We study the newly discovered Pt phosphides $A$Pt${}_3$P ($A=\text{Sr}$, Ca, La) [T. Takayama et al., Phys. Rev. Lett. 108, 237001 (2012)] using first-principles calculations and Migdal-Eliashberg theory. Given the remarkable agreement with the experiment, we exclude the charge-density wave scenario proposed by previous first-principles calculations, and give conclusive answers concerning the superconducting state in these materials. The pairing increases from La to Ca and Sr due to changes in the electron-phonon matrix elements and low-frequency phonons. Although we find that all three compounds are well described by conventional $s$-wave superconductivity and spin-orbit coupling of Pt plays a marginal role, we show that it could be possible to tune the structure from centrosymmetric to noncentrosymmetric opening new perspectives towards the understanding of unconventional superconductivity.

The theoretical understanding of the spin-orbit coupling (SOC) effects at LaAlO${}_3$/SrTiO${}_3$ interfaces and SrTiO${}_3$ surfaces is still in its infancy. We perform first-principles density-functional-theory calculations and derive from these a simple tight-binding Hamiltonian, through a Wannier function projection and group theoretical analysis. We find striking differences to the standard Rashba theory for spin-orbit coupling in semiconductor heterostructures due to multiorbital effects: By far the biggest SOC effect is at the crossing point of the $xy$ and $yz$ (or $zx$) orbitals, and around the $\Gamma$ point a Rashba spin splitting with a cubic dependence on the wave vector $\vec{k}$ is possible.

We study the quantized topological terms in a weak-coupling gauge theory with gauge group $G_g$ and a global symmetry $G_s$ in $d$ space-time dimensions. We show that the quantized topological terms are classified by a pair $(G,{\nu }_d)$, where $G$ is an extension of $G_s$ by $G_g$ and ${\nu }_d$ an element in group cohomology ${\mathcal{H}}^d(G,\mathbb{R}/\mathbb{Z})$. When $d=3$ and/or when $G_g$ is finite, the weak-coupling gauge theories with quantized topological terms describe gapped symmetry enriched topological (SET) phases (i.e., gapped long-range-entangled phases with symmetry). Thus, those SET phases are classified by ${\mathcal{H}}^d(G,\mathbb{R}/\mathbb{Z})$, where $G/G_g=G_s$. We also apply our theory to a simple case $G_s=G_g=Z_2$, which leads to 12 different SET phases in $2+1$ dimensions [(2+1)D], where quasiparticles have different patterns of fractional $G_s=Z_2$ quantum numbers and fractional statistics. If the weak-coupling gauge theories are gapless, then the different quantized topological terms may describe different gapless phases of the gauge theories with a symmetry $G_s$, which may lead to different fractionalizations of $G_s$ quantum numbers and different fractional statistics [if in ($2+1$)D].

We consider the problem of relaxation in a one-dimensional system of interacting electrons. In the limit of weak interactions, we calculate the decay rate of a single-electron excitation, accounting for the nonlinear dispersion. The leading processes that determine the relaxation involve scattering of three particles. We elucidate how particular forms of Coulomb interaction, unscreened and screened, lead to different results for the decay rates and identify the dominant scattering processes responsible for relaxation of excitations of different energies. Interestingly, temperatures much smaller than the excitation energy strongly affect the rate. At higher temperatures the quasiparticle relaxes by exciting copropagating electron-hole pairs, whereas at lowest temperatures the relaxation proceeds via excitations of both copropagating and counterpropagating pairs.

We report on a topological insulating state in a heavy-fermion system away from half filling, which is hidden within a ferromagnetic metallic phase. In this phase, the cooperation of the RKKY interaction and the Kondo effect, together with the spin-orbit coupling, induces a spin-selective gap, bringing about topologically nontrivial properties. This topological phase is robust against a change in the chemical potential in a much wider range than the gap size. We analyze these remarkable properties by using dynamical mean field theory and the numerical renormalization group. Its topological properties support a gapless chiral edge mode, which exhibits a non-Tomonaga-Luttinger liquid behavior due to the coupling with bulk ferromagnetic spin fluctuations. We also propose that the effects of the spin fluctuations on the edge mode can be detected via the NMR relaxation time measurement.

