The Liouville-Lanczos approach to linear-response time-dependent density-functional theory is generalized so as to encompass electron energy loss and inelastic x-ray scattering spectroscopies in periodic solids. The computation of virtual orbitals and the manipulation of large matrices are avoided by adopting a representation of response orbitals borrowed from (time-independent) density functional perturbation theory and a suitable Lanczos recursion scheme. The latter allows the bulk of the numerical work to be performed at any given transferred momentum only once, for a whole extended frequency range. The numerical complexity of the method is thus greatly reduced, making the computation of the loss function over a wide frequency range at any given transferred momentum only slightly more expensive than a single standard ground-state calculation and opening the way to computations for systems of unprecedented size and complexity. Our method is validated on the paradigmatic examples of bulk silicon and aluminum, for which both experimental and theoretical results already exist in the literature.

Magnetic circular dichroism and polarized optical absorption spectra of single-crystal DyFe${}_3$(BO${}_3$)${}_4$ were measured in the region of the crystal transparency from 8700 to 16 000 cm${}^{-1}$ in the temperature range from 90 K up to room temperature. Spectra of d-d and f-f transitions were separated, and f-f transitions ${}^6$$H_{15/2}$ → ${}^6$($F_{9/2}$+$H_{7/2}$), ${}^6$$F_{7/2}$, ${}^6$$F_{5/2}$, and ${}^6$$F_{3/2}$ were studied. From these measurements, temperature dependences of the paramagnetic magneto-optical activity (MOA) of the electric dipole-forbidden f-f transitions were obtained. It was revealed that, in contrast to allowed transitions, temperature dependences of the MOA of some f-f transitions substantially deviate from the Curie-Weiss law. The theories of MOA of allowed and f-f transitions were considered and the experimental results obtained were accounted for. Circular polarizations in magnetic field and linear polarizations of absorption lines were determined. The Zeeman splitting of some absorption lines were found. Symmetries of the crystal field states were analyzed on the bases of the obtained results in $D_3$ local symmetry approximation. A small splitting (≈16.5 cm${}^{-1}$) between the two lowest sublevels of the ground manifold was detected, and symmetries of these states were identified as $E_{1/2}$ ($M$ $=$ ±13/2) and $E_{3/2}$ ($M$ $=$ ±15/2), respectively. Deviation of the local symmetry of the Dy${}^{3+}$ ion from $D_3$ is small, and it was revealed that polarizations of the majority of absorption lines can be accounted for in the $D_3$ symmetry. This also testifies that in the process of some other electron transitions, the equilibrium configuration of the local environment deviates from $D_3$ symmetry stronger than it does in the ground state. In addition, it has been shown that the distortions depend not only on the excited but also on the initial state.

We present an approach for the efficient generation of Wannier functions for Photonic Crystal computations that is based on a combination of group-theoretical analysis and efficient minimization strategies. In particular, we describe the symmetry properties that allow for exponential localization of Wannier functions and how they are related to the underlying Bloch mode symmetries of the photonic band structure and we show that no exponentially localized Wannier functions can be created from the physical modes of a three-dimensional crystal. Moreover, we comment on the use of conjugate gradient and randomized minimization algorithms that—together with the group theoretical considerations—facilitate the efficient numerical determination of maximally localized Wannier functions for many bands. This is a requirement for the accurate computation of Photonic Crystal functional elements and devices.

The band offsets between the Zn-IV-N${}_2$ nitrides, ZnGeN${}_2$ and ZnSnN${}_2$, and two other closely lattice matched semiconductors, ZnO and GaN, are calculated using density functional theory calculations including quasiparticle corrections. The interface dependence as well as the role of strain are investigated. A staggered type-II alignment is found between ZnGeN${}_2$, GaN, and ZnO, with ZnO having the lower and ZnGeN${}_2$ having the higher valence band maximum. The potential benefits of this alignment for photovoltaic applications are pointed out.

