Using the coupled series expansion method developed in this paper, we have investigated the quantum behavior of Coulomb impurity states under external electric and magnetic fields in graphene. Under magnetic field, we have obtained an accurate full spectrum of the attractive and repulsive Coulomb impurities for both massless and massive Dirac electrons and have found that bound states can be tuned between in and out of the gap by Coulomb impurities and a magnetic field. When a linear radial electric field in combination with a magnetic field are applied, the energy levels of Coulomb impurity states experience intercrossing, and they disappear because of Klein tunneling as the electric field exceeds the magnetic field. The results are helpful in controlling Coulomb impurity states by external fields in graphene and the method proves to be an efficient way to obtain accurate solutions of the Dirac equation with various fields.

Physical systems representing qubits typically have one or more accessible quantum states in addition to the two states that encode the qubit. We demonstrate that active involvement of such auxiliary states can be beneficial in constructing entangling two-qubit operations. We investigate the general case of two multistate quantum systems coupled via a quantum resonator. The approach is illustrated with the examples of three systems: self-assembled InAs/GaAs quantum dots, NV centers in diamond, and superconducting transmon qubits. Fidelities of the gate operations are calculated based on numerical simulations of each system.

Understanding how foreign chemical species bond to atomic vacancies in graphene layers can advance our ability to tailor the electronic and magnetic properties of defective graphenic materials. Here, we use ultrahigh-vacuum scanning tunneling microscopy (UHV-STM) and density functional theory to identify the precise structure of hydrogenated single atomic vacancies in a topmost graphene layer of graphite and establish a connection between the details of hydrogen passivation and the electronic properties of a single atomic vacancy. Monovacancy-hydrogen complexes are prepared by sputtering of the graphite surface layer with low-energy ions and then exposing it briefly to an atomic hydrogen environment. High-resolution experimental UHV-STM imaging allows us to determine unambiguously the positions of single missing atoms in the defective graphene lattice and, in combination with the ab initio calculations, provides detailed information about the distribution of low-energy electronic states on the periphery of the monovacancy-hydrogen complexes. We found that a single atomic vacancy where each σ dangling bond is passivated with one hydrogen atom shows a well-defined signal from the nonbonding π state, which penetrates into the bulk with a $\sqrt{3}\times \sqrt{3}R{30}^{\circ }$ periodicity. However, a single atomic vacancy with full hydrogen termination of σ dangling bonds and additional hydrogen passivation of the extended π state at one of the vacancy's monohydrogenated carbon atoms is characterized by complete quenching of low-energy localized states. In addition, we discuss the migration of hydrogen atoms at the periphery of the monovacancy-hydrogen complexes, which dramatically change the vacancy's low-energy electronic properties, as observed in our low-bias, high-resolution STM imaging.

The photoinduced phase formation in a strongly correlated crystal $(\mathrm{EDO-TTF}{)}_2{\mathrm{PF}}_6$ (EDO-TTF: 4,5-ethylenedioxytetrathiafulvalene) is investigated using a 12 fs laser pulse. The formation time is determined as 40 fs with observation of coherence of electron-phonon coupled excited states prior to formation. The temperature-independent dephasing time is determined as ∼22 fs up to 180 K and the frequency of phonon oscillation is ∼38 THz, corresponding to the intramolecular vibrations in EDO-TTF. The phase formation is coherently controlled by relative-phase-controlled two-pulse excitation.

We consider quantum quenches in an integrable quantum chain with tuneable-integrability-breaking interactions. In the case where these interactions are weak, we demonstrate that at intermediate times after the quench local observables relax to a prethermalized regime, which can be described by a density matrix that can be viewed as a deformation of a generalized Gibbs ensemble. We present explicit expressions for the approximately conserved charges characterizing this ensemble. We do not find evidence for a crossover from the prethermalized to a thermalized regime on the time scales accessible to us. Increasing the integrability-breaking interactions leads to a behavior that is compatible with eventual thermalization.

