Abstract
Starting from the random phase approximation for the weakly coupled multiband tightly-bounded electron systems, we calculate the dielectric matrix in terms of intraband and interband transitions. The advantages of this representation with respect to the usual planewave decomposition are pointed out. The analysis becomes particularly transparent in the long wavelength limit, after performing the multipole expansion of bare Coulomb matrix elements. For illustration, the collective modes and the macroscopic dielectric function for a general cubic lattice are derived. It is shown that the dielectric instability in conducting narrow band systems proceeds by a common softening of one transverse and one longitudinal mode. Furthermore, the self-polarization corrections which appear in the macroscopic dielectric function for finite band systems, are identified as a combined effect of intra-atomic exchange interactions between electrons sitting in different orbitals and a finite inter-atomic tunneling.
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References
Pines, D.: Elementary Excitations in Solids. New York, Amsterdam: W.A. Benjamin 1964; Pines, D., Nozières, P.: The Theory of Quantum Liquids, Vol. 1. Reading, Mass.: Addison-Wesley 1989
Adler, S.L.: Phys. Rev.126, 413 (1962)
Wiser, N.: Phys. Rev.129, 62 (1963)
Louie, S.G., Chelikowsky, J.R., Cohen, M.L.: Phys. Rev. Lett.34, 155 (1975)
Hybertsen, M.S., Louie, S.G.: Phys. Rev. B35, 5585 (1987)
Onodera, Y.: Prog. Theor. Phys.49, 37 (1973)
Sinha, S.K., Gupta, R.P., Price, D.L.: Phys. Rev. B9, 2654 (1974)
Barišić, S.: Phys. Rev. B5, 932 and 941 (1972)
Hanke, W.: Phys. Rev. B8, 4585 and 4591 (1973)
For more details see the review article by Hanke, W.: Adv. Phys.27, 287 (1978)
Nozières, P., Pines, D.: Phys. Rev.109, 741 and 762 (1958); Il Nuovo Cimento9, 470 (1958)
Van Vechten, J.A., Martin, R.P.: Phys. Rev. Lett.28, 446 (1972)
Županović, P., Bjeliš, A., Barišić, S.: (to be published)
Cohen, M.H., Keller, F.: Phys. Rev.99, 1128 (1955)
For simplicity, we assume that the Fermi level crosses only one set of degenerate bands (i.e. not more than three bands in a cubic lattice). The generalization to an accidental crossing of more sets with different symmetries is straightforward
Landau, L.D., Lifshitz, E.M.: Quantum Mechanics (Non-Relativistic Theory). Oxford, New York: Pergamon Press 1980
Knox, R.S.: Theory of Excitons. New York: Academic Press 1963
Note that the Wannier excitons, i.e. the discrete bound states at the edges of interband electron-hole continua, follow from the inclusion of the extended RPA (ladder) terms in (3) [see also Hanke, W., Sham, L.J.: Phys. Rev. B12, 4501 (1975)]. The straightforward generalization of the present approach in this direction shows that the dipolar collective modes and the Wannier excitons can coexist [13]
Anderson, P.W.: Concepts in Solids. New York, Amsterdam: W.A. Benjamin 1964
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Županovic, P., Bjelis, A. & Barišić, S. The tight-binding approach to the dielectric response in the multiband systems. Z. Physik B - Condensed Matter 97, 113–118 (1995). https://doi.org/10.1007/BF01317594
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DOI: https://doi.org/10.1007/BF01317594