We theoretically study the conductivity in arrays of metallic grains due to the variable-range multiple cotunneling of electrons with short-range (screened) Coulomb interaction. The system is supposed to be coupled to random stray charges in the dielectric matrix that are only loosely bounded to their spatial positions by elastic forces. The flexibility of the stray charges gives rise to a polaronic effect, which leads to the onset of Arrhenius-type conductivity behavior at low temperatures, replacing conventional Mott variable-range hopping. The effective activation energy logarithmically depends on temperature due to fluctuations of the polaron barrier heights. We present the unified theory that covers both weak and strong polaron effect regimes of hopping in granular metals and describes the crossover from elastic to inelastic cotunneling.

Elastic waves scattered by random rough interfaces separating two distinct media play an important role in modeling phonon scattering and impact upon thermal transport models, and are also integral to ultrasonic inspection. We introduce theoretical formulas for the diffuse field of elastic waves scattered by, and transmitted across, random rough solid-solid interfaces using the elastodynamic Kirchhoff approximation. The new formulas are validated by comparison with numerical Monte Carlo simulations, for a wide range of roughness (rms $\sigma \le \lambda /3$, correlation length ${\lambda }_0\ge$ wavelength $\lambda$), demonstrating a significant improvement over the widely used small-perturbation approach, which is valid only for surfaces with small rms values. Physical analysis using the theoretical formulas derived here demonstrates that increasing the rms value leads to a considerable change of the scattering patterns for each mode. The roughness has different effects on the reflection and the transmission, with a strong dependence on the material properties. In the special case of a perfect match of the wave speed of the two solid media, the transmission is the same as the case for a flat interface. We pay particular attention to scattering in the specular direction, often used as an observable quantity, in terms of the roughness parameters, showing a peak at an intermediate value of rms; this rms value coincides with that predicted by the Rayleigh parameter.

Motivated by the magnetic properties of the spin-chain compounds ${\mathrm{LiCuSbO}}_4\equiv {\mathrm{LiSbCuO}}_4$ and ${\mathrm{Rb}}_2{\mathrm{Cu}}_2{\mathrm{Mo}}_3{\mathrm{O}}_{12}$, we study the ground state of the Heisenberg chain with dimerized nearest-neighbor ferromagnetic (FM) ($J_1,J_1^{\prime }<0$) and next-nearest-neighbor antiferromagnetic ($J_2>0$) couplings. Using the density-matrix renormalization group technique and spin-wave theory, we find a first-order transition between a fully polarized FM and an incommensurate spiral state at $2\alpha =\beta /(1+\beta )$, where $\alpha$ is the frustration ratio $J_2/\left|J_1\right|$ and $\beta$ the degree of dimerization $J_1^{\prime }/J_1$. In the singlet spiral state the spin-gap is vanishingly small in the vicinity of the FM transition, corresponding to a situation of ${\mathrm{LiCuSbO}}_4$. For larger $\alpha$, corresponding to ${\mathrm{Rb}}_2{\mathrm{Cu}}_2{\mathrm{Mo}}_3{\mathrm{O}}_{12}$, and smaller $\beta$ there is a crossover from this frustration induced incommensurate state to an Affleck-Lieb-Kennedy-Tasaki-type valence-bond solid state with substantial spin gaps.

The spin-$\frac{1}{2}$ Heisenberg octahedral chain with regularly alternating monomeric and square-plaquette sites is investigated using various analytical and numerical methods: variational technique, localized-magnon approach, exact diagonalization (ED), and density-matrix renormalization group (DMRG) methods. The model belongs to the class of flatband systems and it has a rich ground-state phase diagram including phases with spontaneously broken translational symmetry. Moreover, it exhibits an anomalous low-temperature thermodynamics close to continuous or discontinuous field-driven quantum phase transitions between three quantum ferrimagnetic phases, tetramer-hexamer phase, monomer-tetramer phase, localized-magnon phase, and two different spin-liquid phases. If the intraplaquette coupling is at least twice as strong as the monomer-plaquette coupling, the variational method furnishes a rigorous proof of the monomer-tetramer ground state in a low-field region and the localized-magnon approach provides exact evidence of a single magnon trapped at each square plaquette in a high-field region. In the rest of the parameter space we have numerically studied the ground-state phase diagram and magnetization process using DMRG and ED methods. It is shown that the zero-temperature magnetization curve may involve up to four intermediate plateaus at zero, one-fifth, two-fifths, and three-fifths of the saturation magnetization, while the specific heat exhibits a striking low-temperature peak in the vicinity of discontinuous quantum phase transitions.