We investigate the scaling and spatial distribution of genuine multiparticle entanglement in three- and four-spin reduced states of the one-dimensional $XY$ model at the quantum phase transition. We observe a logarithmic divergence, show that genuine three- and four-particle entanglement obeys finite-size scaling of the $XY$ model and demonstrate that the genuine three-particle entanglement has a finite spatial range.

We show that the magnon-exchange contribution to the single-particle and transport relaxation rates in ferromagnetic metals, which determine the thermal and electrical conductivities, respectively, at asymptotically low temperatures does not obey a power law as previously thought, but rather shows an exponential temperature dependence. The reason is the splitting of the conduction band, which inevitably results from a nonzero magnetization. At higher temperatures, there is a sizable temperature window where the transport rate shows a $T^2$ temperature dependence, in accord with prior results. This window is separated from the asymptotic regime by a temperature scale that is estimated to range from tens of millidegrees of Kelvin to tens of degrees of Kelvin for typical ferromagnets. We motivate and derive a very general effective theory for metallic magnets that we then use to derive these results. Comparisons with existing experiments are discussed, and predictions for future experiments at low temperatures are made.

The structure and equation of state of the crystalline molecular phase II of carbon dioxide have been investigated at room temperature from 15.5 to 57.5 GPa using synchrotron x-ray diffraction methods. The CO${}_2$ samples were embedded in neon pressure medium in order to provide quasihydrostatic conditions. The x-ray diffraction patterns of phase II are best described by a tetragonal structure, with space group $P{4}_2/mnm$ and 2 molecules per unit cell, in accordance with a previous study [Yoo et al., Phys. Rev. B 65, 104103 (2002)]. There is however a large (15%) difference in the intramolecular C=O bond length between the present study, 1.14(3) Å, and the latter work (1.329–1.366 Å). The present value is similar to that of the free molecule and is in very good agreement with predictions based on density functional theory. The compressibility of CO${}_2$-II determined here also disagrees with the previous study: our value for the zero-pressure bulk modulus, $B_0=8.5\left(3\right)$ GPa [with $B_0^{\prime }={(\partial B/\partial P)}_0=6.29$], is 15.5 times smaller. These findings oppose the view that CO${}_2$-II is an intermediate state between the low-pressure molecular phases and the high-pressure nonmolecular forms, consistent with our previous results for phase IV [Datchi et al., Phys. Rev. Lett. 103, 185701 (2009)]. The x-ray diffraction patterns of CO${}_2$-II above 15 GPa indicate the presence of a large orthorhombic microstrain. Carrying out density functional theory calculations of the elastic tensor and stress-strain relation, we interpret this as due to the softness of the crystal against deviatoric stress in the [110] and symmetry-related directions. Unlike the other dioxides of the group-14 elements, there is however no mechanical or dynamical instability of the $P{4}_2/mnm$ structure in CO${}_2$ up to 57.5 GPa at 295 K, and therefore no symmetry lowering to $Pnnm$.

Full density functional theory calculations successfully demonstrate that a remarkable spontaneous polarization can stably exist in extremely thin ${\mathrm{PbTiO}}_3$ single-wall nanotubes (PTO-SWNTs) folded from (110) nanosheets with a specific chirality of ($m$, 0), whereas ferroelectricity is absent from nanotubes with other chiralities and from the unfolded thin films. In other words, there is chiral selectivity of ferroelectricity. The chirality of the ferroelectric (FE) nanotubes plays a variety of significant roles in (i) the stabilization of a low-energy single-wall tubular structure, (ii) the emergence of antiferrodistortive (AFD) distortion hidden in the ${\mathrm{PbTiO}}_3$ bulk, and (iii) the strong coupling between FE and emergent AFD distortions. The direct FE-AFD coupling stabilizes the remarkable FE distortion in these ultrathin nanotubes through tilting of oxygen octahedra, suggesting improper ferroelectricity. The existence of a large spontaneous polarization suggests that PTO-SWNTs hold promise for applications in advanced sensors and nanoscale energy-harvesting devices.

