Nonvortical Rashba Spin Structure on a Surface withC1hSymmetry

A totally anisotropic peculiar Rashba-Bychkov (RB) splitting of electronic bands was found on the $\mathrm{Tl}/\mathrm{Si}(110)\text{\ensuremath{-}}(1\ifmmode\times\else\texttimes\fi{}1)$ surface with ${C}_{1h}$ symmetry by angle- and spin-resolved photoelectron spectroscopy and first-principles theoretical calculation. The constant energy contour of the upper branch of the RB split band has a warped elliptical shape centered at a $k$ point located between $\overline{\mathrm{\ensuremath{\Gamma}}}$ and the edge of the surface Brillouin zone, i.e., at a point without time-reversal symmetry. The spin-polarization vector of this state is in-plane and points almost the same direction along the whole elliptic contour. This novel nonvortical RB spin structure is confirmed as a general phenomenon originating from the ${C}_{1h}$ symmetry of the surface.