Quantum well stabilized point defect spin qubits

Defect-based quantum systems in in wide bandgap semiconductors are strong candidates for scalable quantum-information technologies. However, these systems are often complicated by charge-state instabilities and interference by phonons, which can diminish spin-initialization fidelities and limit room-temperature operation. Here, we identify a pathway around these drawbacks by showing that an engineered quantum well can stabilize the charge state of a qubit. Using density-functional theory and experimental synchrotron x-ray diffraction studies, we construct a model for previously unattributed point defect centers in silicon carbide (SiC) as a near-stacking fault axial divacancy and show how this model explains these defect's robustness against photoionization and room temperature stability. These results provide a materials-based solution to the optical instability of color centers in semiconductors, paving the way for the development of robust single-photon sources and spin qubits.

A promising approach towards solving this problem is to engineer defect ionization energies by locally manipulating the band gap of the host material. In particular, a quantum well can lower the ionization energy of a point defect's dark state so that the excitation laser will preferentially repopulate the point defect's bright state. The mechanism is schematically depicted in Fig. 1D.
Here, we demonstrate that the combination of a quantum well and a spin qubit in SiC can stabilize the latter against photoionization. Additionally, we demonstrate that such configurations are readily observable in SiC. The generalization of these exemplified local structures to other semiconductor hosts could provide a material-based solution to the optical instability of color centers and pave the way toward robust point-defect-based single photon emitter and spin qubits.

Results
Stacking faults and polytype inclusions are natural sources of quantum wells in semiconductors (21)(22)(23). Such extended defects may additionally incorporate color centers that can exhibit distinct properties compared to their bulk counterparts (24). As both extended defects (25)(26)(27)(28) and applicable color centers (17,20,29) are commonplace in SiC, we take SiC as an exemplary host material for studying complex defect structures. In particular, we investigate divacancy qubits in the vicinity of a single stacking fault in 4H-SiC, in order to understand the consequences of their interaction.
4H-SiC is the most commonly used polytype of SiC. The primitive cells of 4H-SiC and other relevant polytypes are depicted in Fig. 2A-C. We consider a Frank-type stacking fault defect (30), a 1FSF(3,2) stacking fault in the Zhdanov notation, whose structure can be obtained by inserting a single Si-C double layer in cubic stacking order into a perfect 4H-SiC primitive cell (see in Fig. 2D). This configuration was assigned to the so-called "carrot" defect in 4H-SiC (23,31). Stacking faults in 4H-SiC often form quantum-well-like states that can be observed by photoluminescence (21)(22)(23). The considered stacking fault configuration was assigned to the 482 nm PL-emission line (23).
First, we theoretically confirm that the considered stacking fault forms a quantum well.
The band structure of perfect 4H-and 6H-SiC as well as the defective 4H-SiC structure including a 1FSF(3,2) stacking fault are depicted in Hereinafter, we refer to the high and low symmetry configurations as axial and basal plane divacancies, respectively. Recently, each of the divacancy configurations were assigned (32) to the PL1-PL4 divacancy related qubits (17) in 4H-SiC.
In our study, we consider two sets of divacancy configurations within a single model: 1) divacancies in the near-stacking-fault region, i.e. maximally 5 Å away from the stacking fault, and 2) bulk-like divacancy configurations, i.e. at least 14 Å away from the stacking fault. The near-stacking-fault and the bulk-like configurations are marked as ab-ssf and ab-4H in see Fig. 2D, respectively. In this notation, a and b can respectively represent silicon and carbon vacancies in both hexagonal-like and cubic-like environment. Note that due to the presence of the stacking fault, we distinguish three cubic-like lattice sites in the near stacking fault region, named as k1, k2 and k3, and two hexagonal-like lattice sites in the near-stacking-fault region, named as h1 and h2.
In In Fig. 6 and Table S1 in Supplementary Materials, we provide the calculated zero-fieldsplitting parameters for all the considered axial and basal plane configurations, respectively. In agreement with the hyperfine splitting results, ZFSs of the axial configurations form three well-distinguishable groups, see Fig. 6. Note that k2k2-ssf configuration exhibits the largest zero-field-splitting that differs from all the bulk-like axial configurations. Considering the basal plane configurations in Table S1 in Supplementary Materials, a similar trend can be observed as for the hyperfine splitting parameters, i.e. kh-4H and k3h2-ssf as well as hk-4H and h2k2-ssf pairs exhibit comparable zero-field-splitting parameters. PL5'-PL6' (13), that cannot be explained by the possible configurations in perfect bulk 4H-SiC host (PL1-PL4 centers (32)). In many respects, these unexplained, yet generally observable configurations follow the properties of bulk divacancy configurations. On the other hand, they show outstanding stability in room-temperature ODMR measurement (17,33) and photo ionization studies (11). In the latter case, the luminescence of the additional centers, such as the PL6 axial divacancy related room-temperature qubit, do not change by applying an additional repump laser of varying wavelength (11). This is in contrast to the bulk divacancy configurations that exhibit three orders of magnitude increase in the PL intensity by applying an appropriate repump lase (11). This observation indicates that PL6 qubit remains in its bright state under continuous excitation, while bulk divacancy configurations turn into the dark state with higher probability (11).
We propose that the additional divacancy related qubits are relented to divacancyquantum well structures created by a single stacking fault. Indeed, we found three distinguishable configurations, two basal plane and one axial configuration, that can account for the PL5 and PL7 basal plane and PL6 axial divacancy configurations reported in ODMR measurement in 4H-SiC. Furthermore, the calculated hyperfine, zero-fieldsplitting, and ZPL magneto-optical parameters obtained for the k2k2-ssf configuration agree well with the experimental data reported for PL6 divacancy related qubit (see Fig.   4, Fig. 6, and Supplementary Materials). Consequently, we assign the k2k2-ssf combined stacking fault-divacancy configuration to the PL6. The outstanding stability of PL6 qubit may be attributed to the mechanism discussed above and depicted in Fig. 1D.
The observed two additional basal plane divacancy configurations, k1h1-ssf and k2k1-ssf, may be related to the additional two basal plane ODMR centers, PL5 and PL7 (33). Due to the fewer experimental data available for PL5 and PL7 qubits, we cannot conclusively assign them at this point.

