We show, by way of tight-binding and first-principles calculations, that a one-to-one correspondence between electron's crystal momentum k and non-zero orbital angular momentum (OAM) is a generic feature of surface bands. The OAM forms a chiral structure in momentum space much as its spin counterpart in Rashba model does, as a consequence of the inherent inversion symmetry breaking at the surface but not of spin-orbit interaction. Circular dichroism (CD) angle-resolved photoemission (ARPES) experiment is an efficient way to detect this new order, and we derive formulas explicitly relating the CD-ARPES signal to the existence of OAM in the band structure. The cases of degenerate p- and d-orbital bands are considered.
