Magnetic excitations of Kitaev-Heisenberg models on honeycomb lattices

We investigate ground state energies and low-energy excitations of the S = 1/2 Kitaev-Heisenberg model on honeycomb lattices by using dimer series expansions. We find that dimer series expansions can approach the close vicinity of the Kitaev limit, where the Heisenberg interaction is absent, in the lower order expansion than the Ising series expansion. When the system approaches the Kitaev limit, low-lying modes in the zigzag and Néel phases become flatter except for the Bragg wave numbers.