Discussion
The study of point defects embedded in extended defects (39) has received much less attention than that of pure point defects (24). These structures, however, may broaden the palette of point defect qubits and may provide a new avenue for engineering their properties for superior functionality. Through the example of divacancy qubits in close vicinity of a single stacking fault in 4H-SiC, we draw attention to an alternative way of engineering point defect qubit for robust quantum bits.
In particular, we demonstrated that quantum well of a stacking fault can give rise to a mechanism that can stabilize point defect qubits without the application of an additional re-pumping laser. Furthermore, by identifying PL6 room-temperature qubit as a divacancy-stacking fault structure, we demonstrated that defects in quantum wells are important and readily observable in ODMR and PL measurements in SiC.
The particular stability of PL6 center exemplified the stabilization mechanism of stacking fault quantum wells, but our results can be generalized to a wide variety of point defect qubits and single-photon emitters in semiconductors. Stacking faults can also appear in other semiconductors. For example, diamond, an important material for optically addressable spin qubits, also contains stacking faults (40). Thus, incorporating point defects into quantum wells could be an important strategy for discovering a large and robust class of new spin qubits.  (32,45), the basal planar size as well as the k-point grid density are optimized for all the magneto-optical parameters calculated in this study. The large axial size of the supercell allows us to calculate and compare near-stacking-fault and farther, bulk-like divacancies using the same model. To obtain the most accurate ground state hyperfine tensors of first neighbor 13 C and second neighbor 29 Si nuclei, HSE06 functional is used on a PBE relaxed supercell of 704 atoms with 3×3×1 k-point sampling. To obtain the ground state ZFS, we use a 1584 atom supercell with 2×2×1 k-point set, PBE Kohn-Sham wavefunctions, and our in-house implementation for the ZFS tensor calculation (46). In our computational study we concentrate on the most reliable ground state hyperfine and ZFS data, however, to supplement the discussion and our conclusions, we calculate the ZPL energies as well, see Supplementary Materials.