Optical gyrotropy, the lifting of degeneracy between left and right circularly polarized light, can be generated by either time-reversal or chiral symmetry breaking. In the high-$T_c$ superconductor La${}_{2-x}$Ba${}_x$CuO${}_4$ (LBCO), gyrotropy onsets at the same temperature as charge stripe order, suggesting that the rotation of the stripe direction from one plane to the next generates a helical pattern that breaks chiral symmetry. In order to further test this chiral stacking hypothesis it is necessary to develop an understanding of the physical mechanisms by which chirality generates gyrotropy. In this paper we show that, in chiral metals, optical gyrotropy is a consequence of Berry curvature in momentum space. We describe a physical picture showing that gyrotropy in chiral metals is closely related to the anomalous Hall effect in itinerant ferromagnets. We then calculate the magnitude of the gyrotropic response for a given Berry curvature using the semiclassical picture of anomalous velocity and Boltzmann transport theory. To connect this physical picture with experiment, we calculate the Berry curvature in two tight-binding models. The first model is motivated by the structure of LBCO and illustrates how gyrotropy is created when stripe perturbations are added to a simple cubic model. In the second model, we examine the dramatic enhancement of the gyrotropic coefficient when Rashba spin-orbit coupling is introduced. The magnitude of the rotation of polarization on reflection expected based on these models is calculated and compared with experimental data.

A combined experimental and theoretical study on the incorporation of Mn in GaAs has been presented. We have successfully controlled the location of Mn atoms at GaAs(001) surfaces by changing the surface atomic geometry. While Mn atoms prefer to substitute Ga sites at a subsurface layer under the As-rich conditions, the incorporation into interstitial sites becomes more favorable as the surface As coverage is decreased. The present results provide a mechanism for the enhanced incorporation of substitutional Mn atoms in GaMnAs under low-temperature (i.e., As-rich) growth conditions.

Typical Raman spectra of transition-metal dichalcogenides (TMDs) display two prominent peaks, $E_{2g}$ and $A_{1g}$, that are well separated from each other. We find that these modes are degenerate in bulk WSe${}_2$ yielding one single Raman peak in contrast to other TMDs. As the dimensionality is lowered, the observed peak splits in two. In contrast, our ab initio calculations predict that the degeneracy is retained even for WSe${}_2$ monolayers. Interestingly, for minuscule biaxial strain, the degeneracy is preserved, but once the crystal symmetry is broken by a small uniaxial strain, the degeneracy is lifted. Our calculated phonon dispersion for uniaxially strained WSe${}_2$ shows a good match to the measured Raman spectrum, which suggests that uniaxial strain exists in WSe${}_2$ flakes, possibly induced during the sample preparation and/or as a result of the interaction between WSe${}_2$ and the substrate. Furthermore, we find that WSe${}_2$ undergoes an indirect-to-direct band-gap transition from bulk to monolayers, which is ubiquitous for semiconducting TMDs. These results not only allow us to understand the vibrational and electronic properties of WSe${}_2$, but also point to effects of the interaction between the monolayer TMDs and the substrate on the vibrational and electronic properties.

Thermal properties in the metal/graphene (Gr) systems are analyzed by using an atomistic phonon transport model based on Landauer formalism and first-principles calculations. The specific structures under investigation include chemisorbed Ni(111)/Gr, physisorbed Cu(111)/Gr and Au(111)/Gr, as well as Pd(111)/Gr with intermediate characteristics. Calculated results illustrate a strong dependence of thermal transfer on the details of interfacial microstructures. In particular, it is shown that the chemisorbed case provides a generally smaller interfacial thermal resistance than the physisorbed one due to the stronger bonding. However, our calculation also indicates that the weakly chemisorbed interface of Pd/Gr may be an exception, with the largest thermal resistance among the considered. Further examination of the electrostatic potential and interatomic force constants reveals that the mixed bonding force between the Pd and C atoms results in incomplete hybridization of Pd and graphene orbital states at the junction, leading effectively to two phonon interfaces and a larger than expected thermal resistance. Comparison with available experimental data shows good agreement. The result clearly suggests the feasibility of phonon engineering for thermal property optimization at the interface.

