Vortex sheets can be viable defects present in quantum systems. In two dimensions, the vortex sheet is represented by a Line connecting a pair of branch points of half-integer phase rotation. A stationary vortex sheet can exist in a finite system either with a pinning potential or without any pinning potential as long as the rotational symmetry is broken. Despite the rotational symmetry breaking, an angular-momentum-like quantum number is always required for the existence of a stationary vortex sheet. Such a property is closely related to the integrability of a dynamical system. [S1063-651X(98)10012-0].
