  A positroid variety is an intersection of cyclically rotated Grassmannian
Schubert varieties. Each graded piece of the homogeneous coordinate ring of a
positroid variety is the intersection of cyclically rotated (rectangular)
Demazure modules, which we call the cyclic Demazure module. In this note, we
show that the cyclic Demazure module has a canonical basis, and define the
cyclic Demazure crystal.
