  The existence of the $0_3^+$ and $0_4^+$ states around 10 MeV excitation
energy in ${^{12}{\rm C}}$ is confirmed by a fully microscopic 3$\alpha$
cluster model. Firstly, a GCM (generator coordinate method) calculation is
performed by superposing optimized 2$\alpha$+$\alpha$ THSR
(Tohsaki-Horiuchi-Schuck-R\"{o}pke) wave functions with the radius-constraint
method. The obtained two excited $0^+$ states above the Hoyle state are
consistent with the recently observed states by experiment. Secondly, a
variational calculation using the single 2$\alpha$+$\alpha$ THSR wave function
orthogonalized to the ground and Hoyle states is made and it also supports the
existence of the $0_3^+$ state obtained by the GCM calculation. The analysis of
the obtained $0_3^+$ state is made by studying its 2$\alpha$-$\alpha$ reduced
width amplitude, its 2$\alpha$ correlation function, and the large monopole
matrix element between this state and the Hoyle state, which shows that this
$0_3^+$ state is a breathing-like excited state of the Hoyle state. This
character of the $0_3^+$ state is very different from the $0_4^+$ state which
seems to have a bent-arm 3$\alpha$ structure.
