We discuss the choice and implementation of inter-valley potentials in the so-called two bands k⋅p model for the opposite X, Y or Z valleys of silicon. We focus on the description of valley splittings in Si/SiGe heterostructures for spin qubits, with a particular attention to alloy disorder. We demonstrate that the two bands k⋅p model reproduces the valley splittings of atomistic tight-binding calculations in relevant heterostructures (SiGe spikes, wiggle wells...), yet at a much lower cost. We show that the model also captures the effects of valley-orbit mixing and yields the correct inter-valley dipole matrix elements that characterize manipulation, dephasing and relaxation in spin/valley qubits. We simulate a realistic Si/SiGe spin qubit device as an illustration, and discuss electron-phonon interactions in the two bands k⋅p model. Beyond spin qubits, this model enables efficient simulations of SiGe heterostructure devices where spin and valley physics are relevant.
@article{arxiv.2511.20153,
title = {Valley physics in the two bands $\mathbf{k}\cdot\mathbf{p}$ model for SiGe heterostructures and spin qubits},
author = {Tancredi Salamone and Biel Martinez Diaz and Jing Li and Lukas Cvitkovich and Yann-Michel Niquet},
journal= {arXiv preprint arXiv:2511.20153},
year = {2026}
}