Topological insulator on honeycomb lattices and ribbons without inversion symmetry

Abstract

We study the Kane-Mele-Hubbard model with an additional inversion-symmetry-breaking term. Using the topological Hamiltonian approach, we calculate the ${\mathbb{Z}}_2$ invariant of the system as function of spin-orbit coupling, Hubbard interaction $U$, and inversion-symmetry-breaking on-site potential. The phase diagram calculated in that way shows that, on the one hand, a large term of the latter kind destroys the topological non-trivial state. On the other hand, however, this inversion-symmetry-breaking field can enhance the topological state, since for moderate values the transition from the non-trivial 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.

9 pages, 9 figures

References in corpus (29)

• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Experimental discovery of Weyl semimetal TaAs
• Theoretical Discovery/Prediction: Weyl Semimetal states in the TaAs material (TaAs, NbAs, NbP, TaP) class
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
• Discovery of a Weyl Fermion semimetal state in NbAs
• Nonlocal edge state transport in the quantum spin Hall state
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Computing topological invariants without inversion symmetry
• Wannier representation of Z_2 topological insulators
• Variational cluster approach to correlated electron systems in low dimensions
• Simplified topological invariants for interacting insulators
• Correlation effects in two-dimensional topological insulators
• Mott Physics and Topological Phase Transition in Correlated Dirac Fermions
• Self-energy-functional approach: Analytical results and the Mott-Hubbard transition
• Variational cluster approach to spontaneous symmetry breaking: The itinerant antiferromagnet in two dimensions
• First order character and observable signatures of topological quantum phase transitions
• Variational cluster approach to the Hubbard model: Phase-separation tendency and finite-size effects
• Phase diagram of the Kane-Mele-Coulomb model
• Strong Correlation Effects on Topological Quantum Phase Transitions in Three Dimensions
• Topological Invariant and Quantum Spin Models from Magnetic π Fluxes in Correlated Topological Insulators
• Cellular dynamical mean-field theory study of an interacting topological honeycomb lattice model at finite temperature
• Topological invariants in interacting Quantum Spin Hall: a Cluster Perturbation Theory approach

Cited by in corpus (4)

• Antiferromagnetic Chern insulator in centrosymmetric systems
• Self-Energy Dispersion in the Hubbard Model
• Inversion symmetry breaking and criticality in free fermionic lattices
• Comparing the effective enhancement of local and non-local spin-orbit couplings on honeycomb lattices due to strong electronic correlations