Ab initio calculation of spin-orbit coupling for an NV center in diamond exhibiting dynamic Jahn-Teller effect

At a Glance

Metadata	Details
Publication Date	2017-08-24
Journal	Physical review. B./Physical review. B
Authors	Gergő Thiering, Ádám Gali
Institutions	HUN-REN Wigner Research Centre for Physics, Hungarian Academy of Sciences
Citations	106
Analysis	Full AI Review Included

Technical Documentation & Analysis: Spin-Orbit Coupling in NV Centers

This document analyzes the research paper “Ab initio calculation of spin-orbit coupling for NV center in diamond exhibiting dynamic Jahn-Teller effect” to provide technical specifications and align 6CCVD’s advanced MPCVD diamond solutions with the requirements of solid-state quantum research.

Executive Summary

This research provides critical theoretical validation for the behavior of the Nitrogen-Vacancy (NV) center in diamond, a leading solid-state quantum bit (qubit) candidate.

Core Value Proposition: The study quantitatively confirms that the Dynamic Jahn-Teller (DJT) effect is the mechanism responsible for damping (quenching) the intrinsic Spin-Orbit Coupling (SOC) in the NV center’s ³E excited state.
Quantitative Validation: The calculated quenched SOC value (4.8 GHz) closely matches the experimentally observed SOC (5.3 GHz), resolving a long-standing discrepancy in NV center physics.
Mechanism Identified: Strong electron-phonon coupling is identified as the key factor driving the DJT effect, which in turn dictates the multiple intersystem crossing (ISC) rates at cryogenic temperatures.
Methodology: The results were achieved using ab initio supercell Density Functional Theory (DFT), employing the HSE06 hybrid functional and large supercells (up to 1000 atoms) for high-accuracy SOC calculation.
Application Impact: These findings are essential for optimizing the optical initialization and readout fidelity of NV qubits, paving the way for improved quantum information processing and metrology applications.
Material Requirement: Replication and extension of this work rely fundamentally on ultra-high purity, low-strain Single Crystal Diamond (SCD) material, a core offering of 6CCVD.

Technical Specifications

The following hard data points were extracted from the ab initio calculations and experimental comparisons presented in the paper.

Parameter	Value	Unit	Context
Intrinsic Spin-Orbit Coupling (λ_z)	15.8	GHz	Calculated, undamped value for ³E state
Quenched Spin-Orbit Coupling (p * λ_z)	4.8	GHz	Calculated, damped by DJT (0 K)
Experimental Spin-Orbit Coupling (λ_z)	5.3 ± 0.03	GHz	Measured via PLE at T < 20 K
Ham Reduction Factor (p)	0.304	Dimensionless	Quantifies the damping of SOC due to DJT
Jahn-Teller Energy (E_JT)	41.8	meV	Energy difference between high symmetry and distorted configurations
Effective e mode energy (ħω_e)	77.6	meV	Energy of the effective phonon mode
Energy Barrier (δ_BT)	9.1	meV	Barrier between equivalent distorted configurations
Experimental Temperature Range	< 20	K	Temperature required for high-quality PLE measurements
Geometry Optimization Force Limit	10^-4	eV/Å	Stringent convergence criteria for atomic forces
Plane Wave Cutoff	370	eV	Convergence parameter for VASP calculations

Key Methodologies

The theoretical framework relies on highly converged ab initio calculations to accurately model the complex vibronic coupling within the NV center.

Computational Framework: Supercell plane wave spin-polarized Density Functional Theory (DFT) was performed using the VASP 5.4.1 code.
Ion Treatment: Projector-Augmentation-Wave (PAW) method was utilized with standard PAW-potentials.
Supercell Scaling: Calculations utilized a 512-atom cubic supercell, scaled up to a 1000-atom supercell for highly converged hybrid functional SOC calculations.
Electronic Structure Functional: The HSE06 hybrid functional was employed to accurately reproduce the experimental band gap and charge transition levels. The PBE functional was used for comparative test purposes.
Excited State Modeling: The ³E excited state was calculated using the constrained-occupation DFT method (ΔSCF).
Spin-Orbit Coupling (SOC) Calculation: SOC was calculated using a non-collinear approach, fixing the C_3v axis as the quantization axis. The strength of SOC was derived from the half-half occupation of the e states.
Vibronic Coupling Analysis: The DJT effect and the resulting Ham reduction factor (p) were calculated by solving the quadratic DJT Hamiltonian, requiring the extraction of E_JT, ħω_e, and δ_BT parameters from the Adiabatic Potential Energy Surface (APES).

6CCVD Solutions & Capabilities

The successful experimental realization and extension of this theoretical work—particularly the requirement for low-strain, high-fidelity spin measurements at cryogenic temperatures—demands the highest quality Single Crystal Diamond (SCD) material. 6CCVD is uniquely positioned to supply the necessary materials and customization services.

Research Requirement	6CCVD Solution & Capability	Technical Advantage
Ultra-High Purity Substrates (Required to minimize strain and achieve T < 20 K fidelity)	Optical Grade Single Crystal Diamond (SCD)	Guaranteed ultra-low nitrogen concentration (sub-ppb level) and minimal lattice defects, ensuring long spin coherence times (T₂) essential for high-fidelity qubit operation.
Integration into Photonic Devices (Future work requires thin layers for coupling)	Custom Thickness Control (SCD)	SCD plates available from 0.1 µm up to 500 µm thickness, enabling precise integration into waveguides, photonic crystal cavities, and micro-electronic devices.
High-Fidelity Optical Interfaces (Required for efficient PLE and readout)	Precision Polishing Services	SCD surfaces polished to an industry-leading roughness of Ra < 1 nm, minimizing scattering losses and maximizing photon collection efficiency.
Scalable Quantum Sensing Platforms (Moving beyond single NV centers)	Large Area Polycrystalline Diamond (PCD)	PCD wafers available in custom dimensions up to 125 mm, suitable for scalable fabrication of quantum sensor arrays and large-area metrology platforms.
Device Prototyping & Electrical Control (If future experiments require gates or contacts)	In-House Custom Metalization	Internal capability to deposit standard quantum stack metals (Au, Pt, Pd, Ti, W, Cu) with high precision, accelerating the transition from theoretical validation to functional device fabrication.

Engineering Support

The complex interplay between electron-phonon coupling, the dynamic Jahn-Teller effect, and spin-orbit coupling requires specialized material knowledge. 6CCVD’s in-house PhD team specializes in MPCVD growth optimization and defect engineering, offering expert consultation on material selection, surface termination, and post-growth processing for similar NV Center Quantum Bit projects.

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

View Original Abstract

Point defects in solids may realize solid state quantum bits. The spin-orbit\ncoupling in these point defects plays a key role in the magneto-optical\nproperties that determine the conditions of quantum bit operation. However,\nexperimental data and methods do not directly yield this highly important data,\nparticularly, for such complex systems where dynamic Jahn-Teller (DJT) effect\ndamps the spin-orbit interaction. Here, we show for an exemplary quantum bit,\nnitrogen-vacancy (NV) center in diamond, that \emph{ab initio} supercell\ndensity functional theory provide quantitative prediction for the spin-orbit\ncoupling damped by DJT. We show that DJT is responsible for the multiple\nintersystem crossing rates of NV center at cryogenic temperatures. Our results\npave the way toward optimizing solid state quantum bits for quantum information\nprocessing and metrology applications.\n

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevb.96.081115