  Vicinal surfaces of bismuth are unique test-beds for investigating
one-dimensional (1D) spin-polarised surface states that may one day be used in
spintronic devices. In this work, two such states have been observed for the
(112) surface when measured using angle-resolved photoemission spectroscopy
(ARPES) and spin-resolved ARPES, and when calculated using a tight-binding (TB)
model and with density functional theory (DFT). The surface states appear as
elongated Dirac-cones which are 1D and almost dispersionless in the
${k}_{\text{y}}$-direction, but disperse with energy in the orthogonal
${k}_{\text{x}}$-direction to form two ``$\times$''-like features centered at
the ${k}_{\text{y}}$-line through ${\Gamma}$. Unlike many materials considered
for spintronic applications, their 1D nature suggests that conductivity and
spin-transport properties are highly dependent on direction. The
spin-polarisation of the surface states is mainly in-plane and parallel to the
1D state, but there are signs of a tilted out-of-plane spin-component for one
of them. The Bi(112) surface states resemble those found for other vicinal
surfaces of bismuth, strongly indicating that their existence and general
properties are robust properties of vicinal surfaces of bismuth. Furthermore,
differences in the details of the states, particularly related to their
spin-polarisation, suggest that spin-transport properties may be engineered
simply by precise cutting and polishing of the crystal.
