  Recent experimental measurements of light absorption in few-layer black
phosphorus (BP) reveal a series of high and sharp peaks, interspersed by pairs
of lower and broader features. Here, we propose a theoretical model for these
excitonic states in few-layer black phosphorus (BP) within a continuum approach
for the in-plane degrees of freedom and a tight-binding approximation that
accounts for inter-layer couplings. This yields excitonic transitions between
different combinations of the sub-bands created by the coupled BP layers, which
leads to a series of high and low oscillator strength excitonic states,
consistent with the experimentally observed bright and dark exciton peaks,
respectively. The main characteristics of such sub-band exciton states, as well
as the possibility to control their energies and oscillator strengths via
applied electric and magnetic fields, are discussed, towards a full
understanding of the excitonic spectrum of few-layer BP and its tunability.