We report the discovery of magnetoelectric multiferroicity in a family of oxides, $R\mathrm{FeW}{\mathrm{O}}_6$ ($R=\mathrm{Dy}$, Eu, Tb, and Y) that crystallize in a polar aeschynite-type structure ($Pna{2}_1$) with an ordered arrangement of $\mathrm{F}{\mathrm{e}}^{3+}$ and ${\mathrm{W}}^{6+}$ ions. Magnetization and analysis of neutron-diffraction data of $\mathrm{DyFeW}{\mathrm{O}}_6$ reveal a commensurate noncollinear antiferromagnetic ordering of $\mathrm{F}{\mathrm{e}}^{3+}$ spins ($T_{\mathrm{N}}^{\mathrm{Fe}}\sim 18\mathrm{K}$), which induce Dy spins to order at the same temperature. A sudden change in electric polarization $\left(\mathrm{\Delta }P\right)$ appears in all the compounds at $T_{\mathrm{N}}^{\mathrm{Fe}}=15–18\mathrm{K}$. The electric polarization is sensitive to an applied magnetic field, and the coupling between different magnetic $R$-ion and Fe-ion moments suppresses the polarization to a different extent. Although the measured polarization in polycrystalline $\mathrm{DyFeW}{\mathrm{O}}_6$ at 3.5 K is about $3\mu \mathrm{C}/{\mathrm{m}}^2$, a simple calculation of the ionic contribution to polarization with formal charges is $75560\mu \mathrm{C}/{\mathrm{m}}^2$ and it is of the form $\mathbf{P}=(p_x,0,p_z)$ where, $p_x$ comes from magnetic ordering and $p_z$ is associated with the polar structure in the paramagnetic state. These findings open up an avenue to explore further new polar magnets with rare-earth/transition-metal ions in the ordered aeschynite-type structure.

We study the conditions for spontaneously generating an excitonic mass gap due to Coulomb interactions between anisotropic Dirac fermions in uniaxially strained graphene. The mass gap equation is realized as a self-consistent solution for the self-energy within the Hartree-Fock mean-field and static random phase approximations. It depends not only on momentum, due to the long-range nature of the interaction, but also on the velocity anisotropy caused by the presence of uniaxial strain. We solve the nonlinear integral equation self-consistently by performing large scale numerical calculations on variable grid sizes. We evaluate the mass gap at the charge neutrality (Dirac) point as a function of the dimensionless coupling constant and anisotropy parameter. We also obtain the phase diagram of the critical coupling, at which the gap becomes finite, against velocity anisotropy. Our numerical study indicates that with an increase in uniaxial strain in graphene the strength of critical coupling decreases, which suggests anisotropy supports formation of excitonic mass gap in graphene.

We analyze the Hilbert space and ground state structure of bilayer quantum Hall (BLQH) systems at fractional filling factors $\nu =2/\lambda$ ($\lambda$ odd) and we also study the large $SU\left(4\right)$ isospin-$\lambda$ limit. The model Hamiltonian is an adaptation of the $\nu =2$ case [Z. F. Ezawa et al., Phys. Rev. B 71, 125318 (2005)] to the many-body situation (arbitrary $\lambda$ flux quanta per electron). The semiclassical regime and quantum phase diagram (in terms of layer distance, Zeeman, tunneling, etc., control parameters) is obtained by using previously introduced Grassmannian ${\mathbb{G}}_2^4=U\left(4\right)/[U\left(2\right)\times U\left(2\right)]$ coherent states as variational states. The existence of three quantum phases (spin, canted and ppin) is common to any $\lambda$, but the phase transition points depend on $\lambda$, and the instance $\lambda =1$ is recovered as a particular case. We also analyze the quantum case through a numerical diagonalization of the Hamiltonian and compare with the mean-field results, which give a good approximation in the spin and ppin phases but not in the canted phase, where we detect exactly $\lambda$ energy level crossings between the ground and first excited state for given values of the tunneling gap. An energy band structure at low and high interlayer tunneling (spin and ppin phases, respectively) also appears depending on angular momentum and layer population imbalance quantum numbers.

