Topological insulator on honeycomb lattices and ribbons without inversion symmetry

We study the Kane-Mele-Hubbard model with an additional inversion-symmetry-breaking term. Using the topological Hamiltonian approach, we calculate the Z 2 invariant of the system as function of spin-orbit coupling, Hubbard interaction U , and inversion-symmetry-breaking onsite potential. The phase diagram calculated in that way shows that, on the one hand, a large term of the latter kind destroys the topological nontrivial state. On the other hand, however, this inversion-symmetry-breaking field can enhance the topological state since for moderate values the transition from the nontrivial topological to the trivial Mott insulator is pushed to larger values of interaction U . This feature of an enhanced topological state is also found on honeycomb ribbons. With inversion
symmetry, the edge of the zigzag ribbon is magnetic for any value of U . This magnetic moment destroys the gapless edge mode. Lifting inversion symmetry allows for a finite region in interaction strength U below which gapless edge modes exist.