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

Amperean Pairing at the Surface of Topological Insulators