Currently, much effort is being put into detecting unconventional $p$-wave superconductivity in Josephson junctions based on topological insulators (TIs). For that purpose we propose to use superconducting Klein tunneling, i.e., the reflectionless passage of Cooper pairs through a potential barrier in a gated ballistic junction. This phenomenon occurs due to the fact that the supercurrent is carried by helical Andreev bound states (ABSs) characterized by spin-momentum locking similar to the normal-state carriers. We derive the spectrum of the helical ABSs and the corresponding Josephson current for a junction made on the surface of a three-dimensional TI. The superconducting Klein tunneling is predicted to yield a nonsinusoidal current-phase relation and an anomalous critical current $I_c$ that does not vanish with increasing barrier strength. We also analyze the dependence of the $I_c{R}_n$ product (where $R_n$ is the normal-state junction resistance) on the microscopic parameters of the superconductor/TI interface, which leads to lower $I_c{R}_n$ values than expected from previous models of the proximity-effect Josephson junctions.

We report electron doping in the surface vicinity of KTaO${}_3$ by inducing oxygen vacancies via Ar${}^{+}$ irradiation. The doped electrons have high mobility ($>{10}^4$ cm${}^2$/V$$s) at low temperatures, and exhibit Shubnikov–de Haas oscillations with both two- and three-dimensional components. A disparity of the extracted in-plane effective mass, compared to the bulk values, suggests mixing of the orbital characters. Our observations demonstrate that Ar${}^{+}$ irradiation serves as a flexible tool to study low-dimensional quantum transport in $5d$ semiconducting oxides.

Unexpected transport behavior can arise due to anisotropic single-particle scattering in multiband systems. Specifically, we show within a semiclassical Boltzmann approach beyond the relaxation-time approximation that anisotropic scattering between electronlike and holelike Fermi surfaces generically leads to negative transport times, which in turn cause negative magnetoresistance, an extremum in the Hall coefficient, and a reduction of the resistivity. The anisotropy required for this to occur decreases with increasing mismatch between the Fermi-surface radii.

In this work, a study of resonance effects in the Raman spectra of twisted bilayer graphene (tBLG) is presented. The analysis takes into account the effect of the mismatch angle $\theta$ between the two layers, and also of the excitation laser energy on the frequency, linewidth, and intensity of the main Raman features, namely the rotationally induced $R$ band, the $G$ band, and the second-order $G^{\prime }$ (or $2D$) band. The resonance effects are explained based on the $\theta$ dependence of the tBLG electronic structure, as calculated by ab initio methodologies. The twist angle $\theta$ also defines the observation of a “$D$-like” band which obeys the double-resonance process, but relies on the superlattice along with long-range defects in order to fulfill momentum conservation. The study was possible due to the development of a route to produce and identify rotationally stacked bilayer graphene by means of atomic force microscopy (AFM).

We present a scheme for full quantum state tomography tailored for two spin qubits in a double quantum dot. A set of 15 quantum states allows to determine the density matrix in this two-qubit space by projective measurement. In this paper, we choose a set gained from mutually unbiased bases. We determine how those 15 projections can be represented by charge measurements after a spin-to-charge conversion and the application of quantum gates. The quantum gates include exchange-based gates as well as rotations by electron spin resonance (ESR). We assume the experimental realization of ESR operations to be more difficult than the exchange gate operation with respect to fidelity and speed. Therefore it is an important result that the ESR gates can be limited to a $\pi /2$ rotation for one of the electron spins per measurement.

We investigate the structure-property relationships in $AB$O${}_3$ perovskites exhibiting octahedral rotations and cooperative octahedral breathing distortions (CBD) using group theoretical methods. Rotations of octahedra are ubiquitous in the perovskite family, while the appearance of breathing distortions—oxygen displacement patterns that lead to approximately uniform dilation and contraction of the $B$O${}_6$ octahedra—are rarer in compositions with a single, chemically unique $B$ site. The presence of a CBD relies on electronic instabilities of the $B$-site cations, either orbital degeneracies or valence-state fluctuations, and often appear concomitant with charge order metal-insulator transitions or $B$-site cation ordering. We enumerate the structural variants obtained from rotational and breathing lattice modes and formulate a general Landau functional describing their interaction. We use this information and combine it with statistical correlation techniques to evaluate the role of atomic scale distortions on the critical temperatures in representative charge ordering nickelate and bismuthate perovskites. Our results provide microscopic insights into the underlying structure-property interactions across electronic and magnetic phase boundaries, suggesting plausible routes to tailor the behavior of functional oxides by design.

