Experiments with the negatively charged nitrogen vacancy (N$V^-$) in diamond highlight this defect's promise for coherent storage of quantum information. They have also spurred investigations of other color centers in diamond formed by defects that consist of Group IV element (Si, Ge, Sn, Pb) and vacancies which have different atomic structure than the N$V^-$ center. To date, these other color centers have not exhibited coherence quite as impressive as that of the N$V^-$ center. Spectral diffusion and the low Debye-Waller factor are important limitations of the N$V^-$ center that make investigation of the other color centers necessary to advance the field. In this work we use density-functional theory (DFT) to study the thermodynamics and kinetics associated with the N$V$, Si$V$, Ge$V$, Sn$V$ and Pb$V$ color centers in diamond. We find agreement between our theoretical calculations and the charge state of various color centers as observed in intrinsic diamond. We determine the Fermi level values that enhance the production of isolated color centers, which may lead to longer coherence times than their present values.
Experiments with the negatively charged nitrogen vacancy (NV−) in diamond highlight this defect's promise for coherent storage of quantum information. They have also spurred investigations of other color centers in diamond formed by defects that consist of Group IV element (Si, Ge, Sn, Pb) and vacancies which have different atomic structure than the NV− center. To date, these other color centers have not exhibited coherence quite as impressive as that of the NV− center. Spectral diffusion and the low Debye-Waller factor are important limitations of the NV− center that make investigation of the other color centers necessary to advance the field. In this work we use density-functional theory (DFT) to study the thermodynamics and kinetics associated with the NV, SiV, GeV, SnV and PbV color centers in diamond. We find agreement between our theoretical calculations and the charge state of various color centers as observed in intrinsic diamond. We determine the Fermi level values that enhance the production of isolated color centers, which may lead to longer coherence times than their present values.
Color centers play an important role in the development of diamond based devices, both for quantum technological applications as well as sensing applications. 1 Most elements of the periodic table have been considered as color center in diamond at some point in the past, even lanthanides like Eu, due to their sharp spectral properties. 2 Group-IV color centers have more recently gained attention due to their excellent Debye-Waller factor, making them very suitable for optically based quantum applications. However, practical diamond based devices contain several sources of strain, which result in a shifting of the zero-phonon line depending on the type of strain and magnitude experienced by the color center. 3,4 Using density functional theory calculations, we investigate the impact of isotropic and anisotropic strain on the GeV and SnV centers in diamond, with the aim of understanding the experimentally observed distributions of ZPL positions. Using defect concentrations of 1.5% down to 0.1% (64-1000 atom conventional cells) we show that it is possible to extrapolate to experimentally relevant concentrations. 3,4 The calculated ZPL position and strain-induced shifts are presented for both neutral and negatively charged color centers. For the GeV 0 color center, both red and blue shifts are obtained for isotropic strain, while anisotropic strain only gives rise to a redshift. In case of the latter, the absolute magnitude of the shift is also significantly larger. 3 In case of the SnV 0 and SnV-, the position of the ZPL shows a smaller dependence on the color center concentration. In contrast, the ZPL shift is larger than is obtained for the GeV 0 color center. We also note that the impact of the charge state is rather non-trivial. The calculated results are discussed within the context of the experimental observation of distributions of ZPL positions for the SnV and GeV centers. We highlight some of the pitfalls when comparing calculated and experimental results, and indicate how further experimental-theoretical studies can provide insights into the black box of experimentally doped samples.
Color centers in diamonds have emerged as a promising candidate for quantum information and quantum computing applications. Compared to the well-known and widely studied nitrogen-vacancy ${\mathrm{N}}_{\mathrm{C}}\text{\ensuremath{-}}{\mathrm{V}}_{\mathrm{C}}$ (NV) color center with C3v symmetry, the group-IV vacancy color centers ${\mathrm{V}}_{\mathrm{C}}\text{\ensuremath{-}}X\text{\ensuremath{-}}{\mathrm{V}}_{\mathrm{C}}$ (XV, X=Si, Ge, Sn, Pb), exhibit structures with the D3d symmetry, which give rise to more stable coherent optical transitions for the zero-phonon line (ZPL) due to its inversion symmetry. Moreover, it is experimentally found that the ZPL peak of XV centers increases from Si to Sn to Ge to Pb, i.e., it does not vary monotonically with the atomic numbers. So far, the physical origin of the unusual local structures and the abnormal trend of ZPL of the XV centers are not well understood. In this paper, based on density-functional theory calculations and symmetry analysis, we demonstrate that the large size of the X atoms plays a dominant role in moving the X atoms away from the substitution site to the bond-center site between the two carbon vacancies to form the D3d structure that can effectively reduce the local strain energy. Meanwhile, we find that the abnormal trends of ZPL of the XV centers derive from a competition of the $p\ensuremath{-}p$ coupling and $p\ensuremath{-}d$ coupling between X atoms and the divacancy based on the band-coupling mechanism. Our study, therefore, provides insights into the origin of the abnormal trends of ZPL and the local structure of XV centers in diamonds.
