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

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 has been analyzed. To this end, the single-band Hamiltonian Г6 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 noncentrosymmetricity of the crystal and contains the single phenomenological length $R$ characterizing the structure of the interface at atomic scales. The model of a quasi-triangular well created by the field $F$ has been considered. After the unitary transformation to zero boundary conditions, the modified Hamiltonian contains an interface contribution from which the two-dimensional spin Hamiltonian is obtained through averaging over the fast motion along the normal. In the absence of magnetic field $\boldsymbol{\mathrm B}$, this contribution is the sum of the Dresselhaus and Bychkov–Rashba terms with the constants renormalized owing to the interface contribution. In the field $\boldsymbol{\mathrm B}$ 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.