We present a $G_0{W}_0$ implementation that assesses the two major bottlenecks of traditional plane-waves implementations, the summations over conduction states and the inversion of the dielectric matrix, without introducing new approximations in the formalism. The first bottleneck is circumvented by converting the summations into Sternheimer equations. Then, the novel avenue of expressing the dielectric matrix in a Lanczos basis is developed, which reduces the matrix size by orders of magnitude while being computationally efficient. We also develop a model dielectric operator that allows us to further reduce the size of the dielectric matrix without accuracy loss. Furthermore, we develop a scheme that reduces the numerical cost of the contour deformation technique to the level of the lightest plasmon pole model. Finally, the use of the simplified quasiminimal residual scheme in replacement of the conjugate gradients algorithm allows a direct evaluation of the $G_0{W}_0$ corrections at the desired real frequencies, without need for analytical continuation. The performance of the resulting $G_0{W}_0$ implementation is demonstrated by comparison with a traditional plane-waves implementation, which reveals a 500-fold speedup for the silane molecule. Finally, the accuracy of our $G_0{W}_0$ implementation is demonstrated by comparison with other $G_0{W}_0$ calculations and experimental results.

The direction and impact parameter dependence of electronic stopping power, along with its velocity threshold behavior, is investigated in a prototypical small-band-gap semiconductor. We calculate the electronic stopping power of H in Ge, a semiconductor with relatively low packing density, using time-evolving time-dependent density-functional theory. The calculations are carried out in channeling conditions with different impact parameters and in different crystal directions for projectile velocities ranging from 0.05 to 0.6 atomic units. The satisfactory comparison with available experiments supports the results and conclusions beyond experimental reach. The calculated electronic stopping power is found to differ in different crystal directions; however, strong impact parameter dependence is observed only in one of these directions. The distinct velocity threshold observed in experiments is well reproduced, and its nontrivial relation with the band gap follows a perturbation theory argument surprisingly well. This simple model is also successful in explaining why different density functionals give the same threshold even with substantially different band gaps.

Understanding the impact of interfacial electric fields on electronic structure is crucial to improving the performance of materials in applications based on charged interfaces. Supercapacitors store energy directly in the strong interfacial field between a solid electrode and a liquid electrolyte; however, the complex interplay between the two is often poorly understood, particularly for emerging low-dimensional electrode materials that possess unconventional electronic structure. Typical descriptions tend to neglect the specific electrode-electrolyte interaction, approximating the intrinsic “quantum capacitance” of the electrode in terms of a fixed electronic density of states. Instead, we introduce a more accurate first-principles approach for directly simulating charge storage in model capacitors using the effective screening medium method, which implicitly accounts for the presence of the interfacial electric field. Applying this approach to graphene supercapacitor electrodes, we find that results differ significantly from the predictions of fixed-band models, leading to improved consistency with experimentally reported capacitive behavior. The differences are traced to two key factors: the inhomogeneous distribution of stored charge due to poor electronic screening and interfacial contributions from the specific interaction with the electrolyte. Our results are used to revise the conventional definition of quantum capacitance and to provide general strategies for improving electrochemical charge storage, particularly in graphene and similar low-dimensional materials.

We study the conductance $g$ of an electron interferometer created in a two-dimensional electron gas between a nanostructured contact and the depletion region induced by the charged tip of a scanning gate microscope. Using noninteracting models, we study the beating pattern of interference fringes exhibited by the images giving $g$ as a function of the tip position when a parallel magnetic field is applied. The analytical solution of a simplified model allows us to distinguish between two cases: (i) If the field is applied everywhere, the beating of Fabry-Pérot oscillations of opposite spins gives rise to interference rings which can be observed at low temperatures when the contact is open between spin-split transmission resonances. (ii) If the field acts only upon the contact, the interference rings cannot be observed at low temperatures but only at temperatures of the order of the Zeeman energy. For a contact made of two sites in series, a model often used for describing an inversion-symmetric double-dot setup, a pseudospin degeneracy is broken by the interdot coupling and a similar beating effect can be observed without magnetic field at temperatures of the order of the interdot coupling. Eventually, numerical studies of a quantum point contact with quantized conductance plateaus confirm that a parallel magnetic field applied everywhere or only upon the contact gives rises to similar beating effects between spin-split channel openings.

