Edge states and topological phases in non-Hermitian systems

Topological stability of the edge states is investigated for non-Hermitian\nsystems. We examine two classes of non-Hermitian Hamiltonians supporting real\nbulk eigenenergies in weak non-Hermiticity: SU(1,1) and SO(3,2) Hamiltonians.\nAs an SU(1,1) Hamiltonian, the tight-binding model on the honeycomb lattice\nwith imaginary on-site potentials is examined. Edge states with ReE=0 and their\ntopological stability are discussed by the winding number and the index\ntheorem, based on the pseudo-anti-Hermiticity of the system. As a higher\nsymmetric generalization of SU(1,1) Hamiltonians, we also consider SO(3,2)\nmodels. We investigate non-Hermitian generalization of the Luttinger\nHamiltonian on the square lattice, and that of the Kane-Mele model on the\nhoneycomb lattice, respectively. Using the generalized Kramers theorem for the\ntime-reversal operator Theta with Theta^2=+1 [M. Sato et al., arXiv:1106.1806],\nwe introduce a time-reversal invariant Chern number from which topological\nstability of gapless edge modes is argued.\n