrm{P}{\mathrm{r}}^{3+}$ ion and on the molecular-field approximation is used to describe the magnetic characteristics of the system $\mathrm{P}{\mathrm{r}}_x{\mathrm{Y}}_{1-x}\mathrm{F}{\mathrm{e}}_3{\left(\mathrm{B}{\mathrm{O}}_3\right)}_4$. A good agreement between the experimental and calculated temperature dependences of the magnetic susceptibilities and the angle of inclination of Fe moments from the basal plane has been achieved.

A locally gauge-invariant theory of the spin response of a thin film of ${}^3\mathrm{He}\text{−}B$ film is given that describes fluctuation effects arising from the coupled dynamics of the superconducting order parameter (the collective mode) and in-gap Majorana surface states. In contrast to a mean-field calculation of the spin response, which predicts a nonzero imaginary longitudinal spin susceptibility at frequencies inside the bulk gap due to absorption from the Majorana states, our gauge-invariant theory shows that this response is strongly suppressed above the collective mode frequency and vanishes if dipole-dipole interactions are neglected. In the presence of dipole-dipole interactions, in sufficiently thin films, and at ultralow temperatures, the Majorana states lead to a distinctive magnetic-field- and temperature-dependent damping of the collective mode, a feature that may be observable in longitudinal NMR experiments.