We have analyzed by density functional theory calculations the structural and magnetic properties of Fe-Co alloys doped by carbon. In analogy with the formation of martensite in steels we predict that such a structure also forms for Fe-Co alloys in a wide range of concentrations. These alloys are predicted to have a stable tetragonal distortion, which in turn leads to an enhanced magnetocrystalline anisotropy energy of up to 0.75 MJ/m${}^3$ and a saturated magnetization field of 1.9 T.

We have studied in detail the electronic structure of IrO${}_2$ including spin orbit coupling (SOC) and electron-electron interaction, both within the generalized gradient approximation plus Hubbard $U$ (GGA+U) and GGA plus dynamical mean field theory (GGA+DMFT) approximations. Our calculations reveal that the Ir $t_{2g}$ states at the Fermi level largely retain the $J_{\mathrm{eff}}=\frac{1}{2}$ character, suggesting that this complex spin orbit entangled state may be robust even in metallic IrO${}_2$. We have calculated the phase diagram for the ground state of IrO${}_2$ as a function of $U$ and find a metal insulator transition that coincides with a magnetic phase change, where the effect of SOC is only to reduce the critical values of $U$ necessary for the transition. We also find that dynamic correlations, as given by the GGA+DMFT calculations, tend to suppress the spin-splitting, yielding a Pauli paramagnetic metal for moderate values of the Hubbard $U$. Our calculated optical spectra and photoemission spectra including SOC are in good agreement with experiment, demonstrating the importance of SOC in IrO${}_2$.

The Wigner-crystal phase of two-dimensional electrons interacting via the Coulomb repulsion and subject to a strong Rashba spin-orbit coupling is investigated. For low enough electronic densities the spin-orbit band splitting can be larger than the zero-point energy of the lattice vibrations. Then the degeneracy of the lower subband results in a spontaneous symmetry breaking of the vibrational ground state. The ${60}^{\circ }$ rotational symmetry of the triangular (spin-orbit coupling free) structure is lost, and the unit cell of the new lattice contains two electrons. Breaking the rotational symmetry also leads to a (slight) squeezing of the underlying triangular lattice.

The biexciton resonance in the absorption spectra of semiconductor quantum wells is analyzed with quantum-optical spectroscopy by projecting experimental pump-probe measurements into quantum-optical absorption spectra. More specifically, the measurements are converted into phase-space distributions using the cluster-expansion transformation. The quantum-optical responses can then be projected with full convergence, despite the unavoidable experimental noise. The calculations show that classical and quantum excitations produce significantly different results for the biexciton resonance. In particular, quantum-optical spectroscopy monitors the excitation-induced broadening of the biexciton resonance as a function of pump intensity much more sensitively than classical spectroscopy does.

The space and time dependent nonequilibrium Keldysh-Green functions are employed to derive the scattering rates between the condensed microcavity polaritons described by a Gross-Pitaevskii equation and an uncondensed higher lying exciton reservoir. Slowly varying center coordinates and rapidly varying relative coordinates are assumed. For particle-particle and particle-phonon interactions the scattering rates which provide gain to the condensate are calculated explicitly. These processes result in scattering rates which are quadratic and linear in the density of reservoir excitons, respectively. The resulting quantum Boltzmann equation for the reservoir is simplified by assuming local thermal equilibrium to rate equations for the exciton density and their temperature. Using the microscopically calculated (not phenomenologically chosen) transition amplitudes for CdTe microcavity polaritons we demonstrate that our model is able to describe the spontaneous pattern formation for a ring-shaped nonresonant excitation as seen in recent experiments

A general approach is derived for constructing an effective spin-orbit Hamiltonian for nonmagnetic materials, which is useful for calculating spin-dependent properties near an arbitrary point in momentum space with pseudospin degeneracy. The formalism is verified through comparisons with other approaches for III-V semiconductors, and its general applicability is illustrated by deriving the spin-orbit interaction and predicting spin lifetimes for strained ${\mathrm{SrTiO}}_3$ and a two-dimensional electron gas in ${\mathrm{SrTiO}}_3$ (such as at the LaAlO${}_3$/${\mathrm{SrTiO}}_3$ interface). These results suggest robust spin coherence and spin transport properties in ${\mathrm{SrTiO}}_3$-based materials at room temperature.

