  We use microprobe Angle-Resolved Photoemission Spectroscopy to study the
Fermi surface and band dispersion of the CuO2 planes in the high temperature
superconductor, YBa2Cu4O8. We find a strong in-plane asymmetry of the
electronic structure between directions along a and b axes. The saddle point of
the antibonding band lies at a significantly higher energy in the a direction
(pi,0) than the b direction (0,pi), whereas the bonding band displays the
opposite behavior. We demonstrate that the abnormal band shape is due to a
strong asymmetry of the bilayer band splitting, likely caused by a non-trivial
hybridization between the planes and chains. This asymmetry has an important
implication for interpreting key properties of the Y-Ba-Cu-O (YBCO) family,
especially the superconducting gap, transport and results of inelastic neutron
scattering.
