  Motivated by recent experimental progress on triangular lattice heavy-fermion
compounds, we investigate possible Lifshitz transitions and the scanning tunnel
microscope (STM) spectra of the Kondo-Heisenberg model on the triangular
lattice. In the heavy Fermi liquid state, the introduced Heisenberg
antiferromagnetic interaction ($J_H$) results in the twice Lifshitz transition
at the case of the nearest-neighbour electron hopping but with
next-nearest-neighbour hole hopping and the case of the nearest-neighbour hole
hopping but with next-nearest-neighbour electron hopping, respectively. Driven
by $J_H$, the Lifshitz transitions on triangular lattice are all continuous in
contrast to the case in square lattice. Furthermore, the STM spectra shows rich
line-shape which is influenced by the Kondo coupling $J_{K}$, $J_{H}$ and the
ratio of the tunneling amplitude $t_{f}$ versus $t_{c}$. Our work provides a
possible scenario to understand the Fermi surface topology and the quantum
critical point in heavy-fermion compounds.
