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We perform {\it ab initio} many-body calculations to investigate the excitonshift current in small diameter zigzag BN nanotubes and also single BN sheet,using the GW plus Bethe-Salpeter equation (GW-BSE) method with the newlydeveloped efficient algorithms. Our GW-BSE calculations reveal a giant in-gappeak in the shift current spectrum in all the studied BN systems due to theexcitation of the A exciton. The peak value of the excitonic shift current ismore than three times larger than that of the quasiparticle shift current, andis attributed to the gigantic enhancement of the optical dipole matrix elementby the A exciton resonance. The effective exciton shift current conductivity isnearly ten times larger than the largest shift conductivity observed inferroelectric semiconductors. Importantly, the direction of the shift currentin the BN nanotubes is found to be independent of the tube chirality ($n,0$)(or diameter), contrary to the simple rule of $sgn(J_\text{shift})=\text{mod}(n,3)$ predicted by previous model Hamiltonianstudies. Finally, our {\it ab initio} calculations also show that the excitonexcitation energies decrease significantly with the decreasing diameter due tothe curvature-induced orbital rehybridization in small diameter zigzag BNnanotubes.

Large shift current via in-gap and charge-neutral exciton excitations in BN nanotubes and single BN layer