Spin–spin interactions in defects in solids from mixed all-electron and pseudopotential first-principles calculations
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2021-07-29 |
| Journal | npj Computational Materials |
| Authors | Krishnendu Ghosh, He Ma, Mykyta Onizhuk, Vikram Gavini, Giulia Galli |
| Institutions | University of Chicago, University of Michigan |
| Citations | 26 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”- Core Innovation: A novel, computationally efficient mixed All-Electron (AE) and Pseudopotential (PP) Density Functional Theory (DFT) framework using a Finite-Element (FE) basis set for calculating Spin Hamiltonian (SH) parameters.
- Computational Efficiency: The method achieves full AE accuracy by treating only a small cluster of atoms (typically <10) immediately surrounding the defect at the AE level, while the rest of the system (up to 1022 atoms) uses the PP approximation.
- Accuracy Validation: Results for hyperfine (A-tensor) and zero-field splitting (D-tensor) parameters match those obtained from computationally demanding full AE calculations for small systems.
- Large-Scale Capability: The approach enables accurate SH parameter calculations for large supercells (up to 1022 atoms), which is critical for capturing defect-defect and cell-size interaction effects.
- Impact on Dynamics: Accurate AE-derived SH parameters are shown to be essential for quantitative predictions of coherence times (T2), particularly for weakly coupled nuclear spins, where PW-PP methods can introduce errors up to a factor of 7.
- Key Systems Studied: The method was successfully applied to the negatively-charged Nitrogen-Vacancy (NV) center in diamond and the neutral Divacancy (VV) in 4H-SiC.
Technical Specifications
Section titled “Technical Specifications”| Parameter | Value | Unit | Context |
|---|---|---|---|
| Maximum Supercell Size | 1022 | atoms | Hexagonal cell used for VV defect in 4H-SiC |
| AE Treatment Cluster Size | <10 | atoms | Number of atoms requiring All-Electron treatment for converged SH parameters |
| NV D-tensor (FE-mixed) | 2928.31 | MHz | Zero-Field Splitting (ZFS) calculated using the mixed AE-PP approach |
| NV D-tensor (Full AE) | 2939.47 | MHz | ZFS calculated using full FE-AE (63-atom benchmark cell) |
| NV Fermi Contact (N atom) | -2.125 | MHz | Afc value for the nitrogen atom in a 215-atom cell (FE-mixed) |
| NV Hahn-Echo T2 | 0.89 | ms | Predicted coherence time using Cluster Correlation Expansion (CCE) |
| kh-VV T2 (FE-AE) | 0.14 | ms | Ensemble-averaged coherence time for basal divacancy (clock transition) |
| kh-VV T2 (PW-PAW) | 1.04 | ms | Ensemble-averaged coherence time using standard PW-PP method (demonstrates PW error) |
| PW Kinetic Energy Cutoff | 75 | Ry | Standard parameter for Plane-Wave DFT calculations |
Key Methodologies
Section titled “Key Methodologies”The research relies on a specialized computational approach combining Density Functional Theory (DFT) with advanced basis sets and post-processing techniques:
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Mixed All-Electron (AE) and Pseudopotential (PP) DFT:
- Calculations were performed using the DFT-FE code, which utilizes a Finite-Element (FE) basis set.
- The FE basis set is spatially adaptive, allowing for high resolution (AE treatment) in the core region of selected atoms (the defect cluster) and coarser resolution (PP treatment) for the remaining bulk atoms.
- This mixed approach significantly reduces the number of basis functions (M) and electrons (N) compared to full AE calculations, lowering the computational complexity from O(M log(M)N2) to O(M log(M)N2) with smaller M and N.
-
Hyperfine A-tensor Calculation:
- The A-tensor (A = Afc + Asd) was derived from the electronic spin density (ns(r)).
- The Fermi contact term (Afc) requires the accurate value of ns(r) exactly at the nucleus, necessitating the AE treatment for the defect cluster.
- The spin-dipolar term (Asd) calculation was reformulated by solving a Poisson equation (V2Φs(r) = -4πns(r)) to efficiently account for periodic boundary conditions and core region contributions.
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Zero-Field Splitting D-tensor Calculation:
- The D-tensor, arising from magnetic dipole-dipole interaction, was calculated by solving a series of N(N+1)/2 Poisson equations in real space.
- This reformulation avoids computationally expensive double integrals and leverages the efficiency of the FE basis set.
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Coherence Time Prediction (CCE Method):
- The calculated SH parameters (A-tensors) were used as input for the Cluster Correlation Expansion (CCE) method to predict the coherence function (L) and coherence times (T2).
- CCE calculations were performed for both strongly coupled (A > 1 MHz) and weakly coupled (A << 1 MHz) nuclear spins, demonstrating that AE accuracy is critical for predicting T2 in the weakly coupled regime.
Commercial Applications
Section titled “Commercial Applications”| Industry/Field | Relevance of Technology |
|---|---|
| Quantum Computing Hardware | Essential for the design and validation of solid-state qubits (e.g., NV in diamond, VV in SiC). Accurate SH parameters are necessary to model spin dynamics, optimize control pulses, and maximize coherence time (T2). |
| Quantum Sensing and Metrology | Enables precise characterization of defect properties required for high-sensitivity magnetometers and thermometers based on spin defects, ensuring accurate calibration and performance prediction. |
| Semiconductor Defect Engineering | Supports high-throughput computational screening and discovery of new spin qubit candidates in emerging materials (e.g., SiC, AlN, oxides, 2D materials) by providing reliable SH parameters at a reduced computational cost. |
| Quantum Memory and Registers | Crucial for modeling the interaction between the central electron spin and surrounding nuclear spins (spin bath). Accurate AE calculations for weakly coupled spins are vital for designing long-coherence nuclear spin registers. |
| Materials Science Simulation | Provides a robust, scalable methodology for performing AE-level DFT calculations on large, complex periodic systems, applicable to any material property sensitive to core-electron effects. |