Using Monte Carlo simulations, we study the character of the spin-glass (SG) state of a site-diluted dipolar Ising model. We consider systems of dipoles randomly placed on a fraction $x$ of all $L^3$ sites of a simple cubic lattice that point up or down along a given crystalline axis. For $x\lesssim 0.65$ these systems are known to exhibit an equilibrium spin-glass phase below a temperature $T_{\mathrm{sg}}\propto x$. At high dilution and very low temperatures, well deep in the SG phase, we find spiky distributions of the overlap parameter $q$ that are strongly sample dependent. We focus on spikes associated with large excitations. From cumulative distributions of $q$ and a pair correlation function averaged over several thousands of samples we find that, for the system sizes studied, the average width of spikes, and the fraction of samples with spikes higher than a certain threshold, does not vary appreciably with $L$. This is compared with the behavior found for the Sherrington-Kirkpatrick model.

We have studied vortex dynamics excited by the spin-transfer-torque effect and find that the direction of the vortex state can be detected electrically using the homodyne voltage signal generated due to the anisotropic magnetoresistance (AMR) effect. An external in-plane dc magnetic field is required to break the cylindrical symmetry in order to obtain a dc response of the homodyne signal. The sign of this rectified voltage changes with the handedness of the vortex state, which makes it a promising method to detect the vortex state electrically. Vortex dynamics is also observed by direct imaging in a scanning transmission x-ray microscope, allowing verification of the measured AMR signal in the correct power and frequency range. The results of micromagnetic simulations are in good agreement with the experimental data.

We study the interaction-induced connectivity in the Fock space of two particles in a disordered one-dimensional potential. Recent computational studies showed that the largest localization length ${\xi }_2$ of two interacting particles in a weakly random tight-binding chain is increasing unexpectedly slow relative to the single-particle localization length ${\xi }_1$, questioning previous scaling estimates. We show this to be a consequence of the approximate restoring of momentum conservation of weakly localized single-particle eigenstates, and disorder-induced phase shifts for partially overlapping states. The leading resonant links appear among states which share the same energy and momentum. We substantiate our analytical approach by computational studies for up to ${\xi }_1=1000$. A potential nontrivial scaling regime sets in for ${\xi }_1\approx 400$.

The existence of degenerate or gapless edge states is a characteristic feature of topological insulators, but is difficult to detect in the presence of interactions. We propose a new method to obtain the degeneracy of the edge states from the perspective of entanglement entropy, which is very useful to identify interacting topological states. Employing the determinant quantum Monte Carlo technique, we investigate the interaction effect on two representative models of fermionic topological insulators in one and two dimensions, respectively. In the two topologically nontrivial phases, the edge degeneracies are reduced by interactions but remain to be nontrivial.

We explore the optical properties of a meta-atom made of plasmonic nanopatches that possess an increasing degree of complexity. We show that if two nanopatches are strongly coupled and have a different geometrical footprint, the meta-atom exhibits a resonant magnetoelectric response, in addition to the anticipated resonant electric and magnetic response. Thus, it behaves similarly as the so-called omega particle, but with the unique advantage that frequency and strength of this magnetoelectric resonance can be independently tuned and modified with respect to the corresponding values of the electric resonance. This allows a metasurface of such meta-atoms to possess widely controlled reflection and transmission coefficients, e.g., the regimes of strongly asymmetric reflectance and perfect absorption become possible. Alternatively, an individual meta-atom of such kind can act as a directive nanoantenna with zero backscattered fields (Huygens' scatterer).

A thorough investigation of three-dimensional kagome lattices of group IV elements is performed with first-principles calculations. The investigated kagome lattices of silicon and germanium are found to be of similar stability as the recently proposed carbon kagome lattice. Carbon and silicon kagome lattices are both direct-gap semiconductors but they have qualitatively different electronic band structures. While direct optical transitions between the valence and conduction bands are allowed in the carbon case, no such transitions can be observed for silicon. The kagome lattice of germanium exhibits semimetallic behavior but can be transformed into a semiconductor after compression.

Considering finite-temperature screened electron-impurity scattering, we present a kinetic equation approach to investigate transport properties of two-dimensional massive fermions in silicene. We find that the longitudinal conductivity is always nonvanishing when chemical potential lies within the energy gap. This residual conductivity arises from interband correlation and strongly depends on strength of electron-impurity scattering. We also clarify that the electron-impurity interaction makes substantial contributions to the spin and valley Hall conductivities, which, however, are almost independent of impurity density. The dependencies of longitudinal conductivity as well as of spin and valley Hall conductivities on chemical potential, temperature, and gap energy are analyzed.

