Valence-band mixing in first-principles envelope-function theory

Abstract

This paper presents a numerical implementation of a first-principles envelope-function theory derived recently by the author ͓B. A. Foreman, Phys. Rev. B 72, 165345 ͑2005͔͒. The examples studied deal with the valence subband structure of GaAs/ AlAs, GaAs/ Al 0.2 Ga 0.8 As, and In 0.53 Ga 0.47 As/ InP ͑001͒ superlattices calculated using the local-density approximation to density-functional theory and norm-conserving pseudopotentials without spin-orbit coupling. The heterostructure Hamiltonian is approximated using quadratic-response theory, with the heterostructure treated as a perturbation of a bulk reference crystal. The valence subband structure is reproduced accurately over a wide energy range by a multiband envelope-function Hamiltonian with linear renormalization of the momentum and mass parameters. Good results are also obtained over a more limited energy range from a single-band model with quadratic renormalization. The effective kinetic-energy operator ordering derived here is more complicated than in many previous studies, consisting in general of a linear combination of all possible operator orderings. In some cases, the valence-band Rashba coupling differs significantly from the bulk magnetic Luttinger parameter. The splitting of the quasidegenerate ground state of no-common-atom superlattices has non-negligible contributions from both short-range interface mixing and long-range dipole terms in the quadratic density response.

Reliable k⋅p band structure calculation for nanostructures using finite elements

“…In contrast, the k·p envelope function method can be formulated as a partial differential equation system and therefore allows to determine the band structure efficiently using standard numerical techniques. Various simplifications during the perturbative treatment of remote bands obfuscate physical details, such as intervalley-and interface mixing [1,2]. This leads to an ongoing dispute about the precision and validity of the obtained results [3][4][5][6] where the raised arguments apply to the commonly used k·p standard model.…”

Valence‐band effective‐potential evolution for coupled holes

“…It is worthwhile to recall that there had also been several theoretical attempts to spread light on the effective-potential dependency as k T increases [11,12]. However, we do believe that ''monitoring'' the quadratic eigenvalue problem (QEP) via the root-locus-like procedure [9] and plotting the metamorphosis of V eff seem a promising way to get a better insight into a complicated phenomenon referred to as valence-band mixing.…”

“…Some authors had declared a shift upward in energy of the bound states in the effectivepotential well as the transverse wave vector increases [11]. Recently, a valence-band-mixing first-principle theory within the EFA was proposed, which approximated the superlattice potential energy by considering only the linear and quadratic responses to the heterostructure perturbation [12].…”

“…2 Basic theoretical formulation An effective potential is found useful to describe valence-band mixing in the EFA [12]. In the case envisioned here, to determine the operator b W eff for the effective band offset potential, it suffices to use the KL model Hamiltonian [1], considering the transverse quasi-momentumk T ¼ k xêx þ k yêy , because this is the direction of the Brillouin zone where the present KL Hamiltonian is described.…”

Properties of a charge in the nanoheterosystems with quantum wells and barriers

“…A number of works is devoted to the heterostructures with interface planes GaAs/AlAs in which the layers of AlAs are placed in crystals GaAs or vice versa [1][2][3][4]. Electronic properties of such heterostructures are associated with electrons of the Γ-valley of the band spectrum.…”