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Accurate hyperfine tensors for solid state quantum applications - case of the NV center in diamond

MetadataDetails
Publication Date2024-06-04
JournalCommunications Physics
AuthorsIstvĂĄn TakĂĄcs, Viktor IvĂĄdy
InstitutionsEötvös Lorånd University
Citations9
AnalysisFull AI Review Included

This research addresses a critical limitation in modeling solid-state quantum systems: the inaccurate prediction of electron spin-nuclear spin hyperfine interactions for distant nuclei using standard first-principles methods.

  • Problem Solved: Industry-standard DFT codes (like VASP) produced Absolute Relative Errors (ARE) exceeding 100% for hyperfine parameters of nuclear spins located 6-30 A from the NV center in diamond due to finite-size effects.
  • Methodological Advance: An improved real-space integration method was implemented, utilizing a large support lattice (up to 30 A radius) to effectively eliminate errors arising from periodic boundary conditions and long-range dipole-dipole interactions.
  • Accuracy Achieved: The new method, using the HSE06 functional (0.2 mixing parameter), achieved a Mean Absolute Percentage Error (MAPE) of 1.79% for measured 13C nuclear spins at all distances (6-30 A).
  • Performance Gain: This represents a significant improvement, demonstrating a ~100-fold reduction in the Mean Absolute Relative Error (MARE) compared to previous theoretical predictions using standard VASP implementation.
  • Data Output: High-accuracy hyperfine tensors for approximately 104 lattice sites are provided, ready for use in advanced quantum simulations and experimental data matching.

The following table summarizes the key parameters and performance metrics of the first-principles calculations for the NV center in diamond.

ParameterValueUnitContext
Defect SystemNV Center (S=1)N/ANitrogen-Vacancy in Diamond
Supercell Sizes Used512 and 1728AtomsUsed for VASP ground state calculations
Lattice Parameter (Diamond)3.567AExperimental value used in calculations
Plane-Wave Cutoff Energy500eVBasis set convergence criterion
Exchange-Correlation FunctionalHSE06N/AHybrid functional with 0.2 mixing parameter
Real-Space Grid Spacing0.036AUsed for high-resolution spin density integration
Maximum Distance Calculated30ARadius of the support lattice for nuclear spins
Standard VASP Error (ARE)> 100%Typical error for distant spins (6-30 A)
Improved Method Error (MAPE)1.79%Mean Absolute Percentage Error (Data Set III)
Improvement in MARE~100FoldReduction compared to standard VASP
Coherence Time (NV Qubits)Up to 1msTypical room temperature coherence time

The high-accuracy hyperfine tensors were calculated using a modified first-principles workflow based on VASP output files and a novel real-space integration technique.

  1. Ground State Calculation: The electronic structure of the NV center was calculated using the VASP code with the Projector Augmented Wave (PAW) method, employing 512-atom and 1728-atom supercells.
  2. Functional Optimization: The HSE06 hybrid functional was selected, and its mixing parameter was tuned (0.2) to optimize the description of the spin density, which is critical for accurate hyperfine coupling.
  3. Spin Density Generation: The total spin density (σ(r)) was computed on a fine real-space grid (0.036 A spacing) to ensure high spatial resolution for subsequent integration.
  4. Real-Space Integration Implementation: An in-house code was developed to post-process the VASP spin density output, calculating the hyperfine tensor (A) elements, which include the Fermi contact term (AFC) and the magnetic dipole-dipole coupling (ASS).
  5. Finite-Size Correction (Dipole Term): The long-range dipole-dipole interaction term (Wij) was calculated using real-space integration over the full spin density σ(r) (Equation 9), rather than the periodic pseudo-spin density, mitigating errors caused by the interaction of nuclear spins with periodic defect replicas.
  6. Support Lattice Application: Calculations were extended to nuclear spins located outside the supercell boundaries (up to 30 A) by using the converged spin density from the central supercell, ensuring the calculation models an isolated defect system rather than a lattice of interacting defects.
  7. Core Polarization Inclusion: The Fermi contact term was calculated using VASP’s implementation, which includes contributions from core electron spin polarization via the frozen valence approximation.

The provision of highly accurate, finite-size effect-free hyperfine data is crucial for advancing quantum technologies based on solid-state spin qubits.

  • Quantum Computing and Memory:
    • NV Quantum Nodes: Enables high-precision simulation and optimization of multi-qubit systems where 13C nuclear spins serve as highly coherent quantum memory registers coupled to the NV electron spin.
    • Gate Fidelity: Accurate hyperfine tensors are necessary for designing robust, high-fidelity quantum gates and dynamic decoupling sequences.
  • Quantum Sensing and Metrology:
    • Nano-NMR and MRI: The calculated hyperfine tensors act as a theoretical “bar code.” By matching experimental ODMR/NMR data to these theoretical values, individual nuclear spins can be positioned with nanometer precision around the NV center.
    • Defect Identification: Allows for the unambiguous identification of paramagnetic point defects in semiconductors (e.g., SiC, diamond) by comparing measured and computed hyperfine structures.
  • Quantum Internet Infrastructure:
    • Supports the engineering of robust, long-coherence spin qubits required for quantum repeaters and networked quantum communication architectures.
  • Materials Science Research:
    • Provides a validated, high-accuracy computational methodology that can be applied to other promising solid-state qubits (e.g., silicon vacancy in SiC) to accelerate defect characterization and optimization.