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Straining Group-IV Vacancy Color Centers in Diamond: A DFT study of the ZPL position and shift

Thijs G. I. van Wijk, Esin Aylin Melan, Rani Mary Joy, Paulius Pobedinskas, Emerick Yves Guillaume, Ken Haenen, Danny E. P. Vanpoucke

Published Jan 1, 2026• 0 citations
OpenAlex

Abstract

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.

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DFT modeling of strained group-IV color centers in diamond

Thijs G. I. van Wijk, Esin Aylin Melan, Rani Mary Joy +4 more

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].

•Jan 1, 2026•0 citations

Optimizing the Production of Single Color Centers in Diamond

Rodrick Kuate Defo, Efthimios Kaxiras, Steven L. Richardson

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.

arXiv:1905.10832•May 26, 2019•0 citations

Origin of structure and zero-phonon-line anomalies of XV centers in diamond (X=Si, Ge, Sn, Pb)

Chen Qiu, Hui‐Xiong Deng, Songyuan Geng +1 more

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 ${C}_{3v}$ symmetry, the group-IV vacancy color centers ${\mathrm{V}}_{\mathrm{C}}\text{\ensuremath{-}}X\text{\ensuremath{-}}{\mathrm{V}}_{\mathrm{C}}$ (XV, $X=\mathrm{Si}$, Ge, Sn, Pb), exhibit structures with the ${D}_{3d}$ 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 ${D}_{3d}$ 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.

Physical review. B./Physical review. B•Jun 26, 2023•14 citations

New insight into the spin-conserving excitation of the negatively charged nitrogen-vacancy center in diamond

Bei Deng, R. Q. Zhang, Xingqiang Shi

The negatively charged nitrogen-vacancy (N-V(-)) color center in diamond is an important solid-state single photon source for applications to quantum communication and distributed quantum computation. Its full usefulness relies on sufficient radiative emission of the optical photons which requires realizable control to enhance emission into the zero-phonon line (ZPL) but until now is still a challenge. Detailed understanding of the associated excitation process would be of essential importance for such objective. Here we report a theoretical work that probes the spin-conserving optical excitation of the N-V(-) center. Using density-functional-theory (DFT) calculations, we find that the ZPL and the phonon-side band (PSB) depend sensitively on the axial strain of the system. Besides, we find a relatively small PSB appearing at about 100 GPa in the emission spectrum at low temperatures, which provides a means to enhance the coherent emission of the N-V(-) center in quantum optical networks.

Scientific Reports•Jun 3, 2014•16 citations

Strain broadening of the 1042-nm zero phonon line of the NV− center in diamond: A promising spectroscopic tool for defect tomography

Timur Biktagirov, Alexander N. Smirnov, Валерий Александрович Давыдов +4 more

The negatively charged nitrogen-vacancy $({\mathrm{NV}}^{\ensuremath{-}})$ center in diamond is a promising candidate for many quantum applications. Here, we examine the splitting and broadening of the center's infrared (IR) zero-phonon line (ZPL). We develop a model for these effects that accounts for the strain induced by photodependent microscopic distributions of defects. We apply this model to interpret observed variations of the IR ZPL shape with temperature and photoexcitation conditions. We identify an anomalous temperature-dependent broadening mechanism and that defects other than the substitutional nitrogen center significantly contribute to strain broadening. The former conclusion suggests the presence of a strong Jahn-Teller effect in the center's singlet levels and the latter indicates that major sources of broadening are yet to be identified. These conclusions have important implications for the understanding of the center and the engineering of diamond quantum devices. Finally, we propose that, once the major sources of broadening are identified, the IR ZPL has the potential to be a sensitive spectroscopic tool for probing microscopic strain fields and performing defect tomography.

arXiv:1701.05631•Physical review. B./Physical review. B•Aug 18, 2017•16 citations

Observation of a 1.979-eV spectral line of a germanium-related color center in microdiamonds and nanodiamonds

Vladimir S. Krivobok, Евгений Алексеевич Екимов, Sergey G. Lyapin +4 more

Color centers in diamond are considered as a platform for quantum computing and communications, biomedical markers, and nanosensors. Negatively charged split-vacancy centers have outstanding properties due to bright and almost monochromatic luminescence, but they have poor spin coherence and relaxation times. This drawback is believed to be absent in the neutral charge state of the defects. So far only the neutral silicon-vacancy center has been observed in luminescence and absorption spectra. Here we report the observation of its germanium-based analog in luminescence spectra with the zero-phonon line (ZPL) at 1.979 eV in samples containing negatively charged ${\mathrm{GeV}}^{\ensuremath{-}}$ centers. The relationship between the center and Ge dopant is unambiguously confirmed by studies of $^{12}\mathrm{C}$ diamonds containing $^{70}\mathrm{Ge}$, $^{73}\mathrm{Ge}$, or $^{76}\mathrm{Ge}$ isotopes. The intensity ratio of the ZPL of these centers varies with the crystal size, and the intensity of the ${\mathrm{GeV}}^{0}$ centers reaches its maximum in samples 150 nm in size. In the vibronic sideband of this center the local vibrational mode with an energy of 23 meV was identified. The density functional theory calculations yield a ZPL energy value of the ${\mathrm{GeV}}^{0}$ center which is 150 meV higher than the experimentally observed one and matches the values of its relaxational energy as well as the local phonon mode frequency.

