We present here a fully first-principles method for predicting the atomic structure of interfaces. Our method is based on the ab initio random structure searching (AIRSS) approach, applied here to treat two-dimensional defects. The method relies on repeatedly generating random structures in the vicinity of the interface and relaxing them within the framework of density functional theory (DFT). The method is simple, requiring only a small set of parameters that can be easily connected to the chemistry of the system of interest, and efficient, ideally adapted to high-throughput first-principles calculations on modern parallel architectures. Being first-principles, our method is transferable, an important requirement for a generic computational method for the determination of the structure of interfaces. Results for two structurally and chemically very different interfaces are presented here, grain boundaries in graphene and grain boundaries in strontium titanate $\left(\mathrm{SrTiO}{}_3\right)$. We successfully find a previously unknown low energy grain boundary structure for the graphene system, as well as recover the previously known higher energy structures. For the $\mathrm{SrTiO}{}_3$ system we study both stoichiometric and nonstoichiometric compositions near the grain boundary and find previously unknown low energy structures for all stoichiometries. We predict that these low energy structures have long-range distortions to the ground state crystal structure emanating into the bulk from the interface.

We report a combined Raman-scattering and electron spin resonance (ESR) study of the metallic triangular compound $\mathrm{Pd}\mathrm{Cr}{\mathrm{O}}_2$ along with lattice dynamic calculations. Our Raman data reveal (i) an exponential increase of the 706 cm${}^{-1}$ $A_g$ mode involving the out-of-plane motions of the oxygen atoms and (ii) electronic Raman scatterings whose scattering rate is strongly suppressed as the temperature approaches $T_N=37.5$ K. The temperature dependence of the ESR linewidth is described by a critical broadening $\Delta H_{pp}\left(T\right)\propto {(T-T_N)}^{-p}$ with the exponent $p=0.63\pm 0.05$. These are interpreted in terms of coherence of interplane hoppings along the $c$ axis and a reconstruction of electronic bands on approaching $T_N$. Our results suggest a significant role of an interference between metallic and magnetic layers in explaining collective excitations in $\mathrm{Pd}\mathrm{Cr}{\mathrm{O}}_2$.

The discontinuity of guiding-center Hall viscosity (a bulk property) at the edges of incompressible quantum Hall fluids is associated with the presence of an intrinsic electric dipole moment on the edge. If there is a gradient of drift velocity due to a nonuniform electric field, the discontinuity in the induced stress is exactly balanced by the electric force on the dipole. The total Hall viscosity has two distinct contributions: a “trivial” contribution associated with the geometry of the Landau orbits and a nontrivial contribution associated with guiding-center correlations. We describe a relation between the guiding-center edge-dipole moment and “momentum polarization,” which relates the guiding-center part of the bulk Hall viscosity to the “orbital entanglement spectrum (OES).” We observe that using the computationally more-onerous “real-space entanglement spectrum” just adds the trivial Landau-orbit contribution to the guiding-center part. This shows that all the nontrivial information is completely contained in the OES, which also exposes a fundamental topological quantity, $\gamma$ = $\tilde{c}-\nu$, the difference between the “chiral stress-energy anomaly” (or signed conformal anomaly) and the chiral charge anomaly. This quantity characterizes correlated fractional quantum Hall fluids and vanishes in uncorrelated integer quantum Hall fluids.

In order to explore the driving mechanism of the concomitant metal-insulator and structural transitions in quasi-one-dimensional hollandite ${\mathrm{K}}_2{\mathrm{Cr}}_8{\mathrm{O}}_{16}$, electronic structures and phonon properties are investigated by employing the ab initio density functional theory (DFT) calculations. We have found that the imaginary phonon frequency reflecting the structural instability appears only in the DFT + $U$ ($U$: Coulomb correlation) calculation, which indicates that the Coulomb correlation plays an essential role in the structural transition. The lattice displacements of the softened phonon at $X$ explain the observed lattice distortions in ${\mathrm{K}}_2{\mathrm{Cr}}_8{\mathrm{O}}_{16}$ perfectly well, suggesting the Peierls distortion vector Q of $X$ (0, 0, 1/2). The combined study of electronic and phonon properties reveals that half-metallic ${\mathrm{K}}_2{\mathrm{Cr}}_8{\mathrm{O}}_{16}$, upon cooling, undergoes the correlation-assisted Peierls transition to become a Mott-Peierls ferromagnetic insulator at low temperature.

