Topological states in the Hofstadter model on a honeycomb lattice

Abstract

e provide a detailed analysis of a topological structure of a fermion spectrum in the Hofstadter model with different hopping integrals along the $x,y,z$-links ($t_x=t,t_y=t_z=1$), defined on a honeycomb lattice. We have shown that the chiral gapless edge modes are described in the framework of the generalized Kitaev chain formalism, which makes it possible to calculate the Hall conductance of subbands for different filling and an arbitrary magnetic flux $\varphi$. At half-filling the gap in the center of the fermion spectrum opens for $t>t_c=2^{\varphi }$, a quantum phase transition in the 2D-topological insulator state is realized at $t_c$. The phase state is characterized by zero energy Majorana states localized at the boundaries. Taking into account the on-site Coulomb repulsion $U$ (where $U<<1$), the criterion for the stability of a topological insulator state is calculated at $t<<1$, $t\sim U$. Thus, in the case of $U>4\Delta$, the topological insulator state, which is determined by chiral gapless edge modes in the gap $\Delta$, is destroyed.

arXiv comment8 pages, 6 figures

References in corpus (19)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Anyons in an exactly solved model and beyond
• Unpaired Majorana fermions in quantum wires
• Unconventional Integer Quantum Hall effect in graphene
• Topological invariants of edge states for periodic two-dimensional models
• Explicit Solutions of the Bethe Ansatz Equations for Bloch Electrons in a Magnetic Field
• The Colored Hofstadter Butterfly for the Honeycomb Lattice
• Band Collapse and the Quantum Hall Effect in Graphene
• Topologically Universal Spectral Hierarchies of Quasiperiodic Systems
• The Hall conductance, topological quantum phase transition and the Diophantine equation on honeycomb lattice
• Spontaneous breaking of time-reversal symmetry in topological insulators
• Topological Phase Transitions from Harper to Fibonacci Crystals
• Perturbative/nonperturbative aspects of Bloch electrons in a honeycomb lattice
• Edge modes in the Hofstadter model of interacting electrons
• Chern insulator with large Chern numbers. Chiral Majorana fermion liquid
• 4$\pi$ and 8$\pi$ dual Josephson effects induced by symmetry defects
• Topology and Self-Similarity of the Hofstadter Butterfly
• The quantum group, Harper equation and the structure of Bloch eigenstates on a honeycomb lattice

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• A higher-dimensional quasicrystalline approach to the Hofstadter and Fibonacci butterflies topological phase diagram and band conductance: symbolic sequences, Sturmian coding and self-similar rules at all magnetic fluxes
• Exactly solvable chain of interacting electrons with correlated hopping and pairing
• The quantum Hall effect at a weak magnetic field
• Topological Mott transition in a two band model of spinless fermions with on-site Coulomb repulsion
• Robust qubit interactions mediated by photonic topological edge states
• Dirac fermion spectrum of the fractional quantum Hall states