Vortex Pinning in Thin Superfluid Films

Abstract

In a thin superfluid film, a region of reduced superfluid density will attract a vortex. Consider a closed region of size ~ b over which the superfluid density vanishes locally and consider a random distribution of such sites with density N_p << b^-2. When the surrounding superfluid is set into motion, such sites will create and annihilate free vortices¹. Because circulation is conserved, the annihilation of a vortex by a neutral site will cause that site to become “charged” i. e., to take on the circulation of the vortex and similarly for vortex creation. Hence, both charged and neutral sites must be treated simultaneously in the dynamics. This is the phenomenon of ‘vortex pinning’ in the two dimensional limit.