  We study the phase diagram of a Rashba spin-orbit-coupled Bose-Einstein
condensate confined in a two-dimensional toroidal trap. In the immiscible
regime we find an azimuthally periodic density distribution, with the
periodicity highly tuneable as a function of the spin-orbit coupling strength
and which favours an odd number of petals in each component. This allows for a
wide range of states that can be created. We further show that in the miscible
regime, both components possess states with persistent flows with a unit
winding number difference between them and with the absolute values of these
winding numbers depending on the spin-orbit coupling strength. All features of
the odd-petal and the persistent flow states can be explained using a simple
but effective model.