We analyze the thermal fluctuations of a narrow graphene nanoribbon. Using a continuum membranelike model in the harmonic approximation, we study the height-height correlation functions and the destabilization modes corresponding to two different boundary conditions: fixed and free edges. For the first case, the thermal spectrum has a gap and the correlations along the ribbon decay exponentially. Thermal fluctuations produce only local perturbations of the flat situation. However, the long range crystalline order is not distorted. For free edges the situation changes as thermal excitations are gapless. The low energy spectrum decouples into a bulk and an edge excitation. The bulk excitation tends to destabilize the crystalline order producing a homogeneous rippling. Furthermore, we can relate the edge mode to a precluding perturbation leading to scrolled edges, as seen in suspended graphene samples. We also analyze the implications of our results in the thermal conductivity of graphene nanoribbons.

The phase transformations under pressure at 296 K in solid H${}_2$ and D${}_2$ are carefully investigated here up to 290 GPa by combining infrared (IR) and Raman spectroscopy measurements. Two phase transitions, previously detected by Raman studies, are clearly measured at the same pressures for both isotopes. The transition I-III is observed at 215 GPa characterized by a vibron Raman frequency discontinuity and the appearance of a strong IR vibron. At 237 GPa, the III-IV transition is observed associated to a large vibron Raman frequency discontinuity and the appearance of two IR and two Raman vibron modes. There is no sign of free charge carriers in the long-wavelength infrared absorption region, even up to 290 GPa. Hydrogen is thus not entering a metal nor a semimetal state in phase IV. The Raman and IR vibron spectra in phase IV seems to support the alternating layers structural models. However, the comparison for the IR and Raman vibron frequencies between present data and calculations indicates that a graphenelike sheet order is overestimating the coupling between H${}_2$ molecules.

We study the three-dimensional $SU\left(2\right)$-symmetric noncompact ${\text{CP}}^1$ model, with two charged matter fields coupled minimally to a noncompact Abelian gauge field. The phase diagram and the nature of the phase transitions in this model have attracted much interest after it was proposed to describe an unusual continuous transition associated with deconfinement of spinons. Previously, it has been demonstrated for various two-component gauge theories that weakly first-order transitions may appear as continuous ones of a new universality class in simulations of relatively large, but finite systems. We have performed Monte Carlo calculations on substantially larger systems sizes than those in previous works. We find that in some area of the phase diagram where at finite sizes one gets signatures consistent with a single first-order transition; in fact, there is a sequence of two phase transitions with an $O\left(3\right)$ paired phase sandwiched in between. We report (i) a new estimate for the location of a bicritical point and (ii) the first resolution of bimodal distributions in energy histograms at relatively low coupling strengths. We perform a flowgram analysis of the direct transition line with rescaling of the linear system size in order to obtain a data collapse. The data collapses up to coupling constants where we find bimodal distributions in energy histograms.

We investigate the magnetic properties of a range of low-dimensional ferromagnets using a combination of first-principles calculations and atomistic spin dynamics simulations. This approach allows us to evaluate the ground state and finite temperature properties of experimentally well characterized systems such as Co/Cu(111), Co/Cu(001), Fe/Cu(001) and Fe/W(110), for different thicknesses of the magnetic layer. We compare our calculated spin wave spectra with experimental data available in the literature, and find a good quantitative agreement. We also predict magnon spectra for systems for which no experimental data exist at the moment, and estimate the role of temperature effects.

