The spin-1/2 $J_1$-$J_2$ antiferromagnet is a prototypical model for frustrated magnetism and one possible candidate for a realization of a spin-liquid phase. The generalization of this system on the anisotropic square lattice is given by the $J_1$-$J_2$-$J_1^{\prime }$-$J_2^{\prime }$ Heisenberg model, which can be treated by a renormalization group analysis of coupled frustrated chains. The $J_1$-$J_2$-$J_1^{\prime }$-$J_2^{\prime }$-model shows an interesting interplay of Néel order, dimerization, and spin-liquid behavior. Extrapolating the analytical findings supported by numerical results indicates that for the isotropic model the phase at intermediate coupling strength $0.4J_1\lesssim J_2\lesssim 0.6J_1$ is not a spin liquid, but has instead a staggered dimer order.

A detailed study of the one-dimensional ionic Hubbard model with interaction $U$ is presented. We focus on the band insulating (BI) phase and the spontaneously dimerized insulating (SDI) phase which appears on increasing $U$. By a recently introduced continuous unitary transformation [H. Krull et al., Phys. Rev. B 86, 125113 (2012)] we are able to describe the system even close to the phase transition from BI to SDI although the bare perturbative series diverges before the transition is reached. First, the dispersion of single fermionic quasiparticles is determined in the full Brillouin zone. Second, we describe the binding phenomena between two fermionic quasiparticles leading to an $S=0$ and to an $S=1$ exciton. The latter corresponds to the lowest spin excitation and defines the spin gap which remains finite through the transition from BI to SDI. The former becomes soft at the transition, indicating that the SDI corresponds to a condensate of these $S=0$ excitons. This view is confirmed by a BCS mean-field theory for the SDI phase.

Spatial fluctuations of spin-density wave (SDW) and charge-density wave (CDW) in chromium have been compared by combining coherent and simultaneous x-ray diffraction experiments. Despite their close relationship, spatial fluctuations of the spin and of the charge-density waves display a very different behavior: the satellite reflection associated to the charge density displays speckles while the spin one displays an impressive long-range order. This observation is hardly compatible with the commonly accepted magneto-elastic origin of CDW in chromium and is more consistent with a purely electronic scenario where CDW is the second harmonic of SDW. A BCS model taking into account a second-order nesting predicts correctly the existence of a CDW and explains why the CDW is more sensitive to punctual defects.

We show that even in the presence of a transverse magnetic field, the eigenstates of an exciton remain invariant to the full lattice translation group. This is expected if the exciton is viewed as a neutral quasiparticle, but not if one views it as a bound electron-hole pair. Single electron and hole wave functions are invariant only to the magnetic translation group, and their momenta are restricted to the magnetic Brillouin zone; the associated folding is the origin of their Hofstadter butterfly spectra. We find that such folding is not necessary for exciton eigenstates, which are characterized by momenta in the full Brillouin zone and thus have higher symmetry than the Hamiltonian. The magnetic field can have a significant effect on the shape of the exciton dispersion, however. While similar effects have been noted in continuous models, we find qualitatively different behavior for Frenkel excitons, whose origin we clarify. We also derive an analytical solution for the Hofstadter butterfly on a square lattice and analyze its dispersion in the full Brillouin zone.

We develop a correlated-electron minimal model for the normal state of charged phenanthrene ions in the solid state, within the reduced space of the two lowest antibonding molecular orbitals of phenanthrene. Our model is general and can be easily extended to study the normal states of other polycyclic aromatic hydrocarbon superconductors. The main difference between our approach and previous correlated-electron theories of phenacenes is that our calculations are exact within the reduced basis space, albeit for finite clusters. The enhanced exchange of electron populations between these molecular orbitals, driven by Coulomb interactions over and above the bandwidth effects, gives a theoretical description of the phenanthrene trianions that is very different from previous predictions. Exact many-body finite cluster calculations show that while the systems with molecular charges of $-$1 and $-$2 are one- and two-band Mott-Hubbard semiconductors, respectively, molecular charge $-$3 gives two nearly $\frac{3}{4}$-filled bands, rather than a completely filled lower band and a $\frac{1}{2}$-filled upper band. The carrier density per active molecular orbital is thus nearly the same in the normal state of the superconducting aromatics and organic charge-transfer solids, and may be the key to understanding unconventional superconductivity in these molecular superconductors.

