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Computational details:
The first-principles calculations of present work are carried out using a many-body
perturbation theory approach, based on a three-step procedure.1 First, the ground-state
electronic properties of the relaxed BNNRs are obtained by performing DFT-LDA
calculations using a plane-wave approach, as implemented in the QUANTUM-ESPRESSO
package,2 with norm-conserving pseudopotentials and a kinetic energy cutoff of 40 Ry. Each
atomic structure is fully relaxed, until forces acting on each atom are less than 1×10-2 eV/Å.
Periodic boundary condition along the ribbon axis is applied. Both of the vacuum thicknesses
along the non-periodic direction [the direction b and c shown in Fig. 1(a) as an example] are
larger than 15 Å to avoid interaction between images. The Brillouin zone integration is done
by 1×1×45 within the Monkhorst-Pack scheme for all calculations. Second, electronic
quasiparticle corrections are calculated within the G0W0 approximation with 14 Ry and 5 Ry
energy cutoffs for computing the exchange and the correlation parts of self-energy,
respectively. The screening is treated within the plasmon-pole approximation;3 a 5 Ry energy
cutoff and 200 bands are used for calculating the dielectric function. A box-shape truncated
Coulomb interaction is used to simulate truly isolated BNNRs.4 Finally, the electron-hole
interaction is included by solving the Bethe-Salpeter equation (BSE) in the basis set of
quasielectron and quasihole states. Only the resonant part of the BS Hamiltonian is taken into
account (Tamm-Dancoff approximation)
5
in our calculations. For the optical absorption
spectra calculations, five valence bands and ten conduction bands are considered, an energy
cutoff of 7 Ry and 200 bands are included for the calculation of the static screening. All the
GW and BS calculations are performed with the code YAMBO.6
1
G. Onida, L. Reining, and A. Rubio, Rev. Mod. Phys. 74, 601(2002).
2
S. Baroni, A. D. Corso, S. de Gironcoli, P. Giannozzi, C. Cavazzoni, G. Ballabio, S. Scandolo, G.
Chiarotti, P. Focher, A. Pasquarello, K. Laasonen, A. Trave, R. Car, N. Marzari, and A. Kokalj,
http://www. quantum-espresso.org
3
R. W. Godby and R. J. Needs, Phys. Rev. Lett. 62, 1169 (1989).
4
C. A. Rozzi, D. Varsano, A. Marini, E. K. U. Gross, and A. Rubio, Phys. Rev. B 73, 205119 (2006).
5
A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (Dover, New York, 2003),
Chap. 15, p. 565.
6
A. Marini, C. Hogan, M. Grüning, and D. Varsano, Comput. Phys. Commun. 180, 1392 (2009). (See
http://www.yambo-code.org).