Topological invariants in interacting Quantum Spin Hall: a Cluster Perturbation Theory approach

Abstract

Using Cluster Perturbation Theory we calculate Green's functions, quasi-particle energies and topological invariants for interacting electrons on a 2-D honeycomb lattice, with intrinsic spin-orbit coupling and on-site e-e interaction. This allows to define the parameter range (Hubbard U vs spin-orbit coupling) where the 2D system behaves as a trivial insulator or Quantum Spin Hall insulator. This behavior is confirmed by the existence of gapless quasi-particle states in honeycomb ribbons. We have discussed the importance of the cluster symmetry and the effects of the lack of full translation symmetry typical of CPT and of most Quantum Cluster approaches. Comments on the limits of applicability of the method are also provided.

arXiv comment7 pages, 7 figures: discussion improved, one figure added, references updated. Matches version published in New J. Phys

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• Topological invariants for interacting topological insulators: I. Efficient numerical evaluation scheme and implementations
• Topological properties of the bond-modulated honeycomb lattice
• Dynamics and Control of Edge States in Laser-driven Graphene Nanoribbons
• Periodically driven interacting electrons in 1D: a many-body Floquet approach
• Corroborating the bulk-edge correspondence in weakly interacting 1D topological insulators
• Topological insulator on honeycomb lattices and ribbons without inversion symmetry
• Quantum cluster approach to the topological invariants in correlated Chern insulators
• Topological property of a $t_{2g}^5$ system with a honeycomb lattice structure
• Valley selecting current partition at zero-line mode of quantum anomalous Hall topologies
• Correlated electrons in a Crystalline Topological insulator
• Comparing the effective enhancement of local and non-local spin-orbit couplings on honeycomb lattices due to strong electronic correlations