Quantum metrology with a single spin-$\frac{3}{2}$ defect in silicon carbide

We show that implementations for quantum sensing with exceptional sensitivity and spatial resolution can be made using spin-$\frac{3}{2}$ semiconductor defect states. We illustrate this using the silicon monovacancy deep center in hexagonal SiC based on our rigorous derivation of this defect's ground state and of its electronic and optical properties. For a single ${\mathrm{V}}_{\mathrm{Si}}^{-}$ defect, we obtain magnetic field sensitivities capable of detecting individual nuclear magnetic moments. We also show that its zero-field splitting has an exceptional strain and temperature sensitivity within the technologically desirable near-infrared window of biological systems. The concepts and sensing schemes developed here are applicable to other point defects with half spin multiplet ($S\ge \frac{3}{2}$) configurations.

Figure 1

Electronic structure and wave functions of $V_{\mathrm{Si}}^{-}$ in 4H-SiC. Each state has a twofold Kramer's degeneracy. The quartet GS (${}^4{A}_2$) can be optically spin polarized and read-out via the first quartet ES (${}^4{A}_2$) with $d_{\left|\right|}$ dipole moments along the defect's $c$ axis. The dark doublet states (3 ${}^{2}E, {}^2{A}_1$, and ${}^2{A}_2$) are ordered in energy on the right. Nonvanishing spin-orbit matrix elements to GS (ES) are shown by solid (dashed) arrows forming an ISC channel between quartets and doublets. ${\mathrm{\Delta }}_d$ and ${\gamma }_d$ are the energy splittings/shifts induced by the SO and SS interactions. ZFS splittings are labeled $2D$ for the GS and $2{\gamma }_{q1}$ for the ES. (Inset) Local $C_{3\nu }$ symmetry of the defect. $a,b,c,d$ represent the $s{p}^3$ dangling bonds of the surrounding carbon atoms.

Figure 2

(a) GS spin splittings versus magnetic field $B_z$ (along the $c$ axis) with fixed $B_{\perp }$ (along the basal plane). Avoided crossings ACL at the low ($\approx 1.25\mathrm{mT}$) and ACH at the high ($\approx 2.5\mathrm{mT}$) fields shown by vertical dashed lines. Spin projection states $\langle S_z\rangle =m_s$ are color coded. (b) GS energy splittings between spin states $m_s:3/2\leftrightarrow -1/2$ (${\omega }_1$) and $m_s:3/2\leftrightarrow 1/2$ (${\omega }_2$) versus $B_z$, and (c) $B_{\perp }$. (d) (Left) DC sensing: Ramsey pulse sequence. (Right) AC sensing: spin echo.

Figure 3

(a) Change in PL versus measurement time $t$ for a range (25–100 nT) of DC fields. (b) Change in PL versus measurement time $t$ for a range (25–75 nT) of AC fields with a fixed frequency (${\omega }_{\mathrm{AC}}=4.4\mathrm{kHz}$).

Figure 4

(a) ZFS of the GS versus the nonaxial strain ${\sigma }_{\perp }$ ($={\sigma }_{xx}={\sigma }_{xy}/2$ and $z\parallel c$ axis). (b) Fundamental mode of the SiC membrane with frequency $\omega =96.3\mathrm{MHz}$ for an amplitude $\left|A\right|\approx 15\mathrm{nm}$. Surface strain shown by color. Maximum flexural strain ${\sigma }_m=4.34\times {10}^{-4}$ corresponds to the defect placed on the surface at the center of a SiC MEMS membrane with diameter $d=10\mu m$ and thickness $h=0.3\mu m$.