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Many-body theory of effective mass in degenerate semiconductors

G. S. Tripathi

Department of Physics, Berhampur University, Berhampur 760007, Odisha, India

E-mail Address: g.s.tripathi@hotmail.com

Corresponding author.

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S. K. Shadangi

Department of Physics, Berhampur University, Berhampur 760007, Odisha, India

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https://doi.org/10.1142/S0217979218500820Cited by:0 (Source: Crossref)

Abstract

We derive the many-body theory of the effective mass in the effective mass representation (EMR). In the EMR, we need to solve the equation of motion of an electron in the presence of electron–electron interactions, where the wavefunction is expanded over a complete set of Luttinger–Kohn wavefunctions. We use the Luttinger–Ward thermodynamic potential and the Green’s function perturbation to derive an expression for the band effective mass by taking into account the electron–electron interactions. Both quasi-particle and the correlation contributions are considered. We show that had we considered only the quasi-particle contribution, we would have missed important cancellations. Thus the correlated motion of electrons has important effects in the renormalization of the effective mass. Considering the exchange self-energy in the band model, we derive a tractable expression for the band effective mass. We apply the theory to n-type degenerate semiconductors, PbTe and SnTe, and analyze the impact of the theory on the anisotropic effective mass of the conduction bands in these systems.

Keywords:

PACS: 71.45.Gm, 71.18.+y, 71.20.Nr, 71.70.Ej

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