Strong spin–orbit quenching via the product Jahn–Teller effect in neutral group IV qubits in diamond
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2020-10-30 |
| Journal | npj Quantum Materials |
| Authors | Christopher J. Ciccarino, Johannes Flick, Isaac Harris, Matthew E. Trusheim, Dirk Englund |
| Institutions | Harvard University, Massachusetts Institute of Technology |
| Citations | 20 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”- Qubit Candidates: The study focuses on neutral Group IV vacancy centers (SiV0, GeV0, SnV0, PbV0) in diamond, which possess a spin-triplet (S=1) ground state, making them highly promising candidates for solid-state quantum qubits with potential for long spin coherence.
- Dominant Physics: The excited state manifold is governed by a strong Product Jahn-Teller (pJT) effect, resulting from simultaneous orbital instabilities (Eg ⊗ eu ⊗ eg) and strong electron-phonon coupling.
- Methodology: First-principles Density Functional Theory (DFT) calculations were combined with a nonperturbative treatment of Spin-Orbit Coupling (SOC) and second-order electron-phonon coupling to accurately map the complex vibronic level structure.
- Strong Quenching: The dominant pJT interaction causes a significant quenching of the intrinsic SOC. The calculated quenching factors (pu, pg) are extremely small (less than 0.05 for all defects), indicating that the vibronic nature of the system severely limits the spin-orbit interaction.
- Fine Structure Prediction: Despite the quenching, the lowest optically-active 3Eu state is predicted to be weakly split into ms-resolved levels. For the heavier SnV0 and PbV0, this splitting is only a few meV (3.15 meV and 11.31 meV, respectively).
- Engineering Value: The predicted Zero-Phonon Line (ZPL) energies and fine structure splittings provide essential quantitative data required for the experimental identification and coherent manipulation of these novel Group IV0 emitters.
Technical Specifications
Section titled “Technical Specifications”The following parameters were calculated using constrained Kohn-Sham DFT (HSE06 functional) and subsequent numerical diagonalization of the coupled spin-vibronic Hamiltonian for the SnV0 and PbV0 defects.
| Parameter | SnV0 Value | PbV0 Value | Unit | Context |
|---|---|---|---|---|
| Zero-Phonon Line (ZPL) Energy | 1.825 | 2.170 | eV | Energy of the lowest optically-active 3Eu vibronic state (including SOC). |
| Effective Vibrational Energy (ħωE) | 87.7 | 90.8 | meV | Energy of the coupled Eg phonon mode. |
| First-Order Jahn-Teller Instability (EJT(1)) | 217 | 200 | meV | Energy lowering due to constructive pJT interference. |
| Second-Order Vibronic Splitting (γ(2)) | 6.22 | 7.90 | meV | Splitting between the lowest 3A2u and 3Eu vibronic states. |
| Quenched Spin-Orbit Splitting (λu + λg) | 3.15 | 11.31 | meV | Splitting between the ms = ±1 sublevels of the lowest 3Eu state. |
| Spin-Orbit Quenching Factor (pu, pg) | 0.023, 0.032 | 0.040, 0.043 | Dimensionless | Reduction factor of the pure electronic SOC due to pJT (less than 5%). |
| Displacement Amplitude (p(1)) | 0.154 | 0.145 | A | Displacement from the D3d high-symmetry point to the C2h minima. |
| DFT Supercell Size | 512 | Atoms | Carbon atoms in the cubic supercell model. | |
| DFT Energy Cutoff | 400 | eV | Plane wave basis set cutoff (verified up to 800 eV). |
Key Methodologies
Section titled “Key Methodologies”The electronic and vibronic structure of the neutral Group IV defects was determined using a multi-step computational approach:
- First-Principles DFT: Constrained Kohn-Sham Density Functional Theory (DFT) calculations were performed using the VASP code (version 5.4.4) with Projector-Augmented Wave (PAW) pseudopotentials.
- Functional Selection: The hybrid HSE06 exchange-correlation functional was employed to accurately describe the energetics of the defect systems, ensuring accurate band gap and defect level placement.
- Geometry Optimization: Ionic relaxation was performed on a 512-atom cubic supercell until forces on all atoms were below 10-2 eV/A. Both high-symmetry (D3d) and low-symmetry (C2h) excited-state geometries were determined.
- Jahn-Teller Parameterization: The adiabatic Potential Energy Surfaces (PES) were computed from DFT to extract the linear (Fu/g) and quadratic (Gu/g) electron-phonon coupling constants, as well as the static electronic correlation (W).
- Vibronic Hamiltonian Construction: The total Hamiltonian (H = Hosc + HpJT(2) + W) was constructed, including the harmonic oscillator (Hosc) and the product Jahn-Teller interaction (HpJT) up to second order in coupling.
- Nonperturbative SOC Inclusion: The Spin-Orbit Coupling (SOC) Hamiltonian (HSOC) was included directly in the complete spin-resolved orbital basis. This allowed for the nonperturbative calculation of the combined spin-orbit and Jahn-Teller system.
- Numerical Solution: Eigenvalues and eigenvectors of the resulting coupled electron-vibrational Hamiltonian were found by numerical diagonalization, including up to 40 phonons in the expansion.
Commercial Applications
Section titled “Commercial Applications”The detailed understanding of the spin-vibronic structure of neutral Group IV defects is critical for advancing several quantum technologies:
- Quantum Computing and Information Processing: The S=1 spin-triplet ground state provides a robust platform for encoding quantum information. The small, quenched SOC splitting is advantageous as it minimizes decoherence pathways while still allowing for optical spin initialization and readout.
- Quantum Repeaters and Networks: IV0 centers, particularly those with ZPLs in the telecommunications band (e.g., SnV0, PbV0), are strong candidates for quantum network nodes, enabling long-distance entanglement distribution.
- Solid-State Single-Photon Emitters: The precise ZPL energy predictions and vibronic spectra are necessary for engineering and optimizing these defects as coherent, transform-limited single-photon sources, a fundamental component of photonic quantum circuits.
- Quantum Sensing: Defects with stable, optically addressable spin states are utilized in high-resolution quantum sensors for measuring magnetic fields, electric fields, and temperature at the nanoscale.
- Materials Engineering: The theoretical framework developed for handling strong pJT effects and quenched SOC can be applied to the design and analysis of other complex solid-state artificial atoms and color centers in wide-bandgap semiconductors.
View Original Abstract
Abstract Artificial atom qubits in diamond have emerged as leading candidates for a range of solid-state quantum systems, from quantum sensors to repeater nodes in memory-enhanced quantum communication. Inversion-symmetric group IV vacancy centers, comprised of Si, Ge, Sn, and Pb dopants, hold particular promise as their neutrally charged electronic configuration results in a ground-state spin triplet, enabling long spin coherence above cryogenic temperatures. However, despite the tremendous interest in these defects, a theoretical understanding of the electronic and spin structure of these centers remains elusive. In this context, we predict the ground-state and excited-state properties of the neutral group IV color centers from first principles. We capture the product Jahn-Teller effect found in the excited state manifold to second order in electron-phonon coupling, and present a nonperturbative treatment of the effect of spin-orbit coupling. Importantly, we find that spin-orbit splitting is strongly quenched due to the dominant Jahn-Teller effect, with the lowest optically-active 3 E u state weakly split into m s -resolved states. The predicted complex vibronic spectra of the neutral group IV color centers are essential for their experimental identification and have key implications for use of these systems in quantum information science.