Extending the coherence of spin qubits in hexagonal boron nitride by materials engineering: a cluster expansion theory*

Negatively charged boron vacancy (V_B^-) in hexagonal boron nitride (h-BN) has recently emerged as a new promising spin qubit candidate in 2-dimensional materials hosts for solid-state quantum applications [1]. Their spin coherence time (T₂), however, was measured to be very short limited to a few microseconds [2], which is mainly due to their interaction to the inherent dense nuclear spin bath of the h-BN host [3]. In this study, we theoretically propose ways to enhance the quantum coherence of the V_B^- spin in h-BN by using isotopic and strain engineering. We combine density functional theory and cluster correlation expansion to compute the decoherence of V_B^- spins induced by the dense nuclear spin bath of h-BN. We show that inhomogeneous strain can create spatially varying nuclear quadrupole interaction in h-BN, which can significantly suppress the nuclear spin flip-flop dynamics in the bath. In addition, we find that the coherence time of the V_B^- spin can be effectively engineered by adjusting the ratio of ¹⁰B and ¹¹B isotopes in h-BN. We show that the combination of the two methods could increase the T₂ time by 4.5 times larger than the T₂ time in a pristine h-BN bulk. Our results provide not only a fundamental understanding of the decoherence of V_B^- spins in h-BN, but pave the way to engineer their T₂ time, which is crucial for their practical applications.