Vibrational modes of negatively charged silicon-vacancy centers in diamond from ab initio calculations

TL;DR

This study uses ab initio density functional theory to analyze vibrational modes of negatively charged silicon-vacancy centers in diamond, revealing key vibrational resonances and their isotopic shifts relevant for quantum photonics.

Contribution

It provides detailed identification of vibrational modes and their isotopic shifts in SiV centers using large-scale supercell calculations, advancing understanding of their vibrational properties.

Findings

Identification of two main quasi-local vibrational modes with specific symmetries.

Isotopic shifts in vibrational modes explain experimental vibronic features.

Vibrational frequency changes in excited states account for shifts in zero-phonon line energy.

Abstract

Silicon-vacancy (SiV) center in diamond is a photoluminescence (PL) center with a characteristic zero-phonon line energy at 1.681 eV that acts as a solid-state single photon source and, potentially, as a quantum bit. The majority of the luminescence intensity appears in the zero-phonon line; nevertheless, about 30\% of the intensity manifests in the phonon sideband. Since phonons play an essential role in the operation of this system, it is of importance to understand the vibrational properties of the SiV center in detail. To this end, we carry out density functional theory calculations of dilute SiV centers by embedding the defect in supercells of a size of a few thousand atoms. We find that there exist two well-pronounced quasi-local vibrational modes (resonances) with $A_{2u}$ and $E_u$ symmetries, corresponding to the vibration of the Si atom along and perpendicular to the defect symmetry axis, respectively. Isotopic shifts of these modes explain the isotopic shifts of prominent vibronic features in the experimental SiV PL spectrum. Moreover, calculations show that the vibrational frequency of the $A_{2u}$ mode increases by about 30\% in the excited state with respect to the ground state, while the frequency of the $E_u$ mode increases by about 5\%. These changes explain experimentally observed isotopic shifts of the zero-phonon line energy. We also emphasize possible dangers of extracting isotopic shifts of vibrational resonances from finite-size supercell calculations, and instead propose a method to do this correctly.