  Topological quantum phase transitions in superconductivity are discussed on
two dimensional lattices. The main focus is on the Chern number for
superconducting states. Each superconductivity is characterized by the Chern
number, and the quantum phase transition is associated with topological changes
of the quasiparticle Bloch function in the Brillouin zone. For the
superconducting case, the Chern number has several equivalent but different
topological expressions given by vortices, the Dirac monopole and strings. We
demonstrate quantum phase transitions by these topological quantities both for
singlet and triplet cases.
