Large change in biaxial anisotropy of in-plane hole dispersion in a (110) quantum well under [110] uniaxial stress

We present a theoretical study of a valence-subband dispersion in a (110)-oriented quantum well (QW) under [110] uniaxial stress. As an example, we present calculated results for a (110) GaAs QW. The $4\times 4$ Luttinger-Kohn $\mathbf{k}\cdot \mathbf{p}$ Hamiltonian in conjunction with the Bir-Pikus strain Hamiltonian is solved within the infinitely high barrier model in order to obtain the in-plane dispersion curves of valence subbands. Then, confinement energies, effective masses along the two orthogonal in-plane directions ([001] and $\left[1¯10\right]),$ and optical matrix elements for [001] and $\left[1¯10\right]$ polarized light are obtained at zero in-plane momentum ${(k}_{\parallel }=0)$ and are plotted as functions of the [110] uniaxial stress. The confinement energies of the first two subbands show anticrossing behavior as functions of the stress. Due to the drastic change in valence-band mixing near the anticrossing, the effective masses of the two subbands show changes in their signs, magnitudes, and in-plane anisotropies. The most outstanding point is the saddle-point character of the first hole subband at $k_{\parallel }=0,$ which appears under the stress corresponding to the anticrossing and under the larger stress. An intimate relation is shown between the biaxial anisotropy in optical matrix elements and that in the hole effective mass. A simple model based on the tight-binding approximation is presented for understanding the intimate relation between them.