We demonstrate spin-spiral-induced ferroelectricity in epitaxial TbMnO${}_3$ films grown on YAlO${}_3$ substrates down to a film thickness of 6nm. The ferroelectric polarization is identified by optical second-harmonic generation. Using x-ray resonant magnetic scattering we directly prove the existence of a noncollinear magnetic structure in the ferroelectric phase and thus bulk-like multiferroicity. The electric-field-induced reversal of the magnetic domains along with the reversal of the ferroelectric polarization evidences the rigid coupling of magnetic and ferroelectric order and hence a “giant” magnetoelectric effect in the films.

We investigate the doping dependence of the magnetic excitations in the two-superconducting-dome system LaFeAsO${}_{1-x}$D${}_x$. Using inelastic neutron scattering, spin fluctuations at different wave numbers were observed under both superconducting domes around $x$ $=$ 0.1 and 0.4 but vanished at $x$ $=$ 0.2 corresponding to the $T_{\mathrm{c}}$ valley. Theoretical calculations indicate that the characteristic doping dependence of the spin fluctuations is rationally explained as a consequence of the switching of the two intra-orbital nestings within Fe-3$d_{YZ}$${}_{,ZX}$ and Fe-3$d_X$${}_{2-Y2}$ by electron doping. The present results imply that the multiorbital nature plays an important role in the doping and/or material dependence of the $T_{\mathrm{c}}$ of the iron pnictide superconductors.

We consider Ising models in two and three dimensions with nearest neighbor ferromagnetic interactions and long-range, power law decaying, antiferromagnetic interactions. If the strength of the ferromagnetic coupling $J$ is larger than a critical value $J_c$, then the ground state is homogeneous and ferromagnetic. As the critical value is approached from smaller values of $J$, it is believed that the ground state consists of a periodic array of stripes ($d=2$) or slabs ($d=3$), all of the same size and alternating magnetization. Here we prove rigorously that the ground state energy per site converges to that of the optimal periodic striped or slabbed state, in the limit that $J$ tends to the ferromagnetic transition point. While this theorem does not prove rigorously that the ground state is precisely striped or slabbed, it does prove that in any suitably large box the ground state is striped or slabbed with high probability.

Based on the two-dimensional $\pi$-flux model, we study the interaction effects both in nontrivial massive and massless Dirac fermions with the numerical exact diagonalization method. In the presence of the nearest and next-nearest neighbor interactions: For a nontrivial massive Dirac fermion, the topological phase is robust and persists in a finite region of the phase diagram; while for the massless Dirac fermion, charge-density wave and stripe phases are identified and the phase diagram in the $(V_1,V_2)$ plane is obtained. When the next-next-nearest neighbor interaction is further included to massless Dirac fermion, the topological phase expected in the mean-field theory is absent. Our results are related to the possibility of dynamically generating a topological phase from the electronic correlations.

We demonstrate that the volume of the Fermi surface, measured very precisely using de Haas-van Alphen oscillations, can be used to probe changes in the nature and occupancy of localized electronic states. In systems with unconventional ordered states, this allows an underlying electronic order parameter to be followed to very low temperatures. We describe this effect in the field-induced antiferroquadrupolar (AFQ) ordered phase of PrOs${}_4$Sb${}_{12}$, a heavy fermion intermetallic compound. We find that the phase of de Haas-van Alphen oscillations is sensitively coupled, through the Fermi volume, to the configuration of the Pr $f$-electron states that are responsible for AFQ order. In particular, the $\beta$ sheet of the Fermi surface expands or shrinks as the occupancy of two competing localized Pr crystal field states changes. Our results are in good agreement with previous measurements, above 300 mK, of the AFQ order parameter by other methods. In addition, the low-temperature sensitivity of our measurement technique reveals a strong and previously unrecognized influence of hyperfine coupling on the order parameter below 300 mK within the AFQ phase. Such hyperfine couplings could provide insight into the nature of hidden order states in other systems.

Long-range quantum communication for spin qubits is an important open problem. Here we study decoherence of an electron spin qubit that is being transported in a moving quantum dot. We focus on spin decoherence due to spin-orbit interaction and a random electric potential. We find that at the lowest order, the motion induces longitudinal spin relaxation, with a rate linear in the dot velocity. Our calculated spin relaxation time ranges from sub $\mu$s in GaAs to above ms in Si, making this relaxation a significant decoherence channel. Our results also give clear indications on how to reduce the decoherence effect of electron motion.