We report results of first-principles calculations based on the projector augmented wave (PAW) method to explore the structural, thermodynamic, and electronic properties of cubic (3C) and hexagonal (6H, 4H, and 2H) polytypes of II-VI compounds: ZnS, ZnSe, and ZnTe. We find that the different bond stacking in II-VI polytypes remarkably influences the resulting physical properties. Furthermore, the degree of hexagonality is found to be useful to understand both the ground-state properties and the electronic structure of these compounds. The resulting lattice parameters, energetic stability, and characteristic band energies are in good agreement with available experimental data. Trends with hexagonality of the polytype are investigated.

The observation of photocatalytic water splitting on the surface of anatase $\mathrm{Ti}{\mathrm{O}}_2$ crystals has stimulated many investigations of the underlying processes. Nevertheless, a molecular-level understanding of the reaction is not available. This requires knowledge of the crystal facets present, the atomistic structure of the surfaces, and thus the reaction sites involved. In this paper we establish the atomistic structure of two surfaces, vicinal to the low-energy (101) surface. We compute the relative stability and electronic properties of the (514) and (516) surfaces and compare these to the low-index (101), (001), and (100) surfaces. The (516) surface is remarkably stable, and is predicted to contribute significantly to the surface area of a crystallite in equilibrium. We simulate constant current scanning tunneling microscopy images and, by comparing with those measured, we conclude that a surface previously observed in a miscut single crystal is the (516) surface described here. The computed stability of this surface indicates that it will be present in $\mathrm{Ti}{\mathrm{O}}_2$ nanostructures and the relative positions of its band edges suggests that it will play a significant role in the water-$\mathrm{Ti}{\mathrm{O}}_2$ reactions in solar water splitting.

We analyze the Berry phase in III-V semiconductor quantum dots (QDs). We show that the Berry phase is highly sensitive to electric fields arising from the interplay between the Rashba and Dresselhaus spin-orbit (SO) couplings. We report that the accumulated Berry phase can be induced from other available quantum states that differ only by one quantum number of the corresponding spin state. The sign change in the $g$-factor due to the penetration of Bloch wave functions into the barrier materials can be reflected in the Berry phase. We provide characteristics of the Berry phase for three different length scales (spin-orbit length, hybrid orbital length, and orbital radius). We solve the time-dependent Schr$\ddot{\mathrm{o}}$dinger equation by utilizing the Feynman disentangling technique, and we investigate the evolution of spin dynamics during the adiabatic transport of QDs in the two-dimensional plane. Our results can pave the way to building a topological quantum computer in which the Berry phase can be engineered and be manipulated with the application of the spin-orbit couplings through gate-controlled electric fields.

Injection, transmission, and detection of spins in a conducting channel are the basic ingredients of spintronic devices. Long spin lifetimes during transit are an important ingredient in realizing this technology. An attractive platform for this purpose is graphene, which has high mobilities and low spin-orbit coupling. Unfortunately, measured spin lifetimes are orders of magnitude smaller than theoretically expected. A source of spin loss is the resistance mismatch between the ferromagnetic electrodes and graphene. While this has been studied numerically, here we provide a closed form expression for Hanle spin precession which is the standard method of measuring spin lifetimes. This allows for a detailed characterization of the nonlocal spin valve device.

The nature of multiferroic surfaces, more specifically, the energetic, ferroelectric, and noncollinear magnetic properties of $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$ (110) surfaces, is investigated using ab initio (first-principles) calculations based on the fully unconstrained spin-density functional theory. As in the case of other perovskite oxides, the O-terminated surface is found to be energetically favorable. The spontaneous polarization and magnetic moment at the surface rotate in different ways from their counterparts in the bulk, which leads to a unique magnetoelectric response at the surface. The detailed lattice-distortion-mode (symmetry) analysis reveals that the rotation of the ferroelectric polarization results from the additional symmetry breaking due to the surface termination, whereas the rotation of the magnetic moment is predominantly caused by the magnetocrystalline anisotropy. Furthermore, we investigate the effect of epitaxial strain and find that the strain responses of both the polarization and the magnetic moment are markedly enhanced at the surfaces.