An analytical and numerical approach is developed to pinpoint the optimal experimental conditions to irreversibly switch magnetization using surface acoustic waves (SAWs). The layers are magnetized perpendicular to the plane and two switching mechanisms are considered. In precessional switching, a small in-plane field initially tilts the magnetization and the passage of the SAW modifies the magnetic anisotropy parameters through inverse magnetostriction. The SAW triggers precession and, eventually, reversal. Using the micromagnetic parameters of a fully characterized layer of the magnetic semiconductor (Ga,Mn)(As,P), we show that there is a large window of accessible experimental conditions (SAW amplitude/wave-vector, field amplitude/orientation) allowing irreversible switching. As this is a resonant process, the influence of the detuning of the SAW frequency to the magnetic system's eigenfrequency is also explored. Finally, another—nonresonant—switching mechanism is briefly contemplated and found to be applicable to (Ga,Mn)(As,P): SAW-assisted domain nucleation. In this case, a small perpendicular field is applied opposite the initial magnetization and the passage of the SAW lowers the domain nucleation barrier.

MnWO${}_4$ is regarded as a canonical example of multiferroic materials, where the multiferroic activity is caused by a spin-spiral alignment. We argue that, in reality, MnWO${}_4$ has two sources of the spin spirality, which conflict with each other. One source is the Dzyaloshinskii-Moriya (DM) interactions, reflecting the $P2/c$ symmetry of the lattice. The $P2/c$ structure of MnWO${}_4$ has an inversion center that connects two Mn sublattices. Therefore, from the viewpoint of DM interactions, different Mn sublattices are expected to have opposite spin chirality. Another source is competing isotropic exchange interactions, which tend to form a spin-spiral texture with the same chirality in both magnetic sublattices. Thus there is a conflict between DM and isotropic exchange interactions, which makes these two sublattices inequivalent and, therefore, breaks the inversion symmetry. Our theoretical analysis is based on the low-energy model, derived from first-principles electronic structure calculations.

The topological properties of a certain class of spinless three-band Hamiltonians are shown to be summed up by the skyrmion number in momentum space, analogous to the case of a two-band Hamiltonian. A topological tight-binding Hamiltonian on a kagome lattice is analyzed from this viewpoint. When such a Hamiltonian is “folded,” the two bands with opposite Chern numbers merge into a degenerate band exhibiting a non-Abelian gauge connection. A conserved pseudospin current operator can be constructed in this case and used to compute the pseudospin Hall conductance.

We report a theoretical study of spin-wave excitations and electron spin resonance (ESR) in a perpendicular magnetic field in $n$-type narrow-gap quantum well (QW) heterostructures. Using the Hartree-Fock approximation, based on the 8 $\times$ 8 k$·$p Hamiltonian, the many-body corrections to the ESR energy are found to be nonzero in symmetric and asymmetric QWs. We demonstrate a significant enhancement of the ESR energy in the asymmetric QWs, induced by the Bychkov-Rashba spin splitting and exchange interaction in weak and moderate magnetic fields, as well as the exchange-induced divergence of the ESR $g$ factor in the symmetric QWs in weak magnetic fields. We calculate the spin-wave dispersions at odd-valued filling factors of the Landau levels for different values of 2D electron concentration in the symmetric and asymmetric InAs/AlSb QW heterostructures. We predict a gap for the long wavelength spin-wave excitations in symmetric and asymmetric narrow-gap QWs induced by the spin-orbit interaction and subband nonparabolicity. The many-body renormalization of electron spin resonance energies in HgTe/CdHgTe QWs is also qualitatively discussed.

Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry $G$. They can all be smoothly connected to the same trivial product state if we break the symmetry. The Haldane phase of spin-1 chain is the first example of SPT phases which is protected by $\mathit{SO}\left(3\right)$ spin rotation symmetry. The topological insulator is another example of SPT phases which are protected by $U\left(1\right)$ and time-reversal symmetries. In this paper, we show that interacting bosonic SPT phases can be systematically described by group cohomology theory: Distinct $d$-dimensional bosonic SPT phases with on-site symmetry $G$ (which may contain antiunitary time-reversal symmetry) can be labeled by the elements in ${\mathcal{H}}^{1+d}[G,U_T\left(1\right)]$, the Borel $(1+d)$-group-cohomology classes of $G$ over the $G$ module $U_T\left(1\right)$. Our theory, which leads to explicit ground-state wave functions and commuting projector Hamiltonians, is based on a new type of topological term that generalizes the topological $\theta$ term in continuous nonlinear $\sigma$ models to lattice nonlinear $\sigma$ models. The boundary excitations of the nontrivial SPT phases are described by lattice nonlinear $\sigma$ models with a nonlocal Lagrangian term that generalizes the Wess-Zumino-Witten term for continuous nonlinear $\sigma$ models. As a result, the symmetry $G$ must be realized as a non-on-site symmetry for the low-energy boundary excitations, and those boundary states must be gapless or degenerate. As an application of our result, we can use ${\mathcal{H}}^{1+d}[U\left(1\right)⋊Z_2^T,U_T\left(1\right)]$ to obtain interacting bosonic topological insulators (protected by time reversal $Z_2^T$ and boson number conservation), which contain one nontrivial phase in one-dimensional (1D) or 2D and three in 3D. We also obtain interacting bosonic topological superconductors (protected by time-reversal symmetry only), in term of ${\mathcal{H}}^{1+d}[Z_2^T,U_T\left(1\right)]$, which contain one nontrivial phase in odd spatial dimensions and none for even dimensions. Our result is much more general than the above two examples, since it is for any symmetry group. For example, we can use ${\mathcal{H}}^{1+d}[U\left(1\right)\times Z_2^T,U_T\left(1\right)]$ to construct the SPT phases of integer spin systems with time-reversal and $U\left(1\right)$ spin rotation symmetry, which contain three nontrivial SPT phases in 1D, none in 2D, and seven in 3D. Even more generally, we find that the different bosonic symmetry breaking short-range-entangled phases are labeled by the following three mathematical objects: $(G_H,G_{\Psi },{\mathcal{H}}^{1+d}[G_{\Psi },U_T\left(1\right)])$, where $G_H$ is the symmetry group of the Hamiltonian and $G_{\Psi }$ the symmetry group of the ground states.

Recently, a new class of quantum phases of matter—symmetry protected topological states, such as topological insulators—has attracted much attention. In presence of interactions, group cohomology provides a classification of these [Chen et al., Phys. Rev. B 87, 155114 (2013)]. These phases have short-ranged entanglement and no topological order in the bulk. However, when long-range entangled topological order is present, it is much less understood how to classify quantum phases of matter in the presence of global symmetries. Here we present a classification of bosonic gapped quantum phases with or without long-range entanglement in the presence or absence of on-site global symmetries. In $2+1$ dimensions, the quantum phases in the presence of a global symmetry group $SG$, and with topological order described by a finite gauge group $GG$, are classified by the cohomology group $H^3(SG\times GG,U\left(1\right))$. Generally, in $d+1$ dimensions, such quantum phases are classified by $H^{d+1}(SG\times GG,U\left(1\right))$. Although we only partially understand to what extent our classification is complete, we present an exactly solvable local bosonic model, in which the topological order is emergent, for each given class in our classification. When the global symmetry is absent, the topological order in our models is described by the general Dijkgraaf-Witten discrete gauge theories. When the topological order is absent, our models become the exactly solvable models for symmetry protected topological phases [Chen et al., Phys. Rev. B 87, 155114 (2013)]. When both the global symmetry and the topological order are present, our models describe symmetry enriched topological phases. Our classification includes, but goes beyond, the previously discussed projective symmetry group classification. Measurable signatures of these symmetry enriched topological phases and generalizations of our classification are discussed.

We propose design pathways to improve the efficiency of multiple exciton generation in nanoparticle-based solar cells by carrying out ab initio calculations of impact ionization (II) rates in semiconducting nanoparticles (NPs). In NPs with unreconstructed surfaces, quantum confinement has two competing effects: it enhances the effective Coulomb interaction and thus the II rates, but it also blue-shifts the gap, which tends to reduce the II rates. The competition of these effects determines the utility of NP-based solar cells. We report that surface reconstruction of NPs can tip the balance towards the enhancement of II by creating a substantial density of states at lower energies. Our results suggest that manipulating the surfaces of NPs, e.g., by engineering the ligands and embedding structures, may lead to an efficient multiexciton generation within the solar spectrum.