We report peculiar transport fingerprints at the secondary Dirac points created by the interaction between graphene and boron nitride layers. By performing ab initio calculations, the electronic characteristics of the moiré patterns produced by the interaction between layers are first shown to be in good agreement with experimental data, and further used to calibrate the tight-binding model implemented for the transport study. By means of a real-space order-N quantum transport (Kubo) methodology, low-energy (Dirac point) transport properties are contrasted with those of high-energy (secondary) Dirac points, including both Anderson disorder and Gaussian impurities to respectively mimic short-range and long-range scattering potentials. Mean free paths at the secondary Dirac points are found to range from 10 nm to a few hundreds of nm depending on the static disorder, while the observation of satellite resistivity peaks depends on the strength of quantum interferences and localization effects.

We present a first-principles calculation scheme for crystals that diagonalizes an effective Hamiltonian in a small atomic orbital basis set which is expanded in plane waves, yielding initial trial wave functions. A simple relaxation procedure applied to the trial wave functions expanded in a plane-wave basis can be used to generate a set of correction wave functions. We show that a subsequent diagonalization of the effective Hamiltonian in the subspace of the trial and correction wave functions is sufficient to obtain results quite close from a full converged calculation on the plane-wave basis set used for the projection. The proposed method should be simple to implement in other plane-wave computer programs and leads to substantial gains in computation speed while maintaining reasonable accuracy.

We perform a comprehensive analysis of the bimagnon resonant inelastic x-ray scattering (RIXS) intensity spectra of the spatially frustrated $J_x\text{−}{J}_y\text{−}{J}_2$ Heisenberg model on a square lattice in both the antiferromagnetic and the collinear antiferromagnetic phase. We study the model for strong frustration and significant spatial anisotropy to highlight the key signatures of RIXS spectrum splitting which may be experimentally discernible. Based on an interacting spin wave theory study within the ladder approximation Bethe-Salpeter scheme, we find the appearance of a robust two-peak structure over a wide range of the transferred momenta in both magnetically ordered phases. The unfrustrated model has a single-peak structure with a two-peak splitting originating due to spatial anisotropy and frustrated interactions. Our predicted two-peak structure from both magnetically ordered regimes can be realized in iron pnictides.

An electron confined in a quantum dot interacts with its local nuclear spin environment through the hyperfine contact interaction. This interaction combined with external control and relaxation or measurement of the electron spin allows for the generation of dynamic nuclear polarization. The quantum nature of the nuclear bath, along with the interplay of coherent external fields and incoherent dynamics in these systems renders a wealth of intriguing phenomena seen in recent experiments such as electron Zeeman frequency focusing, hysteresis, and line dragging. We develop in detail a fully quantum, self-consistent theory that can be applied to such experiments and that moreover has predictive power. Our theory uses the operator sum representation formalism in order to incorporate the incoherent dynamics caused by the additional, Markovian bath, which in self-assembled dots is the vacuum field responsible for electron-hole optical recombination. The beauty of this formalism is that it reduces the complexity of the problem by encoding the joint dynamics of the external coherent and incoherent driving in an effective dynamical map that only acts on the electron spin subspace. This, together with the separation of time scales in the problem, allows for a tractable and analytically solvable formalism. The key role of entanglement between the electron spin and the nuclear spins in the formation of dynamic nuclear polarization naturally follows from our solution. We demonstrate the theory in detail for an optical pulsed experiment and present an in-depth discussion and physical explanation of our results.