In this work, we present a theoretical study of polaron states in a double-quantum-dot system. We present realistic calculations which combine 8-band $\mathit{k}·\mathit{p}$ model, configuration-interaction approach, and collective-modes method. We investigate the dependence of polaron energy branches on axial electric field. We show that coupling between carriers and longitudinal optical phonons via Fröhlich interaction leads to qualitative and quantitative reconstruction of the optical spectra. In particular, we study the structure of resonances between the states localized in different dots. We show that $p$-shell states are strongly coupled to the phonon replicas of $s$-shell states, in contrast to the weak direct $s-p$ coupling. We discuss also the dependence of the phonon-assisted tunnel coupling strength on the separation between the dots.

${\mathrm{SmB}}_6$ exhibits a small (15–20 meV) band gap at low temperatures due to hybridized $d$ and $f$ electrons, a tiny (3 meV) transport activation energy $E_A$ above 4 K, and surface states accessible to transport below 2 K. We study its magnetoresistance in 60-T pulsed fields between 1.5 and 4 K. The response of the nearly $T$ independent surface states (which show no Shubnikov–de Haas oscillations) is distinct from that of the activated bulk. $E_A$ shrinks by 50% under fields up to 60 T. Data up to 93 T suggest that this trend continues beyond 100 T, in contrast to previous explanations. It rules out emerging theories to explain observed exotic magnetic quantum oscillations.

We study the electronic properties of GaAs nanowires composed of both the zinc-blende and wurtzite modifications using a ten-band $\mathbf{k}·\mathbf{p}$ model. In the wurtzite phase, two energetically close conduction bands are of importance for the confinement and the energy levels of the electron ground state. These bands form two intersecting potential landscapes for electrons in zinc-blende/wurtzite nanostructures. The energy difference between the two bands depends sensitively on strain, such that even small strains can reverse the energy ordering of the two bands. This reversal may already be induced by the non-negligible lattice mismatch between the two crystal phases in polytype GaAs nanostructures, a fact that was ignored in previous studies of these structures. We present a systematic study of the influence of intrinsic and extrinsic strain on the electron ground state for both purely zinc-blende and wurtzite nanowires as well as for polytype superlattices. The coexistence of the two conduction bands and their opposite strain dependence results in complex electronic and optical properties of GaAs polytype nanostructures. In particular, both the energy and the polarization of the lowest intersubband transition depends on the relative fraction of the two crystal phases in the nanowire.

Substitutional solutes in metals generally diffuse by successive exchanges with vacancies, that is, via the so called vacancy mechanism. However, recent density functional theory (DFT) calculations predicted an atypical behavior for the oversized solute atoms (OSAs) in bcc and fcc iron. These solutes exhibit a very strong attraction with a nearby vacancy (V) at a first neighbor (1nn) distance. The attraction is so large that the 1nn OSA-V pair is no longer stable and relaxes spontaneously towards a new configuration where the OSA sits in the middle of the two half-vacancies (V/2). As a consequence, the diffusion of OSAs cannot be described by the standard vacancy mechanism. A new migration mechanism with a new formulation of correlation effects is required. The present study rests on a revised expression of the diffusion coefficient of the OSAs in bcc and fcc lattices, which introduces the concept of macrojumps. The formalism is applied presently to the case of yttrium (Y: a principal alloying element of advanced steels) in iron, using DFT data. But it is directly transferable to other OSAs in cubic metal lattices. At variance with the standard substitutional solutes, the Y atom is found to diffuse more rapidly than iron at all temperatures by orders of magnitude in the two cubic-Fe structures. This finding is opposite to the recent common belief that yttrium is a slow diffusing species in Fe alloys, based on experimental evidences. Several suggestions are proposed to solve this apparent inconsistency.

