Effect of Spatial Dimensionality on the Spin-Coherence Decay in Strongly-Coupled Spin Baths

For quantum-technology applications, spin defects in solids are promising candidates but they are limited by their spin-coherence time. Hence, understanding the processes governing the spin-coherence decay is essential. We numerically calculate the spin-coherence time T2 of the NV--centre electron spin in diamond layers of different thickness in presence of a strongly-coupled disordered electron-spin bath. We show that the spin-coherence time in two-dimensional spin baths is longer than in three-dimensional spin baths. Furthermore, we obtain the corresponding stretched-exponential parameter, which also depends on the spatial dimensionality. We use the partitioning-based cluster-correlation expansion (pCCE) method, which partitions the bath into local subsystems and applies the clustion-correlation expansion method to these subsystems instead of individual spins, thereby offering a better numerical accuracy, especially in two-dimensional geometries.