A tight binding model for quantum spin Hall effect on triangular optical lattice

We propose a tight binding model for the quantum spin Hall system on triangular optical lattice and we determined the edge state spectrum which contains gap traversing states as the hallmark of $\mathds{Z}_{2}$ topological insulator. The advantage of this system is the possibility of implementing it in the fermionic ultracold atomic system whose nearly free electron limit is proposed by B. B\'eri and N. R. Cooper, Phys. Rev. Lett. {\bf 107}, 145301 (2011).