  Unconventional superconductivity on a honeycomb lattice has received
increasing interest since the discovery of graphene primarily due to the
similarities between materials with a honeycomb lattice and cuprate
superconductors. Many theoretical studies have been conducted on
superconductivity on a honeycomb lattice, however, a consistent picture is
still lacking. In this article we have extended the theory of
kinetic-energy-driven superconductivity, which has been developed to
investigate unconventional superconductivity in cuprate superconductors, to
explore superconductivity on a honeycomb lattice within the $t$-$J$ model. Our
results demonstrate that the charge-carrier pair gap parameter with
$d_{x^{2}-y^{2}}+{\rm i}d_{xy}$-wave symmetry exhibits a dome-like shape as a
function of doping, with superconductivity emerging at a certain doping
concentration and disappearing at high doping levels, similar to what has been
observed in cuprate and cobaltate superconductors. Furthermore, the
charge-carrier pair gap parameter decreases with increasing the value of $J/t$
(the antiferromagnetic exchange coupling constant relative to the
nearest-neighbor hopping integral), and approaches zero when $J/t$ reaches a
sufficiently large value. This indicates that the antiferromagnetic order will
suppress the superconducting state and a sufficiently strong exchange coupling
will completely destroy the superconductivity. Taking into account our present
results together with the corresponding results of cuprate and cobaltate
superconductors, it appears that the dome-like shape of the doping dependence
of the charge-carrier pair gap parameter may be a common feature in doped Mott
insulators.