We investigate the role of the nuclear-spin quantum dynamics in hyperfine-induced spin relaxation of hopping carriers in organic semiconductors. The fast-hopping regime, when the carrier spin does not rotate much between subsequent hops, is typical for organic semiconductors possessing long spin coherence times. We consider this regime and focus on a carrier random-walk diffusion in one dimension, where the effect of the nuclear-spin dynamics is expected to be the strongest. Exact numerical simulations of spin systems with up to 25 nuclear spins are performed using the Suzuki-Trotter decomposition of the evolution operator. Larger nuclear-spin systems are modeled utilizing the spin-coherent state $P$-representation approach developed earlier. We find that the nuclear-spin dynamics strongly influences the carrier spin relaxation at long times. If the random walk is restricted to a small area, it leads to the quenching of carrier spin polarization at a nonzero value at long times. If the random walk is unrestricted, the carrier spin polarization acquires a long-time tail, decaying as $1/\sqrt{t}$. Based on the numerical results, we devise a simple formula describing the effect quantitatively.

A unified quantum theory of the elastic and inelastic scattering of low energy He atoms by a physisorbed monolayer solid in the one-phonon approximation is given. It uses a time-dependent wave packet with phonon creation and annihilation components and has a self-consistent feedback between the wave functions for elastic and inelastic scattered atoms. An attenuation of diffraction scattering by inelastic processes thus is inherent in the theory. The atomic motion and monolayer vibrations in the harmonic approximation are treated quantum mechanically and unitarity is preserved. The evaluation of specific one-phonon events includes contributions from diffuse inelastic scattering in other phonon modes. Effects of thermally excited phonons are included using a mean field approximation. The theory is applied to an incommensurate Xe/Pt(111) monolayer (incident energy $E_i=4–16$ meV), a commensurate Xe/graphite monolayer ($E_i\simeq 64$ meV), and an incommensurate Xe/Cu(001) monolayer ($E_i\simeq 8$ meV). The monolayers are very corrugated targets and there are transient closed diffraction and inelastic channels in the calculations. In many cases, the energy gain events have strengths comparable to the energy loss events.

Strain engineering plays a critical role in ferroelectric memories. In this work, we demonstrate dynamic strain modulation on tunneling electroresistance in a four-unit-cell ultrathin $\mathrm{BaTi}{\mathrm{O}}_3$ metal/ferroelectric/semiconductor tunnel junction by applying mechanical stress to the device. With an extra compressive strain induced by mechanical stress, which is dynamically applied beyond the lattice mismatch between the $\mathrm{BaTi}{\mathrm{O}}_3$ layer and the $\mathrm{Nb}:\mathrm{SrTi}{\mathrm{O}}_3$ substrate, the ON/OFF current ratio increases significantly up to a record high value of ${10}^7$, whereas a mechanical erasing effect can be observed when a tensile stress is applied. This dynamic strain engineering gives rise to an efficient modulation of ON/OFF ratio due to the variation of $\mathrm{BaTi}{\mathrm{O}}_3$ polarization. This result sheds light on the mechanism of electroresistance in the ferroelectric tunnel junctions by providing direct evidence for polarization-induced resistive switching, and also provides another stimulus for memory state operation.

A series of atomistic finite temperature simulations on a model of an fcc lattice of maghemite nanoparticles using the stochastic Landau-Lifshitz-Gilbert (sLLG) equation are presented. The model exhibits a ferromagnetic transition that is in good agreement with theoretical expectations. The simulations also reveal an orientational disorder in the orientational order parameter for $T<0.5T_c$ due to pinning of the surface domain walls of the nanoparticles by surface vacancies. The extent of the competition between surface pinning and dipolar interactions provides support for the conjecture that recent measurements on systems of fcc superlattices of iron-oxide nanoparticles provide evidence for dipolar ferromagnetism is discussed.