Graphene, with its quantum Hall topological (Chern) number reflecting the massless Dirac particle, is shown to harbor yet another topological quantum number. This is obtained by combining Středa's general formula for the polarization associated with a second topological number in the Diophantine equation for the Hofstadter problem, and the adiabatic continuity, earlier shown to exist between the square and honeycomb lattices by Hatsugai et al. Specifically, the adiabatic continuity enables us to regard graphene as a simulator of square lattice with half flux quantum per unit cell, which implies, with a semiclassical treatment around rational fluxes implemented here, that the polarization topological numbers in graphene in weak magnetic fields is 1/2 per Dirac cone for the energy region between the van Hove singularities. Possible experimental setups for observing this topological numbers in cold atoms are proposed as well.

We study three-electron-spin decoherence in a semiconductor triple quantum dot with a linear geometry. The three electron spins are coupled by exchange interactions $J_{12}$ and $J_{23}$, and we clarify inhomogeneous and homogeneous dephasing dynamics for a logical qubit encoded in the $\left(S=1/2,S^z=1/2\right)$ subspace. We first justify that qubit leakage via the fluctuating Overhauser field can be effectively suppressed by sufficiently large Zeeman and exchange splittings. In both $J_{12}=J_{23}$ and $J_{12}\ne J_{23}$ regimes, we construct an effective pure dephasing Hamiltonian with the Zeeman splitting $E_Z\gg J_{12},J_{23}$. Both effective Hamiltonians have the same order of magnitude as that for a single-spin qubit, and the relevant dephasing time scales ($T_2^{*},T^{\mathrm{FID}}$, etc.) are of the same order as those for a single spin. We provide estimates of the dynamics of three-spin free induction decay, the decay of a Hahn spin echo, and the decay of echoes from a CPMG pulse sequence for GaAs quantum dots.

We have obtained analytical expressions for the $q$-dependent static spin susceptibility of monolayer transition-metal dichalcogenides, considering both the electron-doped and hole-doped cases. Our results are applied to calculate spin-related physical observables of monolayer ${\mathrm{MoS}}_2$, focusing especially on in-plane/out-of-plane anisotropies. We find that the hole-mediated Ruderman-Kittel-Kasuya-Yosida exchange interaction for in-plane impurity-spin components decays with the power law $R^{-5/2}$ as a function of distance $R$, which deviates from the $R^{-2}$ power law normally exhibited by a two-dimensional Fermi liquid. In contrast, the out-of-plane spin response shows the familiar $R^{-2}$ long-range behavior. We also use the spin susceptibility to define a collective $g$ factor for hole-doped ${\mathrm{MoS}}_2$ systems and discuss its density-dependent anisotropy.

Excitation spectra of square lattice Heisenberg antiferromagnets in magnetic fields are investigated by the spin-wave theory. It is pointed out that a rotonlike structure appears in a narrow range of magnetic fields as a result of strong nonlinear effects. It is shown that the energy gap and the mass of the “roton” are quite sensitive to the magnetic field: the roton gap softens rapidly and eventually closes as a precursor of a quantum phase transition. The possibility of the experimental observation of the roton and a new ground state after its softening are discussed.

We have carefully investigated the $\alpha -\epsilon$ transition pathway of iron under quasihydrostatic pressures. For this purpose, combined measurements of extended x-ray absorption fine structure (EXAFS) and x-ray magnetic circular dichroism at the Fe $K$ edge were performed using a helium pressure-transmitting medium. Collapse of the ferromagnetism simultaneously occurs with the $\alpha -\epsilon$ structural transition, which is in contrast to the scenario that the transition is driven by the pressure-induced instability of the ferromagnetism in $\alpha$ phase of iron. We conclude that shear stress is important to initiate the $\alpha -\epsilon$ transition. Our model to fit the EXAFS profile demonstrates that the local atomic arrangement in $\epsilon$ phase is slightly distorted due to unfinished shuffle motion, whereas shear motion finishes at the beginning of the transition.