Experimental approaches to manipulating light-matter interaction at the nanoscale level have quickly advanced in recent years, leading to the use of surface plasmon amplification by stimulated emission of radiation (spaser) in plasmonic nanocavities. Yet, a well-understood analytical theory to quantitatively explain certain characteristics of the spaser system has still been lacking and is greatly needed. Here, we develop an all-analytical semiclassical theory to investigate the energy exchange between active materials and fields and the spaser performance in a plasmonic nanocavity. The theory incorporates the four-level atomic rate equations in association with the classical oscillator model for active materials and Maxwell's equations for fields, thus allowing one to uncover the relationship between the characteristics of the spaser (the output power, saturation, and threshold) and the nanocavity parameters (quality factor, mode volume, loss, and spontaneous emission efficiency), atomic parameters (number density, linewidth, and resonant frequency), and external parameters (pumping rate). The semiclassical theory has been employed to analyze previous spaser experiments and shows that using a single gold nanoparticle plasmonic nanocavity to ignite the spaser is very difficult due to its high threshold. The theory can be commonly used in understanding and designing all novel microlaser, nanolaser, and spaser systems.

We study the injection $n$ of electrons in a quantum conductor using voltage pulses applied on a contact. We particularly consider the case of Lorentzian voltage pulses. When carrying integer charge, they are known to provide electronic states with a minimal number of excitations, while any other type of pulses are accompanied with a neutral cloud of electron and hole excitations. We focus on the low-frequency shot noise arising when the excitations are partitioned by a single scatterer. Using periodic pulses, the physics can be discussed in the framework of the photon-assisted shot noise. Pulses of arbitrary shape and arbitrary charge are shown to give a marked minimum in the noise when the charge is an integer. The energy-domain characterization of the charge pulse excitations is also given using the shot-noise spectroscopy which reveals the asymmetrical energy spectrum of Lorentzian pulses. Finally, time-domain information is obtained from Hong-Ou-Mandel–type noise correlations when two trains of pulses generated on opposite contacts collide on the scatterer. For integer Lorentzian, the noise versus the time delay between pulse trains is shown to give a measure of the electron wave-packet autocorrelation function. In order to make contact with recent experiments, all the calculations are made at zero and finite temperatures.

A theoretical study of the single-electron coherence properties of Lorentzian and rectangular pulses is presented. By combining bosonization and the Floquet scattering approach, the effect of interactions on a periodic source of voltage pulses is computed exactly. When such excitations are injected into one of the channels of a system of two copropagating quantum Hall edge channels, they fractionalize into pulses whose charge and shape reflect the properties of interactions. We show that the dependence of fractionalization-induced electron/hole pair production in the pulses’ amplitude contains clear signatures of the fractionalization of the individual excitations. We propose an experimental setup combining a source of Lorentzian pulses and a Hanbury Brown–Twiss interferometer to measure interaction-induced electron/hole pair production and more generally to reconstruct single-electron coherence of these excitations before and after their fractionalization.

This paper investigates some of the successes and failures of density functional theory in the study of high-pressure solid hydrogen at low temperature. We calculate the phase diagram, metallization pressure, phonon spectrum, and proton zero-point energy using three popular exchange-correlation functionals: the local density approximation (LDA), the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation, and the semilocal Becke-Lee-Yang-Parr (BLYP) functional. We focus on the solid molecular $P{6}_3/m$, $C2/c$, $Cmca$-12, and $Cmca$ structures in the pressure range from $100<P<500$ GPa over which phases I, II, and III are observed experimentally. At the static level of theory, in which proton zero-point energy is ignored, the LDA, PBE, and BLYP functionals give very different structural transition and metallization pressures, with the BLYP phase diagram in better agreement with experiment. Nevertheless, all three functionals provide qualitatively the same information about the band gaps of the four structures and the phase transitions between them. Going beyond the static level, we find that the frequencies of the vibron modes observed above 3000 cm${}^{-1}$ depend strongly on the choice of exchange-correlation functional, although the low-frequency part of the phonon spectrum is little affected. The largest and smallest values of the proton zero-point energy, obtained using the BLYP and LDA functionals, respectively, differ by more than 10 meV/proton. Including the proton zero-point energy calculated from the phonon spectrum within the harmonic approximation improves the agreement of the BLYP and PBE phase diagrams with experiment. Taken as a whole, our results demonstrate the inadequacy of mean-field-like density functional calculations of solid molecular hydrogen in phases I, II, and III and emphasize the need for more sophisticated methods.