Theory of strained quantum emitters

Abstract

Defects in semiconductors acting as optically active spin qubits are intriguing objects of fundamental study and future technological developments. These defect-based color centers are of particular interest for detection and response to physical variations such as pressure and strain. To investigate the defect emission response to strain, we have studied the vibrational structure of the negatively charged silicon vacancy ($\mathrm{V_{Si}^{-}}$) in 4H-SiC under applied tensile and compressive uniaxial strain using first-principles calculations. The strain variations of the emission spectrum can be explained by differing responses of bulk-like and quasi-localized vibrational modes. In particular, substantial differences are found between the hexagonal ($h$) and quasicubic ($k$) configurations of $\mathrm{V_{Si}^{-}}$ in 4H-SiC that result in a strain-induced improvement of the Debye-Waller factor for $\mathrm{V_{Si}^{-}}(h)$ under $+2\%$ uniaxial strain along the $a$-axis of 4H-SiC. Finally, strain-dependent changes in the phonon sideband enable distinguishing between compressive and tensile strain, opening up the possibility of magnetic field-free strain detection using only spin-conserving transitions of solid-state quantum emitters.

Figures (9)

• Figure 1: (a) Ball-and-stick representation of the silicon vacancy ($\mathrm{V_{Si}}$) defect in 4H-SiC. Silicon and carbon atoms are shown as blue and brown spheres, respectively, while the vacancy site is depicted as a hollow sphere. Two nonequivalent configurations, hexagonal $\mathrm{V_{Si}}(h)$ and quasicubic $\mathrm{V_{Si}}(k)$, are illustrated. The planes labeled h and k indicate the symmetry of the corresponding lattice sites. (b) Schematic representation of single-particle defect levels in the band gap of 4H-SiC showing their occupations in the ground $^{4}A_{2}$ state (bottom) and excited $^{4}A'_{2}$ state (top) of $\mathrm{V_{Si}^{-}}$. The spin-majority channel (left side) is denoted with upward arrows and the spin-minority channel (right side) with downward arrows. Shaded areas correspond to the valence band (VB) in blue and the conduction band (CB) in orange.
• Figure 2: Spectral functions of electron--phonon coupling $S(\hbar\omega)$ (in meV$^{-1}$) for the emission of the $\mathrm{V_{Si}^{-}}$ defect in 4H-SiC under uniaxial strain applied along the $a$-axis. Panels (a)--(c) correspond to the hexagonal $\mathrm{V_{Si}^{-}}(h)$ configuration, while (d)--(f) show results for the quasicubic $\mathrm{V_{Si}^{-}}(k)$ configuration. Each column shows results for strain magnitudes of $0\%$, $+2\%$, and $-2\%$, respectively. Insets illustrate the effective shapes of collective vibrations corresponding to delocalized bulk-like and quasi-localized modes. Amplitudes are scaled for visual clarity.
• Figure 3: Calculated emission lineshapes for supercells with $\mathrm{V_{Si}^{-}}(h)$ and $\mathrm{V_{Si}^{-}}(k)$ defects with zero (middle panels, black curves), $+2\%$ (top panels, blue curves) and $-2\%$ (bottom panels, orange curves) uniaxial strain applied along $a$-axis. The shaded gray areas in the middle panels represent experimental data measured on $\mathrm{V_{Si}^{-}}$ ensembles for the strain-free case. Calculated strain-free lineshapes are also shown as black dotted lines in the top and bottom panels, allowing comparison with the calculated strained lineshapes. Emission lineshapes were computed with the r$^{2}$SCAN functional using HR theory and extrapolated to the dilute limit, approximated by a $25\times25\times8$ supercell with 40 000 atomic sites.
• Figure S1: Illustration of the embedding methodology for defect vibrational structure calculations.
• Figure S2: Comparison of vibrational and optical properties of the $\mathrm{V_{Si}^{-}}(h)$ and $\mathrm{V_{Si}^{-}}(k)$ defects in unstrained 4H-SiC. Shaded areas in light-gray color are experimental emission lineshapes while dashed gray lines are emission lineshapes calculated using HR theory. The solid black line shows the calculated bulk phonon density of states (DOS). Vertical gray lines show the ground-state vibrational localization ratios $\beta$ computed for a $25\times25\times8$ supercell (40 000 atomic sites).