Non-trivial Surface-band Dispersion on Bi(111)

We performed angle-resolved photoelectron spectroscopy of the Bi(111) surface to demonstrate that this surface support edge states of non-trivial topology. Along the $\bar{\mathrm{\Gamma }}\bar{M}$-direction of the surface Brillouin zone, a surface-state band disperses from the projected bulk valence bands at $\bar{\mathrm{\Gamma }}$ to the conduction bands at $\bar{M}$ continuously, indicating the non-trivial topological order of three-dimensional Bi bands. We ascribe this finding to the absence of band inversion at the $L$ point of the bulk Bi Brillouin zone. According to our analysis, a modification of tight-binding parameters can account for the non-trivial band structure of Bi without any other significant change on other physical properties.