Scaling Spin Coherence in Solid-state Defect Qubit*

The electron spin coherence time T₂ is one of the most critical material parameters for qubits. Here we show a scaling relationship of T₂ of solid-state spin qubits on electron and nuclear spins’ parameters based on the cluster correlation expansion (CCE) calculations, constituting a new tool for the qubit material exploration [1,2]. We calculate T₂ for a single nuclear species for all stable spinful species with various spin densities n, and find that the scaling relationship T_2,i ~ n^-1.0|g|^-1.6I^-1.1 for a dilute (< 10²² cm^-3) spinful nuclear bath (g: g-factor of nuclear spin, I: quantum number of nuclear spin). We show the nuclear spin baths are decoupled under external magnetic fields typically encountered in experiments (> 30 mT), and the T₂ of the compounds can be estimated by (Σ_iT_2,i^-2)^-0.5. These relationships enable one to predict T₂ of the materials without extensive computations.

[1] G. Wolfowicz et al., Nat. Rev. Mater. 6, 906 (2021).

[2] S. Kanai et al., arXiv 2102.02986 (2021).