Physical review. B./Physical review. B•Apr 20, 2020•14 citations
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.
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].
Experiments with the negatively charged nitrogen vacancy (NV−V^-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 NV−V^-V− center. To date, these other color centers have not exhibited coherence quite as impressive as that of the NV−V^-V− center. Spectral diffusion and the low Debye-Waller factor are important limitations of the NV−V^-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 NVVV, SiVVV, GeVVV, SnVVV and PbVVV 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 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{C}_{3v}C3v​ symmetry, the group-IV vacancy color centers ${\mathrm{V}}_{\mathrm{C}}\text{\ensuremath{-}}X\text{\ensuremath{-}}{\mathrm{V}}_{\mathrm{C}}$ (XV, X=SiX=\mathrm{Si}X=Si, Ge, Sn, Pb), exhibit structures with the D3d{D}_{3d}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{D}_{3d}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 negatively charged nitrogen-vacancy (N-V(-)) color center in diamond is an important solid-state single photon source for applications to quantum communication and distributed quantum computation. Its full usefulness relies on sufficient radiative emission of the optical photons which requires realizable control to enhance emission into the zero-phonon line (ZPL) but until now is still a challenge. Detailed understanding of the associated excitation process would be of essential importance for such objective. Here we report a theoretical work that probes the spin-conserving optical excitation of the N-V(-) center. Using density-functional-theory (DFT) calculations, we find that the ZPL and the phonon-side band (PSB) depend sensitively on the axial strain of the system. Besides, we find a relatively small PSB appearing at about 100 GPa in the emission spectrum at low temperatures, which provides a means to enhance the coherent emission of the N-V(-) center in quantum optical networks.
The negatively charged nitrogen-vacancy $({\mathrm{NV}}^{\ensuremath{-}})$ center in diamond is a promising candidate for many quantum applications. Here, we examine the splitting and broadening of the center's infrared (IR) zero-phonon line (ZPL). We develop a model for these effects that accounts for the strain induced by photodependent microscopic distributions of defects. We apply this model to interpret observed variations of the IR ZPL shape with temperature and photoexcitation conditions. We identify an anomalous temperature-dependent broadening mechanism and that defects other than the substitutional nitrogen center significantly contribute to strain broadening. The former conclusion suggests the presence of a strong Jahn-Teller effect in the center's singlet levels and the latter indicates that major sources of broadening are yet to be identified. These conclusions have important implications for the understanding of the center and the engineering of diamond quantum devices. Finally, we propose that, once the major sources of broadening are identified, the IR ZPL has the potential to be a sensitive spectroscopic tool for probing microscopic strain fields and performing defect tomography.
Color centers in diamond are considered as a platform for quantum computing and communications, biomedical markers, and nanosensors. Negatively charged split-vacancy centers have outstanding properties due to bright and almost monochromatic luminescence, but they have poor spin coherence and relaxation times. This drawback is believed to be absent in the neutral charge state of the defects. So far only the neutral silicon-vacancy center has been observed in luminescence and absorption spectra. Here we report the observation of its germanium-based analog in luminescence spectra with the zero-phonon line (ZPL) at 1.979 eV in samples containing negatively charged ${\mathrm{GeV}}^{\ensuremath{-}}$ centers. The relationship between the center and Ge dopant is unambiguously confirmed by studies of 12C^{12}\mathrm{C}12C diamonds containing 70Ge^{70}\mathrm{Ge}70Ge, 73Ge^{73}\mathrm{Ge}73Ge, or 76Ge^{76}\mathrm{Ge}76Ge isotopes. The intensity ratio of the ZPL of these centers varies with the crystal size, and the intensity of the GeV0{\mathrm{GeV}}^{0}GeV0 centers reaches its maximum in samples 150 nm in size. In the vibronic sideband of this center the local vibrational mode with an energy of 23 meV was identified. The density functional theory calculations yield a ZPL energy value of the GeV0{\mathrm{GeV}}^{0}GeV0 center which is 150 meV higher than the experimentally observed one and matches the values of its relaxational energy as well as the local phonon mode frequency.