Large shift currents via in-gap and charge-neutral excitons in a monolayer and nanotubes of BN

We perform ab initio many-body calculations to investigate the exciton shift current in small-diameter zigzag BN nanotubes and also single BN sheet, using the $GW$ plus Bethe-Salpeter equation ($GW$-BSE) method with the newly developed efficient algorithms. Our $GW$-BSE calculations reveal a large in-gap peak in the shift current spectrum in all the studied BN systems due to the $A$ exciton. The peak value of the excitonic shift current is more than three times larger than that of the quasiparticle shift current, and is attributed to the significant enhancement of the optical dipole matrix element by the $A$ exciton. The effective exciton shift current conductivity is nearly 10 times larger than the largest shift conductivity observed in ferroelectric semiconductors. Importantly, the direction of the shift current in the BN nanotubes is found to be independent of the tube chirality ($n,0$) (or diameter), contrary to the simple rule of $\text{sgn}({J}_{\text{shift}})=\text{mod}(n,3)$ predicted by previous model Hamiltonian studies. Finally, our ab initio calculations also show that the exciton excitation energies decrease significantly with the decreasing diameter due to the curvature-induced orbital rehybridization in small-diameter zigzag BN nanotubes.