## THE TIGHT-BINDING APPROACH TO THE DIELECTRIC RESPONSE IN THE MULTIBAND SYSTEMS (1995)

### BibTeX

@MISC{Zupanović95thetight-binding,

author = {P. ˇ Zupanović},

title = {THE TIGHT-BINDING APPROACH TO THE DIELECTRIC RESPONSE IN THE MULTIBAND SYSTEMS},

year = {1995}

}

### OpenURL

### 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 plane-wave 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 sys-1 tems, are identified as a combined effect of intra-atomic exchange interactions between electrons sitting in different orbitals and a finite inter-atomic tunneling. PACS: 71.10.+x, 71.45.Gm Key words: random phase approximation, dielectric matrix, collective modes, selfpolarization corrections 2 1

### Citations

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Citation Context ..., 71.45.Gm Key words: random phase approximation, dielectric matrix, collective modes, selfpolarization corrections 21 Introduction Random phase approximation (RPA) is the well-known textbook method =-=[1]-=- for treating the dielectric properties of the weakly interacting electron liquids. Unfortunately the widely used [2 - 5] extension of this method to the multiband systems leads to a cumbersome proble... |

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Citation Context ...hat take part in p-th transition. Inserting this expression together with αc = 0 into eqs.(19,20), one 11gets the dipolar collective modes whose spectrum just coincides with that of Frenkel excitons =-=[17]-=-. It should be noted in this respect that the present RPA result is valid in the weak coupling regime [18]. We remind that the same spectrum is obtained [19] in the opposite strong coupling regime whe... |

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Citation Context ...st coincides with that of Frenkel excitons [17]. It should be noted in this respect that the present RPA result is valid in the weak coupling regime [18]. We remind that the same spectrum is obtained =-=[19]-=- in the opposite strong coupling regime when the bandwidths are negligible with respect to the on-site Coulomb repulsion Vpr(R = 0) between two electrons on different orbitals (i. e. the R = 0 contrib... |

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For more details see the review article by
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Citation Context ...6, 7, 9], i. e. in the calculation of the RPA multiband polarizabilities which appear in the matrix elements ε G,G ′. This led to some simplifications in inverting the dielectric matrix ε G,G ′(q, ω) =-=[10]-=-. We point out below some crucial advantages of the present direct TB representation. We start by calculating the mean values of the components ∑ ρll ′(q, t) ≡ 2 < a k + l (k, t)a ′(k+q, l t) > (1) of... |

1 |
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Citation Context ...at first take into account only the two-site terms in the eq.(5). An analogous procedure can be carried out for any crystal symmetry. We distinguish the following three types of dominant lattice sums =-=[14]-=- in the multipole expansion of the various matrix elements Vpr(q → 0). For both p and r representing intraband transitions [i.e. the transitions within 7partially filled bands, with p = (l1, l1) and ... |

1 |
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(Show Context)
Citation Context ...gets the dipolar collective modes whose spectrum just coincides with that of Frenkel excitons [17]. It should be noted in this respect that the present RPA result is valid in the weak coupling regime =-=[18]-=-. We remind that the same spectrum is obtained [19] in the opposite strong coupling regime when the bandwidths are negligible with respect to the on-site Coulomb repulsion Vpr(R = 0) between two elect... |