  The presence of inherently strong spin-orbit coupling in bismuth, its unique
layer-dependent band topology and high carrier mobility make it an interesting
system for both fundamental studies and applications. Theoretically, it has
been suggested that strong quantum size effects should be present in the
Bi(110) films, with the possibility of Dirac fermion states in the odd-bilayer
(BL) films, originating from dangling $p_z$ orbitals and quantum-spin hall
(QSH) states in the even-bilayer films. However, the experimental verification
of these claims has been lacking. Here, we study the electronic structure of
Bi(110) films grown on a high-$T_c$ superconductor,
Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi2212) using angle-resolved photoemission
spectroscopy (ARPES). We observe an oscillatory behavior of electronic
structure with the film thickness and identify the Dirac-states in the
odd-bilayer films, consistent with the theoretical predictions. In the
even-bilayer films, we find another Dirac state that was predicted to play a
crucial role in the QSH effect. In the low thickness limit, we observe several
extremely one-dimensional states, probably originating from the edge-states of
Bi(110) islands. Our results provide a much needed experimental insight into
the electronic and structural properties of Bi(110) films.
