  We investigated the transport properties of Fe$_{1+y}$Te$_{0.6}$Se$_{0.4}$
single crystals with different amounts of excess Fe prepared by O$_2$
annealing. The O$_2$ annealing remarkably improves transport properties. In
particular, a strongly nonlinear Hall resistivity was observed only in the
fully-annealed crystal, and the magnetoresistance (MR) is drastically enhanced
after annealing, reaching a value larger than 17% at 16 K and 14 T. The obvious
change of transport properties after the annealing indicates that the band
structure of Fe$_{1+y}$Te$_{0.6}$Se$_{0.4}$ is affected by the excess Fe. The
nonlinear Hall resistivity and violation of (modified) Kohler's scaling of the
large MR prove the multiband effects in the Fe$_{1+y}$Te$_{0.6}$Se$_{0.4}$
single crystal. The MR for the fully-annealed crystal develops linearly against
magnetic field from intermediate field (e. g. 2 T at 16 K) to the measurement
limit of 14 T. This phenomenon is interpreted by the existence of Dirac cone
state, in which all the Dirac fermions occupy only the lowest Landau level in
the quantum limit.

Superconductivity;Strongly Correlated Electrons