Multiconfigurational study of the negatively charged nitrogen-vacancy center in diamond

At a Glance

Metadata	Details
Publication Date	2021-01-25
Journal	Physical review. B./Physical review. B
Authors	Churna Bhandari, Aleksander L. Wysocki, Sophia E. Economou, Pratibha Dev, Kyungwha Park
Institutions	Virginia Tech, Howard University
Citations	32
Analysis	Full AI Review Included

Technical Documentation & Analysis: NV^- Center in Diamond

This document analyzes the research paper, “A multiconfigurational study of the negatively charged nitrogen-vacancy center in diamond,” to provide technical specifications and align 6CCVD’s advanced MPCVD diamond capabilities with the requirements for replicating and extending this critical quantum research.

Executive Summary

The research successfully applies advanced multiconfigurational quantum chemistry (CASSCF, SOC, SSC) to accurately model the electronic structure and magnetic properties of the Nitrogen-Vacancy (NV^-) center in diamond, validating its role as a leading solid-state qubit.

Benchmark Validation: The study confirms the NV^- center as an ideal benchmark system by achieving excellent agreement between calculated electronic states and recent experimental data.
Accurate Excitation Energies: Calculated vertical excitation energies for the key ³A₂ (ground) to ³E (excited) triplet state transition (1.93-2.14 eV) closely match experimental zero-phonon line (ZPL) absorption (1.945 eV).
Zero-Field Splitting (ZFS) Precision: The calculated ZFS of the ground state (³A₂) is 2.7 GHz, in strong agreement with the experimental value of 2.88 GHz, confirming the accuracy of the Spin-Spin Coupling (SSC) treatment.
Advanced Correlation: The methodology successfully includes full electron correlation and relativistic effects (Spin-Orbit Coupling, SOC), which are crucial for correctly predicting the ordering and splitting of the excited spin-singlet states (¹E and ¹A₁).
Methodological Screening Tool: The systematic numerical procedure developed is general and can be applied to screen other promising deep defects (color centers) in wide band-gap semiconductors (e.g., SiC, complex oxides) for quantum information applications.
Material Requirement: The success of this theoretical work underscores the necessity of high-purity, defect-engineered Single Crystal Diamond (SCD) for experimental realization of these quantum systems.

Technical Specifications

The following hard data points were extracted from the theoretical calculations and compared against experimental benchmarks, highlighting the precision required for NV^- center characterization.

Parameter	Value	Unit	Context
Ground State Excitation (³A₂ to ³E)	1.93 (70-atom) / 2.14 (162-atom)	eV	Calculated Vertical Excitation Energy (VE)
Experimental ZPL (³A₂ to ³E)	1.945	eV	Zero-Phonon Line (ZPL) Absorption
Singlet Gap (¹E to ¹A₁)	1.07 (70-atom) / 1.35 (162-atom)	eV	Calculated Excitation Energy (Relative to ¹E)
Triplet-Singlet Gap (³E to ¹A₁)	0.52 (70-atom) / 0.54 (162-atom)	eV	Calculated Energy Difference
Ground State ZFS (SSC)	2.7 (Theory) / 2.88 (Exp.)	GHz	³A₂ State Splitting (M_z = 0 to M_z = ±1)
Excited State ZFS (SOC+SSC)	4.6 (70-atom) / 6.2 (162-atom)	GHz	Lowest ³E Degenerate Level Splitting
Cluster Size 1	70	Atoms	C₃₃H₃₆N^- (Hydrogen-passivated)
Cluster Size 2	162	Atoms	C₈₅H₇₆N^- (Hydrogen-passivated)
Required Degeneracy Accuracy	~10	neV	Required for accurate SOC calculation in E IRRep states

Key Methodologies

The study utilized a systematic, multi-step quantum chemistry procedure (beyond standard DFT) to ensure accurate treatment of electron correlation and relativistic effects in the NV^- center.

Cluster Geometry Optimization: C_3v-symmetric hydrogen-passivated diamond clusters (70-atom and 162-atom) were constructed based on DFT-optimized geometries of a 215-atom cubic supercell.
Active Space Selection: A crucial step involved identifying and including two extra unoccupied defect orbitals (E IRRep) beyond the four standard dangling bond orbitals, forming an active space of six electrons and six orbitals (CASSCF(6,6)).
Relativistic Treatment: Scalar relativistic effects were incorporated using the Douglas-Kroll-Hess Hamiltonian and correlation-consistent polarized double-zeta basis sets (cc-pVDZ-DK) for all atoms.
Orbital Symmetrization: The libmsym program and the SUPERSYMMETRY keyword in OpenMolcas were used to maintain C₃ symmetry and orbital degeneracy (accuracy up to ~10 neV), essential for accurate SOC calculations.
Spin-Orbit Coupling (SOC): SOC was included in the converged CASSCF(6,6) wave functions using the Restricted Active Space State Interaction (RASSI) method, primarily affecting the ³E excited state.
Spin-Spin Coupling (SSC): SSC was calculated using first-order perturbation theory over the CASSCF(6,6) wave functions via the ORCA code, applied to both the ³A₂ and ³E spin-triplet states.
Surface Orbital Removal: Surface-dominated orbitals were systematically removed from the converged CASSCF orbitals to mitigate artificial effects arising from the hydrogen-passivated cluster model.