We study the one-dimensional Dyson hierarchical model in the presence of a random field. This is a long range model where the interaction scales with the distance in a power-law-like form, $J\left(r\right)\sim r^{-\rho }$, and we can explore mean-field and non-mean-field behavior by changing $\rho$. We analyze the model at $T=0$ and we numerically compute the non-mean-field critical exponents for Gaussian disorder. We also compute an analytic expression for the critical exponent $\delta$, and give an interesting relation between the critical exponents of the disordered model and the ones of the pure model, which seems to break down in the non-mean-field region. We finally compare our results for the critical exponents with the expected ones in $D$-dimensional short range models and with the ones of the straightforward one-dimensional long range model.

The temperature and magnetic-field dependence of lattice and carrier excitations in MnSi is studied in detail using inelastic light scattering. The pure symmetry components of the electronic response are derived from the polarization-dependent spectra. The $E$ and $T_2$ responses agree by and large with longitudinal and optical transport data. However, an anomaly is observed right above the magnetic ordering temperature $T_{\mathrm{C}}=29$ K that is associated with the fluctuations that drive the transition into the helimagnetic phase first order. The $T_1$ spectra, reflecting mostly chiral spin excitations, have a temperature dependence similar to that of the $E$ and $T_2$ symmetries. The response in the fully symmetric $A_1$ representation has a considerably weaker temperature dependence than that in the other symmetries. All nine Raman active phonon lines can be resolved at low temperature. The positions and linewidths of the strongest four lines in $E$ and $T_2$ symmetry are analyzed in the temperature range $4<T<310$ K. Above 50 K, the temperature dependence is found to be conventional and given by anharmonic phonon decay and the lattice expansion. Distinct anomalies are observed in the range of the helimagnetic transition and in the ordered phase. Applying a magnetic field of 4 T, well above the critical field, removes all anomalies and restores a conventional behavior highlighting the relationship between the anomalies and magnetism. The anomaly directly above $T_{\mathrm{C}}$ in the fluctuation range goes along with an anomaly in the thermal expansion. While the lattice constant changes continuously and has only a kink at $T_{\mathrm{C}}$, all optical phonons soften abruptly, suggesting a direct microscopic coupling between spin order and optical phonons rather than a reaction to magnetostriction effects.

We study the impact of electron-phonon interactions on the many-body instabilities of electrons on the honeycomb lattice and their interplay with repulsive local and nonlocal Coulomb interactions at charge neutrality. To that end, we consider in-plane optical phonon modes with wave vectors close to the $\Gamma$ point as well as to the $K,-K$ points and calculate the effective phonon-mediated electron-electron interaction by integrating out the phonon modes. Ordering tendencies are studied by means of a momentum-resolved functional renormalization-group approach allowing for an unbiased investigation of the appearing instabilities. In the case of an exclusive and supercritical phonon-mediated interaction, we find a Kekulé and a nematic bond ordering tendency being favored over the $s$-wave superconducting state. The competition between the different phonon-induced orderings clearly shows a repulsive interaction between phonons at small- and large-wave-vector transfers. We further discuss the influence of phonon-mediated interactions on electronically driven instabilities induced by on-site, nearest-neighbor, and next-nearest-neighbor density-density interactions. We find an extension of the parameter regime of the spin-density-wave order going along with an increase of the critical scales where ordering occurs and a suppression of competing orders.

Electron donor conjugated polymers blended with electron acceptor fullerene derivatives is one of the promising technologies for organic photovoltaics. However, with the energy conversion efficiency of only 9% in a single bulk heterojunction device structure, these solar cells are not yet competitive with conventional inorganic semiconductor technology. Some of the limitations are large optical band gaps and small electron affinities of polymers preventing the absorption of infrared radiation and leading to energy losses during charge separation at the donor-acceptor interface, respectively. In this work, we compute from first principles the quasiparticle and optical spectra of several different thiophene-, ethyne-, and vinylene-based copolymers using the $GW$ method and the $GW$ plus Bethe-Salpeter equation approach. One of the polymers is identified which has a preferential alignment of the energy levels at the interface with fullerene molecule compared to the reference case of polythiophene.

