Effect of the spin-orbit interaction and the electron phonon coupling on the electronic state in a silicon vacancy

TL;DR

This study investigates how spin-orbit interaction and electron-phonon coupling influence the electronic states around silicon vacancies, revealing extended charge states and splitting of degeneracies that explain experimental elastic softening behaviors.

Contribution

It introduces a Green's function approach to analyze vacancy states, incorporating spin-orbit and electron-phonon effects, and explains experimental observations of elastic softening in silicon.

Findings

Charge states are widely extended, causing large elastic softening.

Spin-orbit coupling splits degeneracies into distinct ground and excited states.

Electron-phonon coupling leads to a ground state responsible for magnetic-field effects.

Abstract

The electronic state around a single vacancy in silicon crystal is investigated by using the Green's function approach. The triply degenerate charge states are found to be widely extended and account for extremely large elastic softening at low temperature as observed in recent ultrasonic experiments. When we include the LS coupling $\lambda_{\rm Si}$ on each Si atom, the 6-fold spin-orbital degeneracy for the $V^{+}$ state with the valence +1 and spin 1/2 splits into $\Gamma_{7}$ doublet groundstates and $\Gamma_{8}$ quartet excited states with a reduced excited energy of $O(\lambda_{\rm Si}/10)$. We also consider the effect of couplings between electrons and Jahn-Teller phonons in the dangling bonds within the second order perturbation and find that the groundstate becomes $\Gamma_{8}$ quartet which is responsible for the magnetic-field suppression of the softening in B-doped silicon.