Spontaneous Hall effect in chiral p-wave superconductor

Details Spontaneous Hall effect in chiral p-wave superconductor Spontaneous Hall effect in chiral p-wave superconductor

2001-02-08

arxiv.org/abs/cond-mat/0102143v1

Phys. Rev. B 64 (2001) 054514

Physics

Condensed Matter

Superconductivity

22 pages including 12 figures

Scientific paper

10.1103/PhysRevB.64.054514

In a chiral superconductor with broken time-reversal symmetry a ``spontaneous Hall effect'' may be observed. We analyze this phenomenon by taking into account the surface properties of a chiral superconductor. We identify two main contributions to the spontaneous Hall effect. One contribution originates from the Bernoulli (or Lorentz) force from spontaneous currents running along the surfaces of the superconductor. The other contribution has a topological origin and is related to the intrinsic angular momentum of Cooper pairs. The latter can be described in terms of a Chern-Simons-like term in the low-energy field theory of the superconductor and has some similarities with the quantum Hall effect. The spontaneous Hall effect in a chiral superconductor is, however, non-universal. Our analysis is based on three approaches to the problem: a self-consistent solution of the Bogoliubov-de Gennes equation, a generalized Ginzburg-Landau theory, and a hydrodynamic formulation. All three methods consistently lead to the same conclusion that the spontaneous Hall resistance of a two-dimensional superconducting Hall bar is of order h/(e k_F\lambda)^2, where k_F is the Fermi wave vector and \lambda is the London penetration depth; the Hall resistance is substantially suppressed from a quantum unit of resistance. Experimental issues in measuring this effect are briefly discussed.

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