Spontaneous Hall effect in a chiral p-wave superconductor - art. no. 054514

In a chiral superconductor with broken time-reversal symmetry a "spontaneou s Hall effect" may be observed. We analyze this phenomenon by taking into a ccount the surface proper-ties of a chiral superconductor. We identify two main contributions to the spontaneous Hall effect. One contribution origina tes from the Bernoulli (or Lorentz) force due to spontaneous currents runni ng along the surfaces of the superconductor. The other contribution has a t opological origin and is related to the intrinsic angular momentum of Coope r pairs. The latter can be described in terms of a Chem-Simons-like term in the low-energy field theory of the superconductor and has some similaritie s with the quantum Hall effect. The spontaneous Hall effect in a chiral sup erconductor is, however, nonuniversal. Our analysis is based on three appro aches to the problem: a self-consistent solution of the Bogoliubov-de Genne s equation, a generalized Ginzburg-Landau theory, and a hydrodynamic formul ation. All three methods consistently lead to the same conclusion that the spontaneous Hall resistance of a two-dimensional superconducting Hall bar i s of order h/(ek(F)lambda)(2), where k(F) is the Fermi wave vector and lamb da is the London penetration depth; the Hall resistance is substantially su ppressed from a quantum unit of resistance. Experimental issues in measurin g this effect are briefly discussed.