Classical molecular dynamics simulations of bicrystalline systems are a commonly used tool for exploring the migration of grain boundaries. Most simulation work to date has focused on measuring the mobility of grain boundaries, assuming it to be an intrinsic property of a boundary of a given geometry. Here we present results from simulations of the migration of a typical high-angle grain boundary that show that the concept of intrinsic mobility fails for defect-free, flat boundaries of the type frequently simulated and that key assumptions often made in analyzing the kinetics of migration do not hold. Our dynamical simulations of grain boundary migration show that the grain boundary velocity is not simply proportional to the driving force for grain boundary motion, as commonly assumed, and shows a strong and complex dependence on the system size. By analyzing the migration mechanism at the larger mesoscale we show that defect-free, flat boundaries must migrate via the homogeneous nucleation and growth of islands of transformed crystal volume on the grain boundary surface. We present a detailed analysis of the kinetics of this process, which only emerges in simulations of large grain boundary areas. An island-based mesoscale mechanism implies an energy barrier for migration that is inversely proportional to the driving force for migration—in the experimental (zero-force) limit such boundaries must be immobile. This calls into question the concept of an intrinsic mobility for defect-free, flat grain boundaries and suggests that mobility of real boundaries at low temperatures is rather a function of their morphology and defect content and at high temperatures is a result of thermal roughening.

Magnetization and sound propagation reveal a number of unusual spontaneous and field-induced transformations in ferrimagnetic ${\mathrm{TmFe}}_5{\mathrm{Al}}_7$ ($T_{\mathrm{C}}$ = 193 K). The rare-earth sublattice was found to provide a uniaxial magnetic anisotropy, whereas the iron sublattice favors an easy-plane anisotropy. A competition between them results in a first-order spin-reorientation transition at 64 K as the magnetic moments rotate from the $c$ axis to the basal plane of a tetragonal structure. The transition is preceded by a first-order magnetization process of type II along the hard axis. Remarkably, the intersublattice Tm-Fe exchange interaction is weakened at the spin-reorientation transition. Concomitantly, the spontaneous magnetic moment disappears, and the ferrimagnetic state changes to antiferromagnetic. With increasing temperature, the strength of the Tm-Fe exchange is recovered, and the ferrimagnetism is restored at 82 K through another first-order phase transformation. Below 40 K, a first-order field-induced transition occurs for a magnetic field applied along the easy [001] axis. It reflects a rotation of the magnetic moments towards the forced ferromagnetic state observed above 30 T. Along the hard [100] axis the ferromagnetic saturation is not reached even at 60 T.

The nucleation of a dislocation loop for basal and prismatic slips of a magnesium single crystal was studied via atomistic simulations. The metadynamics method was applied in order to overcome the time-scale restrictions that occur in conventional molecular dynamics simulations. The activation free energy of a dislocation loop nucleation is also evaluated via the metadynamics method. In particular, from the temperature dependence, we showed that a linear relationship between the enthalpic and entropic contributions to the activation free energy is satisfied. We found that the difference between the dependence of the activation free energy on the temperature for basal and prismatic slips is related to the structure of the $\Gamma$ surface.

We study dispersions of Fermi arcs in the Weyl semimetal phase by constructing an effective model. We calculate how the surface Fermi-arc dispersions for the top and bottom surfaces merge into the bulk Dirac cones in the Weyl semimetal at both ends of the arcs, and show that they have opposite velocities. This result is common to general Weyl semimetals, and is also confirmed by a calculation using a tight-binding model. Furthermore, by changing a parameter in the system while preserving time-reversal symmetry, we show that two Fermi arcs evolve into a surface Dirac cone when the system transits from the Weyl semimetal to the topological insulator phase. We also demonstrate that choices of surface terminations affect the pairing of Weyl nodes, from which the Fermi arcs are formed.

