Excited states of a phosphorus pair in silicon: Effects of valley-orbital interaction and electron-electron interactions

TL;DR

This study combines first-principles calculations with quantum chemistry to analyze the excited states of phosphorus pairs in silicon, revealing valley-orbital interactions' effects on optical and charge-transfer states relevant for quantum technologies.

Contribution

It introduces a comprehensive framework integrating band-structure and quantum chemistry to accurately model impurity pair excitations in silicon, including valley effects and new low-energy excitations.

Findings

Valley-orbital interactions open a gap between 1s and 2p transitions.

Charge-transfer states appear in triplet sectors due to valley degrees of freedom.

Predicted new excitations below 20 meV not previously analyzed.

Abstract

Excitations of impurity complexes in semiconductors can not only provide a route to fill the terahertz gap in optical technologies, but can also connect local quantum bits to scale up solid-state quantum-computing devices. However, taking into account both the interactions among electrons/holes, and the host band structures, is challenging. Here we combine first-principles band-structure calculations with quantum-chemistry methodology to evaluate the ground and excited states of a pair of phosphorous donors in silicon within s single framework. We use a broken-symmetry Hartree-Fock approach, followed by a time-dependent Hartree-Fock method to compute the excited states. Our Hamiltonian for each valley includes an anisotropic kinetic energy term, which splits the 2p_0 and 2p_+- transitions of isolated donors by ~4 meV, in good agreement with experiments. Our single-valley calculations show the optical response is a strong function of the optical polarisation, and suggest the use of valley polarisation to control optics and reduce oscillations in exchange interactions. When taking into account all valleys, including valley-orbital interactions, we find a gap opens between the 1s to 2p transition and low-energy charge-transfer states within 1s manifolds (which become optically allowed because of inter-donor interactions). In contrast to the single-valley case, we find charge-transfer excited states also in the triplet sector, thanks to the valley degrees of freedom. These states have a qualitatively correct energy as compared with the previous experiments; additionally, we predict new excitations below 20 meV that have not been analysed previously. A statistical average of nearest-neighbour pairs at different separations suggests that THz radiation could be used to excite pairs spin-selectively. Our approach can readily be extended to other donors and to other semiconducting hosts.