The origin of electronic states at the basis of the 2DEG found in conducting $\mathrm{LaAlO}{}_3/\mathrm{SrTiO}{}_3$ interfaces (5 u.c. $\mathrm{LaAlO}{}_3$) is investigated by resonant photoemission experiments at the Ti $L$${}_{2,3}$ and La $M_{4,5}$ edges. As shown by the resonant enhancement at the Ti $L_{2,3}$ edge, electronic states at $E_F$ receive a dominant contribution from Ti $3d$ states. Both Ti and La resonance effects in the valence-band region are used to estimate the valence-band maxima at the two sides of the junction. Through a comparison with the valence-band states of the $\mathrm{LaAlO}{}_3$ and $\mathrm{SrTiO}{}_3$ parent compounds, we reconstruct the band diagram of the heterojunction, which is revealed to be type I (straddling gap), with a large notch of the band profile at the interface as compared with the reference insulating (3 u.c. $\mathrm{LaAlO}{}_3$) interface.

We develop an energy density matrix that parallels the one-body reduced density matrix (1RDM) for many-body quantum systems. Just as the density matrix gives access to the number density and occupation numbers, the energy density matrix yields the energy density and orbital occupation energies. The eigenvectors of the matrix provide a natural orbital partitioning of the energy density while the eigenvalues comprise a single-particle energy spectrum obeying a total energy sum rule. For mean-field systems the energy density matrix recovers the exact spectrum. When correlation becomes important, the occupation energies resemble quasiparticle energies in some respects. We explore the occupation energy spectrum for the finite 3D homogeneous electron gas in the metallic regime and an isolated oxygen atom with ground-state quantum Monte Carlo techniques implemented in the qmcpack simulation code. The occupation energy spectrum for the homogeneous electron gas can be described by an effective mass below the Fermi level. Above the Fermi level evanescent behavior in the occupation energies is observed in similar fashion to the occupation numbers of the 1RDM. A direct comparison with total energy differences shows a quantitative connection between the occupation energies and electron addition and removal energies for the electron gas. For the oxygen atom, the association between the ground-state occupation energies and particle addition and removal energies becomes only qualitative. The energy density matrix provides an avenue for describing energetics with quantum Monte Carlo methods which have traditionally been limited to total energies.

We investigate the formation of self-trapped holes (STH) in three prototypical perovskites (${\mathrm{SrTiO}}_3$, ${\mathrm{BaTiO}}_3$, ${\mathrm{PbTiO}}_3$) using a combination of density functional theory (DFT) calculations with local potentials and hybrid functionals. First we construct a local correction potential for polaronic configurations in ${\mathrm{SrTiO}}_3$ that is applied via the DFT + $U$ method and matches the forces from hybrid calculations. We then use the DFT + $U$ potential to search the configuration space and locate the lowest energy STH configuration. It is demonstrated that both the DFT + $U$ potential and the hybrid functional yield a piecewise linear dependence of the total energy on the occupation of the STH level, suggesting that self-interaction effects have been properly removed. The DFT + $U$ model is found to be transferable to ${\mathrm{BaTiO}}_3$ and ${\mathrm{PbTiO}}_3$, and STH formation energies from DFT + $U$ and hybrid calculations are in close agreement for all three materials. STH formation is found to be energetically favorable in ${\mathrm{SrTiO}}_3$ and ${\mathrm{BaTiO}}_3$ but not in ${\mathrm{PbTiO}}_3$, which can be rationalized by considering the alignment of the valence band edges on an absolute energy scale. In the case of ${\mathrm{PbTiO}}_3$ the strong coupling between Pb $6s$ and O $2p$ states lifts the valence band minimum (VBM) compared to ${\mathrm{SrTiO}}_3$ and ${\mathrm{BaTiO}}_3$. This reduces the separation between VBM and STH level and renders the STH configuration metastable with respect to delocalization (band hole state). We expect that the present approach can be adapted to study STH formation also in oxides with different crystal structures and chemical compositions.

