Optical absorption in small BN and C nanotubes

We present a theoretical study of the optical absorption spectrum of small boron-nitride and carbon nanotubes using time-dependent density-functional theory and the random phase approximation. Both for C and BN tubes, the absorption of light polarized perpendicular to the tube-axis is strongly suppressed due to local field effects. Since BN-tubes are wide band-gap insulators, they only absorb in the ultra-violet energy regime, independently of chirality and diameter. In comparison with the spectra of the single C and BN-sheets, the tubes display additional fine-structure which stems from the (quasi-) one-dimensionality of the tubes and sensitively depends on the chirality and tube diameter. This fine structure can provide additional information for the assignment of tube indices in high resolution optical absorption spectroscopy.Comment: 5 pages, 3 figure

Reduced Density-Matrix Functional Theory: correlation and spectroscopy

In this work we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the calculation of total energies, occupation numbers, removal/addition energies, and spectral functions. We use the exactly solvable Hubbard molecule at 1/4 and 1/2 filling as test systems. This allows us to analyze the underlying physics and to elucidate the origin of the observed trends. For comparison we also report the results of the $GW$ approximation, where the self-energy functional is approximated, but no further hypothesis are made concerning the approximations of the observables. In particular we focus on the atomic limit, where the two sites of the molecule are pulled apart and electrons localize on either site with equal probability, unless a small perturbation is present: this is the regime of strong electron correlation. In this limit, using the Hubbard molecule at 1/2 filling with or without a spin-symmetry-broken ground state, allows us to explore how degeneracies and spin-symmetry breaking are treated in RDMFT. We find that, within the used approximations, neither in RDMFT nor in $GW$ the signature of strong correlation are present in the spin-singlet ground state, whereas both give the exact result for the spin-symmetry broken case. Moreover we show how the spectroscopic properties change from one spin structure to the other. Our findings can be generalized to other situations, which allows us to make connections to real materials and experiment

Ab initio GW many-body effects in graphene

We present an {\it ab initio} many-body GW calculation of the self-energy, the quasiparticle band plot and the spectral functions in free-standing undoped graphene. With respect to other approaches, we numerically take into account the full ionic and electronic structure of real graphene and we introduce electron-electron interaction and correlation effects from first principles. Both non-hermitian and also dynamical components of the self-energy are fully taken into account. With respect to DFT-LDA, the Fermi velocity is substantially renormalized and raised by a 17%, in better agreement with magnetotransport experiments. Furthermore, close to the Dirac point the linear dispersion is modified by the presence of a kink, as observed in ARPES experiments. Our calculations show that the kink is due to low-energy $\pi \to \pi^*$ single-particle excitations and to the $\pi$ plasmon. Finally, the GW self-energy does not open the band gap.Comment: 5 pages, 4 figures, 1 tabl

Enhancements to the GW space-time method

We describe the following new features which significantly enhance the power of the recently developed real-space imaginary-time GW scheme (Rieger et al., Comp. Phys. Commun. 117, 211 (1999)) for the calculation of self-energies and related quantities of solids: (i) to fit the smoothly decaying time/energy tails of the dynamically screened Coulomb interaction and other quantities to model functions, treating only the remaining time/energy region close to zero numerically and performing the Fourier transformation from time to energy and vice versa by a combination of analytic integration of the tails and Gauss-Legendre quadrature of the remaining part and (ii) to accelerate the convergence of the band sum in the calculation of the Green's function by replacing higher unoccupied eigenstates by free electron states (plane waves). These improvements make the calculation of larger systems (surfaces, clusters, defects etc.) accessible.Comment: 10 pages, 6 figure

Transforming nonlocality into frequency dependence: a shortcut to spectroscopy

Measurable spectra are theoretically very often derived from complicated many-body Green's functions. In this way, one calculates much more information than actually needed. Here we present an in principle exact approach to construct effective potentials and kernels for the direct calculation of electronic spectra. In particular, the potential that yields the spectral function needed to describe photoemission turns out to be dynamical but {\it local} and {\it real}. As example we illustrate this ``photoemission potential'' for sodium and aluminium, modelled as homogeneous electron gas, and discuss in particular its frequency dependence stemming from the nonlocality of the corresponding self-energy. We also show that our approach leads to a very short derivation of a kernel that is known to well describe absorption and energy-loss spectra of a wide range of materials

Density-based mixing parameter for hybrid functionals

A very popular ab-initio scheme to calculate electronic properties in solids is the use of hybrid functionals in density functional theory (DFT) that mixes a portion of Fock exchange with DFT functionals. In spite of their success, a major problem still remains, related to the use of one single mixing parameter for all materials. Guided by physical arguments that connect the mixing parameter to the dielectric properties of the solid, and ultimately to its band gap, we propose a method to calculate this parameter from the electronic density alone. This method is able to cut significantly the error of traditional hybrid functionals for large and small gap materials, while retaining a good description of structural properties. Moreover, its implementation is simple and leads to a negligible increase of the computational time.Comment: submitte

Robustness of electronic screening effects in electron spectroscopies: example of V2_2O5_5

In bulk and low-dimensional extended systems, the screening of excitations by the electron cloud is a key feature governing spectroscopic properties. Widely used computational approaches, especially in the framework of many-body perturbation theory, such as the GW approximation and the resulting approximate Bethe-Salpeter equation, are explicitly formulated in terms of the screened Coulomb interaction. In the present work we explore the effect of screening in absorption and electron energy loss spectroscopy, concentrating on the effect of local distortions on the screening and elucidating the resulting changes in the various spectra. Using the layered bulk oxide V$_2$O$_5$ as prototype material, we show in which way local distortions affect the screening, and in which way changes in the screening impact electron energy loss and absorption spectra including excitons. We highlight cancellations that make many-body effects in the spectra very robust with respect to structural modifications, while the band structure undergoes significant changes and the nature of the excitations may also be affected. This yields insight concerning the structure-properties relations that are crucial for the use of V$_2$O$_5$ as energy storage material, and more generally, that may be used to optimize the analysis and the calculation of electronic spectra in complex materials

Approximations for many-body Green's functions: insights from the fundamental equations

Several widely used methods for the calculation of band structures and photo emission spectra, such as the GW approximation, rely on Many-Body Perturbation Theory. They can be obtained by iterating a set of functional differential equations relating the one-particle Green's function to its functional derivative with respect to an external perturbing potential. In the present work we apply a linear response expansion in order to obtain insights in various approximations for Green's functions calculations. The expansion leads to an effective screening, while keeping the effects of the interaction to all orders. In order to study various aspects of the resulting equations we discretize them, and retain only one point in space, spin, and time for all variables. Within this one-point model we obtain an explicit solution for the Green's function, which allows us to explore the structure of the general family of solutions, and to determine the specific solution that corresponds to the physical one. Moreover we analyze the performances of established approaches like $GW$ over the whole range of interaction strength, and we explore alternative approximations. Finally we link certain approximations for the exact solution to the corresponding manipulations for the differential equation which produce them. This link is crucial in view of a generalization of our findings to the real (multidimensional functional) case where only the differential equation is known.Comment: 17 pages, 7 figure