The magnon dispersion of ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$ has been studied by polarized and unpolarized neutron scattering experiments on crystals containing 0, 1, and 10% of Ti. Ti is inserted in order to enable the growth of large, partially detwinned crystals. One percent of Ti has a negligible impact on structural and magnetic properties. Also for 10% Ti content magnetic properties still change very little, but the insulating phase is stabilized up to at least 700 K and structural distortions are reduced. The full dispersion of transverse magnons studied for 1% Ti substitution can be well described by a conventional spin-wave model with interaction and anisotropy parameters that agree with density functional theory calculations. Spin-orbit coupling strongly influences the magnetic excitations, as it is most visible in large energies of the magnetic zone-center modes arising from magnetic anisotropy. Additional modes appear at low energy near the antiferromagnetic zone center and can be explained by a sizable magnetic moment of 0.11 Bohr magnetons, which the density functional theory calculations find located on the apical oxygens. The energy and the signal strength of the additional branch are well described by taking into account this oxygen moment with weak ferromagnetic coupling to the Ru moments.

We investigate the effect of the Dzyaloshinskii-Moriya interaction (DMI) on magnetic domain nucleation in a ferromagnetic thin film with perpendicular magnetic anisotropy. We propose an extended droplet model to determine the nucleation field as a function of the in-plane field. The model can explain the experimentally observed nucleation in a Co/Ni microstrip with an interfacial DMI. The results are also reproduced by micromagnetic simulation based on the string model. The electrical measurement method proposed here can be widely used to quantitatively determine the DMI energy density.

Bilayered $\mathrm{S}{\mathrm{r}}_3\mathrm{R}{\mathrm{u}}_2{\mathrm{O}}_7$ is an unusual metamagnetic metal with inherently antiferromagnetic (AFM) and ferromagnetic (FM) fluctuations. Partial substitution of Ru by Mn results in the establishment of a metal-insulator transition (MIT) at $T_{\mathrm{MIT}}$ and AFM ordering at $T_{\mathrm{M}}$ in $\mathrm{S}{\mathrm{r}}_3{\left(\mathrm{R}{\mathrm{u}}_{1-x}\mathrm{M}{\mathrm{n}}_x\right)}_2{\mathrm{O}}_7$. Using elastic neutron scattering, we investigated the effect of Mn doping on the magnetic structure, in-plane magnetic correlation lengths and their correlation to the MIT in $\mathrm{S}{\mathrm{r}}_3{\left(\mathrm{R}{\mathrm{u}}_{1-x}\mathrm{M}{\mathrm{n}}_x\right)}_2{\mathrm{O}}_7$ ($x=0.06$ and 0.12). With the increase of Mn doping ($x$) from 0.06 to 0.12 or the decrease of temperatures for $x=0.12$, an evolution from an in-plane short-range to long-range antiferromagnetic (AFM) ground state occurs. For both compounds, the magnetic ordering has a double-stripe configuration, and the onset of magnetic correlation with an anisotropic behavior coincides with the sharp rise in electrical resistivity and specific heat. Since it does not induce a measurable lattice distortion, the double-stripe antiferromagnetic order with anisotropic spin texture breaks symmetry from a $C_{4v}$ crystal lattice to a $C_{2v}$ magnetic sublattice. These observations shed light on an age-old question regarding the Slater versus Mott-type MIT.

An optimized interatomic potential has been constructed for silicon using a modified Tersoff model. The potential reproduces a wide range of properties of Si and improves over existing potentials with respect to point defect structures and energies, surface energies and reconstructions, thermal expansion, melting temperature, and other properties. The proposed potential is compared with three other potentials from the literature. The potentials demonstrate reasonable agreement with first-principles binding energies of small Si clusters as well as single-layer and bilayer silicenes. The four potentials are used to evaluate the thermal stability of free-standing silicenes in the form of nanoribbons, nanoflakes, and nanotubes. While single-layer silicene is found to be mechanically stable at zero Kelvin, it is predicted to become unstable and collapse at room temperature. By contrast, the bilayer silicene demonstrates a larger bending rigidity and remains stable at and even above room temperature. The results suggest that bilayer silicene might exist in a free-standing form at ambient conditions.