  We investigate the pairing symmetry of the Kondo-Heisenberg model on
triangular lattice, which is believed to capture the core competition of Kondo
screening and local magnetic exchange interaction in heavy electron compounds.
On the dominant background of the heavy fermion state, the introduction of the
Heisenberg antiferromagnetic interaction ($J_H$) leads to superconducting
pairing instability. Depending on the strength of the interactions, it is found
that the pairing symmetry prefers an extended $s$-wave for small $J_H$ and high
conduction electron density but a chiral $d_{x^2-y^2}+id_{xy}$-wave for large
$J_H$ and low conduction electron density, which provides a phase diagram of
pairing symmetry from the calculations of the ground-state energy. The
transition between these two pairing symmetries is found to be first-order.
Furthermore, we also analyze the phase diagram from the pairing strengths and
find that the phase diagram obtained is qualitatively consistent with that
based on the ground-state energy. In addition, we propose an effective
single-band BCS Hamiltonian, which is able to describe the low-energy
thermodynamic behaviors of the heavy fermion superconducting states. These
results further deepen the understanding of the antiferromagnetic interaction
which results in a geometric frustration for the model studied. Our work may
provide a possible scenario to understand the pairing symmetry of the heavy
fermion superconductivity, which is the one of active issues in very recent
years.

Strongly Correlated Electrons;Superconductivity