Polarization-dependent density-functional theory and quasiparticle theory: Optical response beyond local-density approximations
- Department of Physics, Ohio State University, 174 West 18th Avenue, Columbus, Ohio 43210-1106 (United States)
The polarization ({ital P}) dependence of the exchange-correlation energy ({ital E}{sub {ital xc}}) of semiconductors results in an effective field ({partial_derivative}{sup 2}{ital E}{sub {ital xc}}/{partial_derivative}{ital P}{sup 2}){ital P}{equivalent_to}{gamma}{sub 1}{ital P} in the Kohn-Sham equations [Gonze {ital et} {ital al}., Phys. Rev. Lett {bold 74}, 4035 (1995)]. This effective field is absent in local-density approximations such as LDA and GGA. We show that in the long-wavelength limit {gamma}{sub 1}{approx_equal}{chi}{sub {ital LDA}}{sup {minus}1}{minus}{chi}{sub {ital expt}}{sup {minus}1} where {chi} is the linear susceptibility. We find that {gamma}{sub 1} scales roughly linearly with average bond length suggesting a {ital simple}, {ital weakly} {ital material}-{ital dependent} function {ital E}{sub {ital xc}}[{ital P}]. For medium-gap group IV and III-V semiconductors {gamma}{sub 1} is remarkably constant: {gamma}{sub 1}={minus}0.25{plus_minus}0.05. Using the average LDA band gap mismatch {Delta} and the average quasiparticle gap {ital E}{sub {ital g}} a simplified quasiparticle approach yields {chi}{sub {ital LDA}}{sup {minus}1}{minus}{chi}{sub {ital QP}}{sup {minus}1}{approx_equal}{minus}{Delta}/({ital E}{sub {ital g}}{chi})={minus}0.27 {asterisk}0.10 in good agreement with the value of {gamma}{sub 1}. However, for materials containing first-row elements (B,C,N,O) {gamma}{sub 1} varies by a factor of 2 while {Delta}/({ital E}{sub {ital g}}{chi}) is roughly constant. That is, the simple quasiparticle estimate fails to reproduce the polarization dependence of {ital E}{sub {ital xc}}[{ital P}]. For nonlinear response functions, an analysis of {ital E}{sub {ital xc}}[{ital P}] leads to Miller-like expressions {chi}{sub {ital expt}}{sup ({ital n})}{approx_equal}[{chi}{sub {ital expt}}/{chi}{sub {ital LDA}}]{sup {ital n}+1 }{chi}{sub {ital LDA}}{sup ({ital n})}, {ital n}= 2, 3, where the formula for {chi}{sup (3)} is valid only when {chi}{sup (2)}=0.
- OSTI ID:
- 390380
- Journal Information:
- Physical Review, B: Condensed Matter, Vol. 54, Issue 12; Other Information: PBD: Sep 1996
- Country of Publication:
- United States
- Language:
- English
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