  The surface of a 3D topological insulator is described by a helical electron
state with the electron's spin and momentum locked together. We show that in
the presence of ferromagnetic fluctuations the surface of a topological
insulator is unstable towards a superconducting state with unusual pairing,
dubbed Amperean pairing. The key idea is that the dynamical fluctuations of a
ferromagnetic layer deposited on the surface of a topological insulator couple
to the electrons as gauge fields. The transverse components of the magnetic
gauge fields are unscreened and can mediate an effective interaction between
electrons. There is an attractive interaction between electrons with momenta in
the same direction which makes the pairing to be of Amperean type. We show that
this attractive interaction leads to a $p$-wave pairing instability of the
Fermi surface in the Cooper channel.
