  Two Bi2201 model systems are employed to demonstrate how, beside the Cu-O
\sigma-band, a second band of purely O2p\pi character can be made to cross the
Fermi level owing to its sensitivity to the local crystal field. This result is
employed to explain the particle-hole symmetry breaking across the pseudo-gap
recently reported by Shen and co-workers, see M. Hashimoto et al., Nature
Physics 6, (2010) 414. Support for a two-bands-on-a-checkerboard candidate
mechanism for High-Tc superconductivity is claimed.