6CCVD Solutions & Capabilities

The accurate theoretical modeling of the NV^- center demands high-quality, engineered diamond materials for experimental validation and application development. 6CCVD provides the necessary MPCVD diamond substrates and customization services to meet these stringent requirements.

Applicable Materials

Research Requirement	6CCVD Material Recommendation	Rationale and Application
High-Purity Host Lattice (NV^- Qubit)	Optical Grade Single Crystal Diamond (SCD)	Essential for achieving the long spin coherence times (T₂) required for quantum sensing and computing, minimizing background defects (e.g., substitutional nitrogen).
Screening Other Defects (SiV, GeV, etc.)	Boron-Doped Diamond (BDD)	BDD substrates are critical for electrochemical applications and for studying charge-state control of defects, enabling extension of the theoretical screening methodology.
Scaling and Integration	Polycrystalline Diamond (PCD)	For large-area applications (up to 125 mm wafers) requiring high thermal management and integration into complex electronic or photonic systems.

Customization Potential

The paper notes that future work may involve external perturbations such as electric fields and strains. 6CCVD’s in-house capabilities directly support the fabrication of devices required for these advanced experiments.

Customization Service	Technical Relevance to NV^- Research	6CCVD Capability
Custom Dimensions & Thickness	Required for creating specific device geometries or isolating defects in thin films.	SCD/PCD plates/wafers up to 125 mm. Thickness control from 0.1 µm to 500 µm (SCD/PCD) and substrates up to 10 mm.
Surface Preparation	Minimizing surface defects and orbital contamination (as discussed in the paper).	Ultra-low Roughness Polishing: Ra < 1 nm for SCD and Ra < 5 nm for inch-size PCD, ensuring optimal optical and electronic interfaces.
Device Integration	Applying external electric fields or microwave control for qubit manipulation.	Custom Metalization: Internal capability for deposition of Au, Pt, Pd, Ti, W, and Cu contacts for electrode fabrication and microwave circuitry.

Engineering Support

6CCVD’s commitment extends beyond material supply. Our in-house team of PhD material scientists and engineers provides critical support for quantum material development.

Material Optimization: We assist researchers in optimizing MPCVD growth parameters to achieve specific nitrogen concentrations or defect densities necessary for NV^- ensemble or single-defect studies.
Defect Engineering Consultation: Our experts can advise on the optimal material selection (SCD vs. PCD, doping levels) and post-processing techniques (e.g., irradiation and annealing) required to maximize the yield and stability of NV^- centers for similar quantum sensing and information applications.
Global Logistics: We ensure reliable global shipping (DDU default, DDP available) to deliver sensitive quantum materials directly to research facilities worldwide.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

Deep defects in wide band gap semiconductors have emerged as leading qubit candidates for realizing quantum sensing and information applications. Due to the spatial localization of the defect states, these deep defects can be considered as artificial atoms/molecules in a solid state matrix. Here we show that unlike single-particle treatments, the multiconfigurational quantum chemistry methods, traditionally reserved for atoms/molecules, accurately describe the many-body characteristics of the electronic states of these defect centers and correctly predict properties that single-particle treatments fail to obtain. We choose the negatively charged nitrogen-vacancy (NV$^-$) center in diamond as the prototype defect to study with these techniques due to its importance for quantum information applications and because its properties are well-known, which makes it an ideal benchmark system. By properly accounting for electron correlations and including spin-orbit coupling and dipolar spin-spin coupling in the quantum chemistry calculations, for the NV$^-$ center in diamond clusters, we are able to: (i) show the correct splitting of the ground (first-excited) triplet state into two levels (four levels), (ii) calculate zero-field splitting values of the ground and excited triplet states, in good agreement with experiment, and (iii) calculate the energy differences between ground and exited spin-triplet and spin-singlet states, as well as their ordering, which are also found to be in good agreement with recent experimental data. The numerical procedure we have developed is general and it can screen other color centers whose properties are not well known but promising for applications.

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevb.103.014115