Unconventional Energy Bands and Chirality of Ultracold Atoms in Trilayer Honeycomb Lattice

We investigate ultracold fermionic atoms in the trilayer honeycomb lattice. In the low energy approximation, we derive an effective Hamiltonian for pseudospins. The energy spectrum shows a cubic form of the wavevector and is gapless. The quasiparticles and quasiholes are chiral and show Berry's phase π when thewavevector adiabatically evolves along a closed circle. Furthermore, the experimental detection of the energy spectrum is proposed with Bragg scattering techniques.