The elucidation of the mechanism of SnV− formation in diamond is especially important as the SnV− color center has the potential to be a superior single-photon emitter when compared to the NV and to other Group IV impurity-vacancy color centers in diamond. The typical formation of SnV involves placing Sn in diamond by ion implantation, but the formation of a charged SnV species requires an additional complication. This complication is related to the energy cost associated with electronic transitions within the host diamond. Effectively, producing the SnV− charge state using an electron obtained from a band edge of the host diamond is less energetically favorable than having the SnV− receive an electron from a neighboring donor dopant. Among donor dopants, substitutional N (NC) is always present in even the purest synthetic or natural diamond sample. The mechanism of electron donation by NC has been proposed by Collins for charging the NV in diamond and it has been used to interpret many experimental results. Therefore, in this paper, we use density functional theory (DFT) to explore the pathways for the formation of the SnV− charge state due to electron donation arising from the presence of NC in the host diamond. Explicitly, defect concentrations are calculated in equilibrium in each of the explored pathways to determine the yield of the SnV− throughout each of the pathways. The importance of our work is to suggest experimental ways of enhancing the yield of charged states like the SnV− in diamond for transformative applications in optoelectronics and quantum information.
Diamond color centers are considered as viable candidates for solid state qubits and single photon sources for quantum technological applications ranging from quantum sensing to quantum information processing [1]. Color centers are created through ion beam implantation or incorporation during chemical vapor deposition. This way most elements of the periodic table have been considered at some point in the past, even lanthanides like Eu, due to their sharp spectral properties [2]. However, in recent years, group-IV color centers have been gaining attention due to their excellent Debye-Waller factor, making them very suitable for optically based quantum applications. In such applications, a sharp and robust zero-phonon line (ZPL) are prime qualities sought after. Unfortunately, practical diamond based devices contain several sources of strain, originating from the ion beam implantation and annealing during device fabrication. This strain results in a shifting of the ZPL depending on the type of strain and magnitude experienced by the color center [3,4,5]. Using density functional theory (DFT) calculations, the impact of isotropic and anisotropic strain on the GeV and SnV centers in diamond is investigated, with the aim of understanding the experimentally observed distributions of ZPL positions. By using defect concentrations of 1.5% down to 0.1% (64-1000 atom conventional cells) we show that it is possible to extrapolate to experimentally relevant concentrations [3,4,5]. The calculated ZPL position and strain-induced shifts are presented for both neutral and negatively charged color centers. For the GeV 0 color center, both red and blue shifts are obtained for isotropic strain, while anisotropic strain only gives rise to a redshift. In case of the latter, the absolute magnitude of the shift is also significantly larger [3]. In case of the SnV 0 and SnV-, the position of the ZPL shows a smaller dependence on the color center concentration. In contrast, the ZPL shift for SnV centers is larger than the one obtained for the GeV 0 color center [4,5]. We also note that the impact of the charge state is rather non-trivial. The calculated results are discussed within the context of the experimental observation of distributions of ZPL positions for the SnV and GeV centers [3,4]. We highlight some of the pitfalls when comparing calculated and experimental results, and indicate how further experimental-theoretical studies can provide insights into the black box of experimentally doped samples [4,5].
The elucidation of the mechanism of SnV− formation in diamond is especially important as the SnV− color center has the potential to be a superior single-photon emitter when compared to the NV and to other Group IV color centers. The typical formation of the SnV involves placing Sn in diamond by ion implantation, but the formation of a charged SnV species requires an additional complication. This complication is related to the energy cost associated with electronic transitions within the host diamond. Effectively, producing the SnV− charge state using an electron obtained from a band edge of the host diamond is less energetically favorable than having the SnV− receive an electron from a neighboring donor dopant. Among donor dopants, substitutional N (NC) is always present in even the purest synthetic or natural diamond sample. The mechanism of electron donation by NC has been proposed by Collins for charging the NV in diamond and it has been used to interpret many experimental results. Therefore, in this paper we use DFT to explore the pathways for the formation of the SnV− charge state due to electron donation arising from the presence of NC in the host diamond. Explicitly, defect concentrations are calculated in equilibrium in each of the explored pathways to determine the yield of the SnV− throughout each of the pathways. The importance of our work is to suggest experimental ways of enhancing the yield of charged states like the SnV− in diamond for transformative applications in optoelectronics and quantum information.
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.