Spin splitting of two dimensional states in the conduction band of asymmetric heterostructures: contribution from the atomically sharp interface

TL;DR

This paper analyzes how atomically sharp interfaces influence spin splitting in two-dimensional electron states in asymmetric heterostructures, incorporating boundary conditions, spin-orbit effects, and electric fields to match experimental observations.

Contribution

It introduces a boundary condition model accounting for atomic-scale interface effects, including spin-orbit interaction, to explain spin splitting in 2D heterostructures.

Findings

Interfacial effects renormalize Dresselhaus and Rashba constants.

Off-diagonal g-factor components depend linearly on magnetic field and Landau level.

Model qualitatively agrees with experimental data.

Abstract

The effect of an atomically sharp impenetrable interface on the spin splitting of the spectrum of two-dimensional electrons in heterostructures based on (001) III-V compounds has been analyzed. To this end, the single band Hamiltonian $\Gamma_{6c}$ for envelope functions is supplemented by a general boundary condition taking into account the possibility of the existence of Tamm states. This boundary condition also takes into account the spin-orbit interaction, the asymmetry of a quantum well, and the lack of inversion symmetry in the crystal and contains the single phenomenological length $R$ characterizing the structure of the interface at atomic scales. The model of a quasitriangular well created by the electric field $F$ has been considered. After the unitary transformation to zero boundary conditions, in the modified Hamiltonian interfacial contribution appears, from which the two-dimensional spin Hamiltonian is obtained through averaging over the fast motion along the normal. In the absence of magnetic field $\boldsymbol B$, this contribution is the sum of the Dresselhaus and the Bychkov-Rashba terms with the constants renormalized owing to the interfacial contribution. In the field $\boldsymbol B$ containing the quantizing component $B_z$, the off - diagonal (in cubic axes) components of the $g$-factor tensor are linear functions of $|B_z|$ and the number of the Landau level $N$. The results are in qualitative agreement with the experimental data.