The Group-IV-Vacancy Color Center in Diamond

TL;DR

The work provides a refined, self-consistent theoretical framework for Group-IV vacancy centers in diamond, unifying intrinsic interactions (spin-orbit coupling and electron-phonon coupling) with external controls (strain, electric, light, and magnetic fields) to enable predictable quantum behavior. It derives the electronic hole orbitals from the six X–C bonds, clarifies the four energy manifolds and their ordering, and formulates a two-mode electron-phonon coupling in the hole basis, complemented by a central-field spin-orbit term with material-dependent λ_X. A key novelty is the joint-reflection symmetry, which explains degeneracies under transverse magnetic fields and links strain to orbital spin dynamics, offering a route to strain sensing and Stark-shift predictions. The framework reconciles prior modeling discrepancies (Hepp, Thiering, Meesala) by refining the quench-factor approach and providing analytic and numerical tools for spectra, transitions, and external-field responses, thereby advancing the engineering of XV centers for quantum information processing.

Abstract

Group-IV vacancy (G4V, or XV, where X = Si, Ge, Sn, Pb) color centers constitute a novel and promising class of defects in diamonds. This chapter reviews and refines the theoretical models for the XV systems, encompassing the intrinsic interactions, including spin-orbit coupling and electron-phonon interactions, and the external interactions involving strain, electric, light, and magnetic fields. Based on the refined model, we predict their properties, explain the experimental data, and suggest follow-up experiments. This article established a solid foundation for controlling the XV system, thus paving the way for quantum information processing.

Figures (9)

• Figure 1: Atomic structure of the XV center in diamond. (a) The unit cell of the diamond crystal, where $a_0 = 3.567 \, \text{\r{A}}$ is the diamond lattice constant. (b) The atomic structure of the XV center. The two transparent spheres indicate the positions of the missing carbon atoms, while the solid brown sphere represents the X atom. The six solid blue spheres surrounding the X atom represent the six nearest carbon atoms. Adapted from Ref. HeppThesis.
• Figure 2: The X–C bonds as the basis states ($\{\ket{\sigma_i}\}$) for representing the electronic orbital states. (a) The arrangement of the X–C bonds and the Cartesian coordinate system for the XV center system. Adapted from Ref. thiering2018ab. (b) Sketch of the speculated shape of the electron orbital of an X–C bond. It is formed by combining an $sp^3d^2$ hybridized orbital from the X atom with an $sp^3$ hybridized orbital from the carbon atom, resembling a $\sigma$ covalent bond. The black dots represent the X and carbon nuclei, while the red (blue) color in the electron orbital indicates the positive (negative) phase of the orbital components. A local Cartesian coordinate system $\{x_i, y_i, z_i\}$ for the $i$-th carbon atomic core $C_i$ is also shown. The $z_i$-axis is aligned along the X–C bond direction.
• Figure 3: Illustrations of the eigenstates in the $+z$ half of the XV center: (a) $\ket{\psi_{0}^{\rm upp}}$, (b) $\ket{\psi_{x}^{\rm upp}}$, and (c) $\ket{\psi_{y}^{\rm upp}}$. Red (blue) shading represents the $+$ ($-$) phase of the corresponding part of the eigenstate, and the color intensity reflects the wavefunction population. Black dots denote the X and carbon atomic cores.
• Figure 4: Dimensions of the XV system. The three carbon atoms and their corresponding dangling bonds on the $+z$ ($-z$) sides are depicted in dark blue (light blue). The central X atom is shown in yellow. Here, $a_0$ denotes the diamond lattice constant, same as shown in Fig. \ref{['fig:XV_structure']}.
• Figure 5: Shape of the orbitals of eigenstates (a) $\ket{\psi_{+,+1}}$ and (b) $\ket{\psi_{-,+1}}$. The state $\ket{\psi_{+,+1}}$ has no node on the $z=0$ plane, while the state $\ket{\psi_{-,+1}}$ does. The state $\ket{\psi_{+,+1}}$ corresponds to the second-to-top energy state of an electron or the first-excited state of the hole. The state $\ket{\psi_{-,+1}}$ corresponds to the top energy state of an electron or the ground state of the hole. Different colors represent different phases of the orbital components.