  It is shown that it is possible for bound fermions on a cosmic string to form
a superconducting state. Due to the attractive force between them, particles
moving in opposite directions along the string form bound pairs. This involves
a similar mechanism to superconductivity in metals at low temperatures. The
method of Gorkov is used to analyse the system. In contrast to the situation in
metals, the unusual properties of the string fermion spectrum allow a massless
Abelian gauge field to provide the required attractive force. This results in
far stronger superconductivity than usual. A massive gauge field can also be
used, in which case the standard results apply.