We report a first-principles study on the elastic, vibrational, and electronic properties of the recently synthesized phosphorene. By calculating the Grüneisen parameters, we evaluate the frequency shift of the Raman and infrared active modes via symmetric biaxial strain. We also study a strain-induced semiconductor-metal transition, the gap size, and the effective mass of carriers in various strain configurations. Furthermore, we unfold the emergence of a peculiar Dirac-shaped dispersion for specific strain conditions including the zigzag-oriented tensile strain. The observed linear energy spectrum has distinct velocities corresponding to each of its linear branches and is limited to the $\Gamma \text{−}X$ direction in the first Brillouin zone.

Elemental phosphorous is believed to have several stable allotropes that are energetically nearly degenerate, but chemically reactive. These structures may be capped by monolayers of hexagonal boron nitride $(h-\mathrm{BN})$ or graphene to prevent chemical degradation under ambient conditions. We perform ab initio density functional calculations to simulate scanning tunneling microscopy (STM) images of different layered allotropes of phosphorus and study the effect of the capping layers on these images. At scanning energies within its intrinsic conduction gap, protective monolayers of insulating $h-\mathrm{BN}$ allow to distinguish between the different structural phases of phosphorus underneath due to the electronic hybridization with orbitals from the upmost phosphorus atoms: $h-\mathrm{BN}$ capping monolayers thus provide a promising route to tell few-layer phosphorus allotropes from one another with local probes.

A one-dimensional quantum charge pump transfers a quantized charge in each pumping cycle. This quantization is topologically robust, being analogous to the quantum Hall effect. The charge transferred in a fraction of the pumping period is instead generally unquantized. We show, however, that with specific symmetries in parameter space the charge transferred at well-defined fractions of the pumping period is quantized as integer fractions of the Chern number. We illustrate this in a one-dimensional Harper-Hofstadter model and show that the fractional quantization of the topological charge pumping is independent of the specific boundary conditions taken into account. We further discuss the relevance of this phenomenon for cold atomic gases in optical superlattices.

Silicene systems, due to the buckled structure of the lattice, manifest remarkable intrinsic spin-orbit interaction triggering a topological phase transition in the low-energy regime. Thus, we found that protected edge states are present in silicene antidots and dots, being polarized in valley-spin pairs. We have also studied the effect of the lattice termination on the properties of the single electron energy levels and electron density distribution of silicene antidots and dots situated in a perpendicular magnetic field. Our calculations confirmed that the topological edge states are propagating over the perimeter of the antidot/dot for both ideal or realistic edge termination containing roughness on the atomic length scale. The valley polarization and the slope of the energy lines as a function of the magnetic field is, however, reduced when the antidot or dot has a rough edge.

The theory of Hall transport of spins in a correlated paramagnetic phase is developed. By identifying the thermal Hall current operator in the spin language, which turns out to equal the spin chirality in the pure Heisenberg model, various response functions can be derived straightforwardly. Subsequent reduction to the Schwinger-boson representation of spins allows a convenient calculation of thermal and spin Hall coefficients in the paramagnetic regime using self-consistent mean-field theory. A comparison is made to results from the Holstein-Primakoff reduction of spin operators appropriate for ordered phases.

We present an analytical derivation of the electromagnetic response of a spherical object coated by a conductive film, here exemplified by a graphene coating. Applying the framework of Mie-Lorenz theory augmented to account for a conductive boundary condition, we derive the multipole scattering coefficients, modified essentially through the inclusion of an additive correction in numerator and denominator. By reductionist means, starting from the retarded response, we offer simple results in the quasistatic regime by analyzing the multipolar polarizability and associated dispersion equation for the localized plasmons. We consider graphene coatings of both dielectric and conducting spheres, where the graphene coating in the former case introduces the plasmons and in the latter case modifies in interesting ways the existing ones. Finally, we discuss our analytical results in the context of extinction cross section and local density of states. Recent demonstrations of fabricated spherical graphene nanostructures make our study directly relevant to experiments.

The atomistic study of kink pairs on screw dislocations in body-centered cubic (bcc) metals is challenging because interatomic potentials in bcc metals still lack accuracy and kink pairs require too many atoms to be modeled by first principles. Here, we circumvent this difficulty using a one-dimensional line tension model whose parameters, namely the line tension and Peierls barrier, are reachable to density functional theory calculations. The model parameterized in V, Nb, Ta, Mo, W, and Fe, is used to study the kink-pair activation enthalpy and spatial extension. Interestingly, we find that the atomistic line tension is more than twice the usual elastic estimates. The calculations also show interesting group tendencies with the line tension and kink-pair width larger in group V than in group VI elements. Finally, the present kink-pair activation energies are shown to compare qualitatively with experimental data and potential origins of quantitative discrepancies are discussed.