  Topological phases and topological phase transitions (TPT) are among the most
fantastic phenomena in Nature. Here we show that injecting a current may lead
to new topological phases, especially new gapless topological metallic phases
with extended Fermi surfaces (FSs) through novel class of TPTs in the bulk or
the boundary. Specifically, we study the quantum anomalous Hall (QAH) system in
a square lattice under various forms of injecting currents. In addition to the
previously known Chern insulator (which will be called even Chern insulator
here), band insulator and band metal (BM), we find three new topological phases
we name as: the gapped odd Chern insulator (Odd CI), the gapless odd Chern
metal (Odd CM) and even Chern metal (Even CM). The Chern number may not be
effective anymore in characterizing the topological gapless phases with
extended FS. It is the Hall conductance which acts as the new topological
invariant in such gapless systems. Its jump is a universal integer or
non-integer across the even CM/BM or odd CM/BM TPT respectively where there is
also a corresponding TPT in the Longitudinal (L-)edge modes. The Odd/even CM to
BM transition is a novel class of TPT without any non-analyticity in the ground
state energy density. This presents the first example of a TPT which is not a
quantum phase transition (QPT). The original bulk-edge correspondence is
enriched into bulk/Longitudinal (L-)/Transverse (T-) edge correspondence. The
L-edge reconstruction may happen earlier, later or at the same time as the bulk
TPT respectively in the even CI/odd CI/odd CM sequence with the edge dynamic
exponent $ z_L=3 $, in the even CI/even CM/odd CM sequence with $ z_L=2 $ or a
direct even CI/odd CM with a flat edge. The disappearance of the T-edge always
happen at the same time as the bulk TPT with a universal edge critical
behaviour.
