  Coherent motion of electrons in a twisted quantum ring is considered to
explore the effect of torsion inherent to the ring. Internal torsion of the
ring composed of helical atomic configuration yields a non-trivial quantum
phase shift in the electrons' eigenstates. This torsion-induced phase shift
causes novel kinds of persistent current flow and an Aharonov-Bohm like
conductance oscillation. The two phenomena can occur even when no magnetic flux
penetrates inside the twisted ring, thus being in complete contrast with the
counterparts observed in untwisted rings.
