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We derive electronic structure models for weakly interacting bilayers such as graphene-graphene and graphene-hexagonal boron nitride, based on density functional theory calculations followed by Wannier transformation of electronic states. These transferable interlayer coupling models can be applied to investigate the physics of bilayers with arbitrary translations and twists. The functional form, in addition to the dependence on the distance, includes the angular dependence that results from higher angular momentum components in the Wannier $p_z$ orbitals. We demonstrate the capabilities of the method by applying it to a rotated graphene bilayer, which produces the analytically predicted renormalization of the Fermi velocity, van Hove singularities in the density of states, and Moir{e} pattern of the electronic localization at small twist angles. We further extend the theory to obtain the effective couplings by integrating out neighboring layers. This approach is instrumental for the design of van der Walls heterostructures with desirable electronic features and transport properties and for the derivation of low-energy theories for graphene stacks, including proximity effects from other layers.
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We derive electronic tight-binding Hamiltonians for strained graphene, hexagonal boron nitride and transition metal dichalcogenides based on Wannier transformation of {it ab initio} density functional theory calculations. Our microscopic models include strain effects to leading order that respect the hexagonal crystal symmetry and local crystal configuration, and are beyond the central force approximation which assumes only pair-wise distance dependence. Based on these models, we also derive and analyze the effective low-energy Hamiltonians. Our {it ab initio} approaches complement the symmetry group representation construction for such effective low-energy Hamiltonians and provide the values of the coefficients for each symmetry-allowed term. These models are relevant for the design of electronic device applications, since they provide the framework for describing the coupling of electrons to other degrees of freedom including phonons, spin and the electromagnetic field. The models can also serve as the basis for exploring the physics of many-body systems of interesting quantum phases.
We study the frictional drag in high mobility, strongly interacting GaAs bilayer hole systems in the vicinity of the filling factor $ u=1$ quantum Hall state (QHS), at the same fillings where the bilayer resistivity displays a reentrant insulating phase. Our measurements reveal a very large longitudinal drag resistivity ($rho^{D}_{xx}$) in this regime, exceeding 15 k$Omega/Box$ at filling factor $ u=1.15$. $rho^{D}_{xx}$ shows a weak temperature dependence and appears to saturate at a finite, large value at the lowest temperatures. Our observations are consistent with theoretical models positing a phase separation, e.g. puddles of $ u=1$ QHS embedded in a different state, when the system makes a transition from the coherent $ u=1$ QHS to the weakly coupled $ u=2$ QHS.
The cubic (c) and monoclinic (m) polymorphs of Gd2O3 were studied using the combined analysis of several materials science techniques - X-ray diffraction (XRD), scanning electron microscopy (SEM), X-ray photoelectron spectroscopy (XPS), and photoluminescence (PL) spectroscopy. Density functional theory (DFT) based calculations for the samples under study were performed as well. The cubic phase of gadolinium oxide (c-Gd2O3) synthesized using a precipitation method exhibits spheroidal-like nanoclusters with well-defined edges assembled from primary nanoparticles with an average size of 50 nm, whereas the monoclinic phase of gadolinium oxide (m-Gd2O3) deposited using explosive pyrolysis has a denser structure compared with natural gadolinia. This phase also has a structure composed of three-dimensional complex agglomerates without clear-edged boundaries that are ~21 nm in size plus a cubic phase admixture of only 2 at. % composed of primary edge-boundary nanoparticles ~15 nm in size. These atomic features appear in the electronic structure as different defects ([Gd...O-OH] and [Gd...O-O]) and have dissimilar contributions to the charge-transfer processes among the appropriate electronic states with ambiguous contributions in the Gd 5p - O 2s core-like levels in the valence band structures. The origin of [Gd...O-OH] defects found by XPS was well-supported by PL analysis. The electronic and atomic structures of the synthesized gadolinias calculated using DFT were compared and discussed on the basis of the well-known joint OKT-van der Laan model, and good agreement was established.
Motivated by the increasing number of systems featuring multiple bands at low energy, we address the Boltzmann approach to transport in a multiband weakly disordered non-interacting crystal subject to a small electric field. In general, the multiband structure leads to a considerable complication of the Boltzmann equation. Indeed, even in the presence of elastic impurity scattering one needs to compute for each band and momentum the dressed velocities, which account for scattering events. Here we provide a semi-analytical solution to the Boltzmann equation that reduces such a challenging numerical task to the much simpler numerical computation of a small tensor whose dimension is set by the number of bands at the Fermi level. This approach further allows us to discuss the interplay of symmetry and disorder for different impurity types, including those originating from random-matrix Wigner ensembles. As an example of application we consider the 2D isotropic Rashba metal and we discuss, in a full analytical fashion, how different types of disorder may break the exactness of the relaxation-time approximation and induce transport anisotropy, and may allow one to identify the presence of spin-orbit coupling as deviations of the conductivity from Drude behavior.
We conduct a combined experimental and theoretical study of the quantum-confined Stark effect in GaAs/AlGaAs quantum dots obtained with the local droplet etching method. In the experiment, we probe the permanent electric dipole and polarizability of neutral and positively charged excitons weakly confined in GaAs quantum dots by measuring their light emission under the influence of a variable electric field applied along the growth direction. Calculations based on the configuration-interaction method show excellent quantitative agreement with the experiment and allow us to elucidate the role of Coulomb interactions among the confined particles and -- even more importantly -- of electronic correlation effects on the Stark shifts. Moreover, we show how the electric field alters properties such as built-in dipole, binding energy, and heavy-light hole mixing of multiparticle complexes in weakly confining systems, underlining the deficiencies of commonly used models for the quantum-confined Stark effect.
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