  We analytically study the electronic structures and optical properties of
zigzag-edged black phosphorene nanoribbons (ZPNRs) utilizing the tight-binding
(TB) Hamiltonian and Kubo formula. By solving the discrete Schordinger equation
directly, we obtain the energy spectra and wavefunctions for a $N$-ZPNR with
$N$ number of transverse zigzag atomic chains, and classify the eigenstates
according to the lattice symmetry. We then obtain the optical transition
selection rule of ZPNRs based on the symmetry analysis and the analytical
expressions of the optical transition matrix elements. Under an incident light
linearly-polarized along the ribbon, importantly, we find that the optical
transition selection rule for the $N$-ZPNR with even- or odd-$N$ is
qualitatively different. In specification, for even-$N$ ZPNRs the inter-
(intra-) band selection rule is $\Delta n=$odd (even), since the parity of the
wavefunction corresponding to the $n$th subband in the conduction (valence)
band is $(-1)^{n}[(-1)^{(n+1)}]$ due to the presence of the $C_{2x}$ symmetry.
In contrast, all optical transitions are possible among all subbands due to the
absence of the $C_{2x}$ symmetry. Our findings provide a further understanding
on the electronic states and optical properties of ZPNRs, which are useful in
the explanation of the optical experiment data on ZPNR samples.
