  The ground state of the bipartite $t$-$J$ model must satisfy a specific sign
structure, based on which the single-hole and two-hole ground state
$Ans\ddot{a}tze$ on honeycomb lattice are constructed and studied by a
variational Monte Carlo (VMC) method. The VMC results are in good agreement
with the exact diagonalization (ED) calculation. For the single-hole case, the
degenerate ground states are characterized by quantum numbers of a spin-1/2 and
an orbital angular momentum $L_z=\pm 2$. The latter is associated with the
emergent chiral spin/hole currents mutually surrounding the hole/spin-1/2 as a
composite object or ``twisted hole''. A vanishing quasiparticle spectral weight
is shown in the large-sample limit. In the two-hole ground state, the holes
form a spin-singlet pairing with $d$+$id$ symmetry in the Cooper channel, but
are of $s$-wave symmetry as a tightly bound pair of the ``twisted holes''. Such
a pairing mechanism of dichotomy can be attributed to eliminating the local
spin currents which has nothing to do with the long-range antiferromagnetic
correlation. Superconducting ground state at finite doping is briefly discussed
in terms of the tightly bound hole pairs as the building blocks.
