Nonconventional screening of Coulomb interaction in hexagonal boron nitride nanoribbons

Abstract

Strong excitonic effects is a very subtle issue in pristine hexagonal boron nitride (h-BN) and h-BN nanoribbons (h-BNNRs) due to large band gaps and reduced dimensionality. One of the reasons for such a large exciton binding energy (as large as 2.5 eV) is weak dielectric screening. Employing first-principles calculations in conjunction with the constrained random-phase approximation, we determine the strength of the Coulomb matrix elements for pristine h-BN and h-BNNRs with armchair and zigzag edges. Due to the nonconventional screening, the calculated off-site $U$ parameters for passivated h-BNNRs turn out to be rather sizable. Coulomb interaction is weakly screened at short distances and antiscreened at intermediate distances. Transition from screening to antiscreening takes place at a distance as low as 8 \AA{} in narrow passivated h-BNNR. The critical distance for the onset of antiscreening in hydrogen-terminated h-BNNRs is longer than in zero-dimensional molecules and clusters, but shorter than in graphene nanoribbons and carbon nanotubes. With increasing the width of the passivated h-BNNRs from the critical point about 12.6 \AA{}, the antiscreening effect is not observed. For completeness, on-site and long-range Coulomb interactions for metallic nonpassivated zigzag h-BNNRs are also reported.