Density functional theory study on magnetically detecting positively charged nitrogen-vacancy center in diamond

Abstract

A quantum-chemical study of the positive charge-state of the nitrogen-vacancy center in diamond is presented. Charge control of this promising qubit candidate is a focus of diamond quantum technology research, as currently charge stability relating to surfaces and nearby defects causes some difficulties for quantum applications. To demonstrate full charge control over the nitrogen vacancy, all three charge states should be identified and the processes that lead to charge state changes understood. However, experimental markers for the positive state remain elusive compared to the readily detectable zero-phonon lines of the neutral and negative. In this work we present predicted hyperfine and zero-field splitting tensors as clear signatures of the normally spinless ${\mathrm{NV}}^{+}\phantom{\rule{4pt}{0ex}}(^{1}\mathrm{A}_{1}$ ground state) by probing a long-lived spin-triplet excited-state $\ensuremath{\sim}0.7$ eV above the ${\mathrm{NV}}^{+}$ ground state. We find a relatively narrow excitation energy range of approximately 0.7--1.1 eV between excitation into an $^{3}\mathrm{E}$ state and conversion into the neutral charge state. To provide insight into the thermal stability of the positive charge state, we have calculated binding and diffusion energies for both charged and uncharged systems. We predict, given that the activation energies are only weakly charge state dependent, all three charge states would diffuse in the 1600--$1900{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\text{C}$ range, but the positive state has a significantly lower binding energy, suggesting that it will dissociate at temperatures around $1000{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$ rather than migrate.