  The interesting properties of Kagome bands, consisting of Dirac bands and a
flat band, have attracted extensive attention. However, the materials with only
one Kagome band around the Fermi level cannot possess physical properties of
Dirac fermions and strong correlated fermions simultaneously. Here, we propose
a new type of band structure --- double Kagome bands, which can realize
coexistence of the two kinds of fermions. Moreover, the new band structure is
found to exist in a new two-dimensional material, phosphorus carbide P2C3. The
carbide material shows good stability and unusual electronic properties. Strong
magnetism appears in the structure by hole doping of the flat band, which
results in spin splitting of the Dirac bands. The edge states induced by Dirac
and flat bands coexist on the Fermi level, indicating outstanding transport
characteristics. In addition, a possible route to experimentally grow P2C3 on
some suitable substrates such as the Ag (111) surface is also discussed.
