Nonconventional screening of Coulomb interaction in hexagonal boron nitride nanoribbons

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 Å 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 Å, the antiscreening effect is not observed. For completeness, on-site and long-range Coulomb interactions for metallic nonpassivated zigzag h-BNNRs are also reported.

Figure 1

h-BN nanoribbons with two types of edges: (a) $N_a=8$ (8-Ah-BNNR:H) and (b) $N_a=9$ (9-Ah-BNNR:H) are armchair ribbons having different width. $N_a$ is the number of dimer lines across the ribbon width. (c)–(e) Zigzag ribbons of $N_z=8$ (8-Zh-BNNR:H), $N_z=9$ (9-Zh-BNNR:H), and $N_z=7$ (7-Zh-BNNR), respectively. $N_z$ is the number of zigzag chains across the ribbon width.

Figure 2

Nonmagnetic orbital-projected band structure of (a) 8-Zh-BNNR:H, (b) 8-Ah-BNNR:H, and (c) 7-Zh-BNNR. The Fermi level is set to zero energy.

Figure 3

DFT-PBE and Wannier-interpolated band structure of nonmagnetic (a) 8-Ah-BNNR:H and (b) 7-Zh-BNNR. Dashed lines denote the Fermi energy, which is set to zero.

Figure 4

Calculated partially screened on-site interaction $U$ (blue line) and fully screened Coulomb interaction $W$ (red line) of $p_z$ electrons for (a) 8-Ah-BNNR:H, (b) 7-Zh-BNNR:H, (c) 9-Ah-BNNR:H, and (d) 8-Zh-BNNR:H.

Figure 5

Projected DOS for (a) edge B, (b) inner B, (c) edge N, and (d) inner N of 8-Ah-BNNR; and (e) edge B, (f) inner B, (g) edge N, and (h) inner N of 8-Zh-BNNR:H.

Figure 6

Bare, partially, and fully screened Coulomb interaction for B-N $p_z$ electrons as a function of distance $r$ for (a), (b) 8-Ah-BNNR:H and (c),(d) 8-Zh-BNNR:H. Here, $U(\parallel )$ and $U(\perp )$ correspond to interactions along the ribbon and across the ribbon, respectively.

Figure 7

The difference $V-W$ between bare interaction $V$ and fully screened interaction $W$ as a function of distance $r$ between B-N atoms along the ribbon for the edge and central atoms of (a) 9-Ah-BNNR:H and (b) 6-Zh-BNNR:H.

Figure 8

The difference $V-W$ value as a function of distance $r$ for central atoms of (a) $N_a=2$ to $N_a=11$ Ah-BNNR:H and (b) $N_z=3$ to $N_z=9$ Zh-BNNR:H.

Figure 9

(a) Hubbard $U$ and fully screened interactions $W$ for 7-Zh-BNNR. (b) Bare, partially $U$, and fully $W$ screened off-site interactions as a function of distance $r$ for 7-Zh-BNNR.

Figure 10

Orbital-projected DOS for (a) edge N [atom number 1 in Fig. 1], (b) inner N (atom number 7), (c) edge B (atom number 14), and (d) inner B (atom number 8) of 7-Zh-BNNR.