Local vibrational modes of Si vacancy spin qubits in SiC

Silicon carbide is a very promising platform for quantum applications because of the extraordinary spin and optical properties of point defects in this technologically friendly material. These properties are strongly influenced by crystal vibrations, but the exact relationship between them and the behavior of spin qubits is not fully investigated. We uncover the local vibrational modes of the Si vacancy spin qubits in as-grown 4H-SiC. We apply microwave-assisted spectroscopy to isolate the contribution from one particular type of defects, the so-called V2 center, and observe the zero-phonon line together with seven equally separated phonon replicas. Furthermore, we present first-principles calculations of the photoluminescence line shape, which are in excellent agreement with our experimental data. To boost up the calculation accuracy and decrease the computation time, we extract the force constants using machine-learning algorithms. This allows us to identify the dominant modes in the lattice vibrations coupled to an excited electron during optical emission in the Si vacancy. A resonance phonon energy of 36 meV and a Debye-Waller factor of about $6\%$ are obtained. We establish experimentally that the activation energy of the optically induced spin polarization is given by the local vibrational energy. Our findings give insight into the coupling of electronic states to vibrational modes in SiC spin qubits, which is essential to predict their spin, optical, mechanical, and thermal properties. The approach described can be applied to a large variety of spin defects with spectrally overlapped contributions in SiC as well as in other three- and two-dimensional materials.

Figure 1

Room-temperature and low-temperature PL from ${\mathrm{V}}_{\mathrm{Si}}$ in pristine 4H-SiC. At $T=300\mathrm{K}$, the shadow area around 970 nm indicates the spectral resolution $\mathrm{\Delta }\lambda =5.5$ nm. At $T=15\mathrm{K}$, the zero-phonon lines of two distinct ${\mathrm{V}}_{\mathrm{Si}}$ centers, V1 (ZPL at 863 nm) and V2 (ZPL at 918 nm), are clearly observed. The spectral resolution is $\mathrm{\Delta }\lambda =1.2$ nm $(\approx 2\mathrm{meV})$.

Figure 2

(a) Schematic representation of the V1 and V2 ${\mathrm{V}}_{\mathrm{Si}}$ defects associated with different crystallographic sites in 4H-SiC, according to [45]. (b) A scheme of the V2 spin pumping process. The red line presents the V2 spin center excited by an 808-nm laser. It relaxes to the ground state by two processes: radiative recombination (solid lines) and spin-dependent relaxation through the metastable states (MS) (dashed lines). The double arrow shows spin manipulation by the MW field at 70 MHz. (c) The V2 ODMR spectrum at room temperature and low temperature. The arrow indicates the resonance frequency of 70 MHz at zero magnetic field. (d) The V2 ODMR contrast at 70 MHz as a function of detection energy over the PL spectrum at room temperature.

Figure 3

(a) Evolution of the $\mathrm{\Delta }\mathrm{PL}$ spectrum with temperature under applied MW field at 70 MHz. (b) Temperature dependence of the spectrally integrated V2 $\mathrm{\Delta }\mathrm{PL}$ and the DW factor. The solid line is a fit to Eq. (1) with the activation energy $E_A=39\pm 4\mathrm{meV}$. (c) Temperature dependence of the ODMR contrast $\mathrm{\Delta }\mathrm{PL}/\mathrm{PL}$ detected at the V2 ZPL and the integrated PL. The solid line is a fit to Eq. (1) with the activation energy $E_A=39\pm 3\mathrm{meV}$ and $\mathrm{\Delta }\mathrm{PL}\left(0\right)$ replaced with $\mathrm{\Delta }\mathrm{PL}/\mathrm{PL}\left(0\right)$.

Figure 4

(a) Low-temperature ($T=15\mathrm{K}$) $\mathrm{\Delta }\mathrm{PL}$ of V2 as a function of the detection wavelength at the MW frequency of 70 MHz. The vertical axis for $\mathrm{PL}$ is the lock-in voltage of the modulated photodiode signal. The V2 ZPL (at 1.35 eV) and PSB are clearly resolved. The local vibrational energy read from two adjacent peaks is $\mathrm{\Delta }{E}_{\exp }=37\mathrm{meV}$. The dashed line represents the calculation of the V2 PSB as described in the text. (b) Zoom-in of the V2 ZPL. (c) A configuration coordinate diagram for the V2 phonon modes. The blue arrows show transitions from the ES to different vibrational levels of the GS.

Figure 5

(a) The arrangement of electronic states before (${\mathrm{Q}}_g$) and after (${\mathrm{Q}}_e$) excitations calculated using HSE06 functional. The states (dark lines) filled by electrons represented by arrows for spin-up and -down. The hollow circle denotes hole. (b) A schematic configuration coordinate diagram for the GS and ES showing the energy scale for different transitions.

Figure 6

(a) Pristine SiC phonon dispersion curves and the unfolded phonon curves of defective SiC along high-symmetry directions. (b) Electron-phonon spectral function accompanied by partial Huang-Rhys factors. (c) The calculated partial PSB in the energy range of 1.0–1.35 eV. (d) Schematic representations of atomic displacements of ${\mathrm{E}}_1$, TA(M), ${\mathrm{D}}_1$, and ${\mathrm{D}}_2$ modes. Blue and green balls denote silicon and carbon atoms, respectively. Arrows are proportional to the displacements and come from the real part of the eigenvectors at the $\mathrm{\Gamma }$ point. The defect site is shown by a red circle.