<i>Ab initio</i> investigation of the Cr substitutional defect in α-quartz for quantum applications

Spin defects based on transition metals in wide-bandgap oxides represent compelling building blocks for quantum information technologies because they host highly localized electronic states with spin-dependent optical selection rules. Here, we assess α-quartz silicon dioxide (SiO2) as a promising platform for quantum technological applications by substituting an Si atom with Cr (denoted as CrSi). For our investigation, we use the r2SCAN exchange correlation functional due to its favorable accuracy-to-computational-cost ratio for defect energetics and structure. The r2SCAN functional provides a better accuracy than the typical generalized gradient approximation functionals. We also employ multi-reference complete active space self-consistent field to capture the d-electron excited states, particularly the low-spin states that density functional theory cannot accurately describe due to their multi-reference characters. The CrSi defect introduces deep, well-localized in-gap states and yields a paramagnetic ground state. These features are desirable for quantum applications because they can enable optical spin control. We calculate the excitation energy and the zero-field splitting for the relevant charge and spin configuration. We find that CrSi has an excitation energy between 1.26 and 1.33 eV for the first spin-allowed excitation, while the zero-field splitting (ZFS) parameters D (axial) and E (rhombic) are approximately 425 and 136 MHz, respectively. Comparison with the β-quartz host indicates that α-quartz allows a lower excitation energy and an appropriately moderate ZFS, making it a promising solid-state qubit platform.