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Spin–spin interactions in defects in solids from mixed all-electron and pseudopotential first-principles calculations

MetadataDetails
Publication Date2021-07-29
Journalnpj Computational Materials
AuthorsKrishnendu Ghosh, He Ma, Mykyta Onizhuk, Vikram Gavini, Giulia Galli
InstitutionsUniversity of Michigan, University of Chicago
Citations26
AnalysisFull AI Review Included

Technical Documentation & Analysis: Spin-Spin Interactions in Solid-State Qubits

Section titled “Technical Documentation & Analysis: Spin-Spin Interactions in Solid-State Qubits”

This document analyzes the research paper “Spin-spin interactions in defects in solids from mixed all-electron and pseudopotential first-principles calculations” to provide technical specifications and align the findings with 6CCVD’s advanced CVD diamond capabilities for quantum technology applications.


The research validates a novel computational approach for accurately modeling solid-state spin qubits, highlighting the critical role of host material purity and precise material parameters.

  • Computational Advancement: A mixed All-Electron (AE) and Pseudopotential (PP) Density Functional Theory (DFT) framework was developed using a Finite-Element (FE) basis set (FE-mixed).
  • Accuracy Achieved: The FE-mixed approach achieved full AE accuracy for calculating Spin Hamiltonian (SH) parameters (hyperfine A-tensor and zero-field splitting D-tensor) in large supercells (up to 1022 atoms).
  • Material Focus: The study centered on the Nitrogen-Vacancy (NV) center in Diamond and the Divacancy (VV) center in Silicon Carbide (SiC)—key platforms for quantum computing and sensing.
  • Criticality of AE Data: Traditional Plane-Wave Pseudopotential (PW-PP) methods were shown to significantly overestimate hyperfine couplings for weakly coupled nuclear spins, leading to errors in predicted coherence times ($T_{2}$) by factors up to 4.
  • Qubit Dynamics: Accurate SH parameters are essential for quantitative predictions of coherence times, demonstrating the need for high-purity, well-characterized host materials like those supplied by 6CCVD.
  • Scalability: The method enables accurate SH parameter calculation for systems containing over 1000 atoms, supporting the design of complex, large-scale quantum registers.

The following hard data points were extracted from the computational results and benchmarks presented in the paper.

ParameterValueUnitContext
Maximum Supercell Size Modeled1022AtomsVV center in 4H-SiC
NV-Diamond D-tensor (D3) (FE-mixed)2928.31
NV-Diamond D-tensor (D3) (Full FE-AE)2939.47
Fermi Contact Term (N atom) (FE-mixed)-2.125MHz215-atom cell, AE accuracy
Fermi Contact Term (N atom) (Full FE-AE)-2.096MHz215-atom cell, Benchmark
Ensemble-Averaged T2 (NV-Diamond) (FE-AE)1.35µsInhomogeneous dephasing time
Hahn-Echo T2 (NV-Diamond)0.89msCoherence time under dynamical decoupling
T2 Prediction Error (PW-PP vs. AE)Up to 4FactorVariance for basal kh-VV in SiC clock transitions
Required AE Atoms<10AtomsNumber of atoms requiring AE treatment for converged results

The following is a concise summary of the computational and analytical techniques used to achieve high-accuracy Spin Hamiltonian parameter calculations.

  1. Computational Framework: Mixed All-Electron (AE) and Pseudopotential (PP) Density Functional Theory (DFT) was employed to balance accuracy and computational cost, treating only the atoms immediately surrounding the defect at the AE level.
  2. Basis Set: A Finite-Element (FE) basis set was utilized, leveraging its spatial adaptivity to provide high resolution in the core regions (required for AE accuracy) and coarser resolution in the valence regions.
  3. Spin Hamiltonian (SH) Calculation: The SH parameters (A and D tensors) were determined from first-principles electronic structure calculations.
  4. D-tensor Evaluation: The zero-field splitting D-tensor calculation was reformulated in real-space by solving a series of Poisson equations, significantly reducing the computational complexity associated with double integrals.
  5. Coherence Time Modeling: The Cluster Correlation Expansion (CCE) method was used to compute the dynamical properties of the spin defects, specifically the inhomogeneous dephasing time ($T_{2}^{*}$) and the Hahn-echo coherence time ($T_{2}$).
  6. Material Structures: Cubic supercells were used for NV-diamond, and hexagonal or orthorhombic supercells were used for the divacancy (VV) centers in 4H-SiC.

The research underscores the necessity of ultra-high-purity, precisely engineered host materials—specifically diamond—to realize the long coherence times predicted by accurate computational models. 6CCVD provides the foundational MPCVD diamond substrates required to replicate and advance this research in solid-state quantum systems.

Research Requirement (Paper)6CCVD Solution & CapabilityTechnical Advantage
High-Purity Host Material (NV Centers)Optical Grade Single Crystal Diamond (SCD)SCD substrates offer the ultra-low native defect density and high crystalline quality essential for creating isolated, high-performance NV centers with minimal background noise.
Minimizing Nuclear Spin Noise (Long T2)Isotopically Engineered Diamond6CCVD specializes in MPCVD growth, enabling the supply of high-purity 12C-enriched SCD. This isotopic purification is critical for reducing the nuclear spin bath, directly supporting the millisecond coherence times ($T_{2}$) discussed in the paper.
Large-Scale Device IntegrationCustom Dimensions (Plates/Wafers)6CCVD offers SCD and PCD plates/wafers up to 125mm, supporting the scaling of quantum experiments and the fabrication of large-area arrays necessary for complex quantum registers.
Near-Surface Qubit StudiesPrecision Polishing (Ra < 1nm for SCD)Ultra-smooth surfaces (Ra < 1nm) are vital for minimizing surface-related noise and ensuring reliable optical initialization and readout of near-surface spin defects used in quantum sensing.
Device Integration & ControlIn-House Metalization Services6CCVD provides custom metalization (Au, Pt, Pd, Ti, W, Cu) required for integrating diamond substrates into microwave or electrical control circuitry, essential for implementing the dynamical decoupling schemes (like Hahn-Echo) used to achieve long $T_{2}$.
Controlled Defect Layer ThicknessCustom Thickness SCD/PCD LayersSCD and PCD layers are available from 0.1µm to 500µm, allowing engineers to precisely control the active layer thickness for optimized defect implantation and subsequent thermal or irradiation treatments.

The paper demonstrates that accurate prediction of Qubit dynamics requires highly precise material parameters derived from complex computational methods. 6CCVD’s in-house PhD team of material scientists and engineers offers expert consultation on material selection, isotopic purity requirements, and substrate preparation (polishing, metalization) necessary for NV-Diamond and VV-SiC Qubit dynamics projects. We ensure the material specifications align perfectly with the stringent requirements of advanced quantum research.

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