  Ground-state and magnetocaloric properties of a double-tetrahedral chain, in
which nodal lattice sites occupied by the localized Ising spins regularly
alternate with triangular clusters half filled with mobile electrons, are
exactly investigated by using the transfer-matrix method in combination with
the construction of the $N$th tensor power of the discrete Fourier
transformation. It is shown that the ground state of the model is formed by two
non-chiral phases with the zero residual entropy and two chiral phases with the
finite residual entropy $S = Nk_{\rm B}\ln 2$. Depending on the character of
the exchange interaction between the localized Ising spins and mobile
electrons, one or three magnetization plateaus can be observed in the
magnetization process. Their heights basically depend on the values of Land\'e
$g$-factors of the Ising spins and mobile electrons. It is also evidenced that
the system exhibits both the conventional and inverse magnetocaloric effect
depending on values of the applied magnetic field and temperature.
