Cooper Instability in a Half-filled Landau Level.

Son’s theory of the half-filled Landau level, in which the composite fermion is a Dirac particle, is examined in the thesis. The variant of the theory studied is one in which the Dirac fermion is massive, which ought to simulate Landau level mixing. We tried to find whether there is an instability for Cooper pair formation within the RPA approximation. Similar analysis had been done for massless case and it was discovered that there is no instability in the static case. Addition of the mass to the theory did not change the conclusions in the static case, but the instabilities have been found within a different quasi-particle representation.