We investigate the effect of electron-phonon interactions on the coherence properties of single photons emitted from a semiconductor cavity QED (quantum electrodynamics) system, i.e., a quantum dot embedded in an optical cavity. The degree of indistinguishability, governing the quantum mechanical interference between two single photons, is calculated as a function of important parameters describing the cavity QED system and the phonon reservoir, e.g., cavity quality factor, light-matter coupling strength, temperature, and phonon lifetime. We show that non-Markovian effects play an important role in determining the coherence properties for typical parameter values and establish the conditions under which a Markovian approximation may be applied. The calculations are performed using a recently developed second-order perturbation theory, and the limits of validity are established by comparing to an exact diagonalization approach. We find that for large cavity decay rates the perturbation theory may break down.

We study the quantum mechanical states of electrons situated on a cylindrical surface of finite axial length to model a semiconductor core-shell nanowire. We calculate the conductance in the presence of a longitudinal magnetic field by weakly coupling the cylinder to semi-infinite leads. Spin effects are accounted for through Zeeman coupling and Rashba spin-orbit interaction (SOI). Emphasis is on manifestations of flux-periodic oscillations and we show how factors such as impurities, contact geometry, and spin affect them. Oscillations survive and remain periodic in the presence of impurities, noncircular contacts, and SOI, while Zeeman splitting results in aperiodicity, beating patterns, and additional background fluctuations. Our results are in qualitative agreement with recent magnetotransport experiments performed on GaAs/InAs core-shell nanowires. Lastly, we propose methods of data analysis for detecting the presence of Rashba SOI in core-shell systems and for estimating the electron $g$ factor in the shell.

${\mathrm{NdO}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$ is a new layered superconductor. We have studied the low-lying electronic structure of the single-crystalline ${\mathrm{NdO}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$ superconductor, whose superconducting transition temperature is 4.83 K, with angle-resolved photoemission spectroscopy. The Fermi surface consists of two small electron pockets around the $X$ point and shows little warping along the $k_z$ direction. Our results demonstrate the multiband and two-dimensional nature of the electronic structure. The comparison between the photoemission data and the band calculations gives the renormalization factor of $\sim$1.14, indicating the rather weak electron correlations in this material. Moreover, we found that the actual electron doping level and Fermi surface size are much smaller than what are expected from the nominal composition, which could be largely explained by the bismuth deficiency. The small Fermi pocket size and the weak electron correlations found here put strong constraints on theory, and suggest that the ${\mathrm{BiS}}_2$-based superconductors could be conventional BCS superconductors mediated by the electron-phonon coupling.

We address the fundamental question how the spatial Kondo correlations are building up in time assuming an initially decoupled impurity spin ${\vec{S}}_{\mathrm{imp}}$. We investigate the time-dependent spin-correlation function $\chi (\vec{r},t)=\langle {\vec{S}}_{\mathrm{imp}}\vec{s}\left(\vec{r}\right)\rangle \left(t\right)$ in the Kondo model with antiferromagnetic and ferromagnetic couplings, where $\vec{s}\left(\vec{r}\right)$ denotes the spin density of the conduction electrons after switching on the Kondo coupling at time $t=0$. We present data obtained from a time-dependent numerical renormalisation group (TD-NRG) calculation. We gauge the accuracy of our two-band NRG by the spatial sum rules of the equilibrium correlation functions and the reproduction of the analytically exactly known spin-correlation function of the decoupled Fermi sea. We find a remarkable building up of Kondo correlation outside of the light cone defined by the Fermi velocity of the host metal. By employing a perturbative approach exact in second-order of the Kondo coupling, we connect these surprising correlations to the intrinsic spin-density entanglement of the Fermi sea. The thermal wavelength supplies a cutoff scale at finite temperatures beyond which correlations are exponentially suppressed. We present data for the frequency dependent retarded spin-spin susceptibility and use the results to calculate the real-time response of a weak perturbation in linear response: within the spatial resolution no response outside of the light cone is found.