Superconductivity with nonzero Chern numbers

In strongly correlated electron systems it often happens that electronic bands acquire nonzero Chern numbers, either by spin chirality or by spin-orbit coupling. It implies that the phase of the wave functions cannot be defined uniquely all over the Brillouinzone, and one should be careful in defining order parameters. In this paper, we will develop a theory of condensation happening in bands with nonzero Chem numbers. We take the model on the honeycomb lattice proposed by Haldane as an example, and explain what will happen when superconductivity occurs in a band with a nonzero Chern number. It can also be related to quantization of spin Hall conductivity. (C) 2003 Elsevier Science B.V. All rights reserved.