Dielectric properties of multiband electron systems: I - Tight-binding formulation

The screened electron-electron interaction in a multi-band electron system is calculated within the random phase approximation and in the tight-binding representation. The obtained dielectric matrix contains, beside the usual site-site correlations, also the site-bond and bond-bond correlations, and thus includes all physically relevant polarization processes. The arguments are given that the bond contributions are negligible in the long wavelength limit. We analyse the system with two non-overlapping bands in this limit, and show that the corresponding dielectric matrix reduces to a $2\times2$ form. The intra-band and inter-band contributions are represented by diagonal matrix elements, while the off-diagonal elements contain the mixing between them. The latter is absent in insulators but may be finite in conductors. Performing the multipole expansion of the bare long-range interaction, we show that this mixing is directly related to the symmetry of the atomic orbitals participating in the tight-binding electronic states. In systems with forbidden atomic dipolar transitions, the intra-band and inter-band polarizations are separated. However, when the dipolar transitions are allowed, the off-diagonal elements of the dielectric matrix are of the same order as diagonal ones, due to a finite monopole-dipole interaction between the intra-band and inter-band charge fluctuations.Comment: 32 pages, LaTeX, to appear in Z.Phys.

Effects of transverse electron dispersion on photo-emission spectra of quasi-one-dimensional systems

The random phase approximation (RPA) spectral function of the one-dimensional electron band with the three-dimensional long range Coulomb interaction shows a broad feature which is spread on the scale of the plasmon energy and vanishes at the chemical potential. The fact that there are no quasi-particle $\delta$-peaks is the direct consequence of the acoustic nature of the collective plasmon mode. This behaviour of the spectral function is in the qualitative agreement with the angle resolved photo-emission spectra of some Bechgaard salts. In the present work we consider the modifications in the spectral function due to finite transverse electron dispersion. The transverse bandwidth is responsible for the appearance of an optical gap in the long wavelength plasmon mode. The plasmon dispersion of such kind introduces the quasi-particle $\delta$-peak into the spectral function at the chemical potential. The cross-over from the Fermi liquid to the non-Fermi liquid regime by decreasing the transverse bandwidth takes place through the decrease of the quasi-particle weight as the optical gap in the long wavelength plasmon mode is closing.Comment: 2 pages, 2 figures, ISCOM'0

Dielectric properties of multiband electron systems: II - Collective modes

Starting from the tight-binding dielectric matrix in the random phase approximation we examine the collective modes and electron-hole excitations in a two-band electronic system. For long wavelengths (${\bf q}\rightarrow0$), for which most of the analysis is carried out, the properties of the collective modes are closely related to the symmetry of the atomic orbitals involved in the tight-binding states. In insulators there are only inter-band charge oscillations. If atomic dipolar transitions are allowed, the corresponding collective modes reduce in the asymptotic limit of vanishing bandwidths to Frenkel excitons for an atomic insulator with weak on-site interactions. The finite bandwidths renormalize the dispersion of these modes and introduce a continuum of incoherent inter-band electron-hole excitations. The possible Landau damping of collective modes due to the presence of this continuum is discussed in detail.Comment: 25 pages, LaTeX, to appear in Z.Phys.

Photo-emission properties of quasi-one-dimensional conductors

We calculate the self-energy of one-dimensional electron band with the three-dimensional long range Coulomb interaction within the random phase approximation, paying particular attention to the contribution coming from the electron scatterings on the collective plasmon mode. It is shown that the spectral density has a form of wide feature at thr frequency scale of the plasmon frequency, without the presence of quasi-particle delta-peaks. The relevance of this result with respect to experimental findings and to the theory of Luttinger liquids is discussed.Comment: 4 pages, 2 figure