We investigate, within the envelope function approximation, the low-energy states of trions in graphene quantum dots (QDs). The presence of valley pseudospin in graphene as an electron degree of freedom apart from spin adds convolution to the interplay between exchange symmetry and the electron-electron interaction in the trion, leading to new states of trions as well as a low-energy trion spectrum different from those in semiconductors. Due to the involvement of valley pseudospin, it is found that the low-energy spectrum is nearly degenerate and consists of states all characterized by having an antisymmetric (pseudospin) $\otimes$ (spin) component in the wave function, with the spin (pseudospin) part being either singlet (triplet) or triplet (singlet), as opposed to the spectrum in a semiconductor whose ground state is known to be nondegenerate and always a spin singlet in the case of $X^{-}$ trions. We investigate trions in the various regimes determined by the competition between quantum confinement and electron-electron interaction, both analytically and numerically. The numerical work is performed within a variational method accounting for electron mass discontinuity across the QD edge. The result for electron-hole correlation in the trion is presented. Effects of varying quantum dot size and confinement potential strength on the trion binding energy are discussed. The “relativistic effect” on the trion due to the unique relativistic type electron energy dispersion in graphene is also examined.

The formation of self-assembled nanoislands is an important and much-studied feature of strained layer epitaxial growth. The varied island shapes such as pyramids, hut clusters, and elongated nanowires are considered promising building blocks for nanodevice applications. However, even some basic aspects of their growth and energetics are not fully understood. In particular, for Ge on Si (001), it has been recently proposed that the low surface energy of $\left\{105\right\}$ facets renders the (001) surface unstable even neglecting bulk strain energy. Here we calculate how the competition between strain, surface energies, and edge energies determines the equilibrium shapes of epitaxial islands. In particular, we examine the novel regimes that can arise when the (001) surface becomes unstable against faceting. Our calculations thus provide an overview of the equilibrium island shapes as a natural starting point for consideration of possible kinetic effects.

The dielectric response of two-dimensional (2D) ${\mathrm{Ti}}_3{\mathrm{C}}_2$ stacked sheets was investigated by high-resolution transmission electron energy-loss spectroscopy and ab initio calculations in the 0.2–30-eV energy range. Intense surface plasmons (SPs), evidenced at the nanometer scale at energies as low as 0.3 eV, are shown to be the dominant screening process up to at least 45-nm-thick stacks. This domination results from a combination of efficient free-electron dynamics, begrenzungs effect, and reduced interband damping. It is shown that, in principle, the SPs energies can be tuned in the mid-infrared, from 0.2 to 0.7 eV, by controlling the sheets' functionalization and/or thickness. This point evidences a new attribute of this new class of 2D materials.

Symmetry plays an important role in physics providing a means of classification and a route to understanding. Here we show that an apparently unsymmetrical structure, in our example an ellipse/spheroid, has a more symmetrical partner with an identical spectrum and through which its electromagnetic properties can be classified and calculated analytically. We use the powerful tool of transformation optics to establish this relationship which has wide application beyond the simple example we give in this paper.

We explore the field-induced magnetic phases of an $S=1$ $XXZ$ model with single-ion anisotropy and large Ising-like anisotropy on a Shastry-Sutherland lattice over a wide range of Hamiltonian parameters and applied magnetic field. The multitude of ground-state phases are characterized in detail in terms of their thermodynamic properties, and the underlying classical (Ising limit) spin arrangements for the plateau phases are identified by calculating the static structure factors. The enlarged local Hilbert space of the $S=1$ spins results in several ground state phases that are not realized for $S=1/2$ spins. These include the quantum paramagnetic state that is ubiquitous to $S=1$ spins with single-ion anisotropy, two different spin supersolid phases (with distinct longitudinal ordering), and a magnetization plateau that arises as a direct descendant of the 1/3 plateau due to quantum fluctuations that are not possible for $S=1/2$ spins. We predict the same mechanism will lead to plateaus at smaller fractions of 1/3 for higher spins. The full momentum dependence of the longitudinal and transverse components of the static structure factor is calculated in the spin supersolid phase to demonstrate the simultaneous existence of diagonal and off-diagonal long-range order as well as the different longitudinal orderings.