A study on correlation effects in two dimensional topological insulators

Abstract

We investigate correlation effects in two dimensional topological insulators (TI). In the first part, we discuss finite size effects for interacting systems of different sizes in a ribbon geometry. For large systems, there are two pairs of well separated massless modes on both edges. For these systems, we analyze the finite size effects using a standard bosonization approach. For small systems, where the edge states are massive Dirac fermions, we use the inhomogeneous dynamical mean field theory (DMFT) combined with iterative perturbation theory as an impurity solver to study interaction effects. We show that the finite size gap in the edge states is renormalized for weak interactions, which is consistent with a Fermi-liquid picture for small size TIs. In the second part, we investigate phase transitions in finite size TIs at zero temperature focusing on the effects of possible inter-edge Umklapp scattering for the edge states within the inhomogeneous DMFT using the numerical renormalization group. We show that correlation effects are effectively stronger near the edge sites because the coordination number is smaller than in the bulk. Therefore, the localization of the edge states around the edge sites, which is a fundamental property in TIs, is weakened for strong coupling strengths. However, we find no signs for "edge Mott insulating states" and the system stays in the topological insulating state, which is adiabatically connected to the non-interacting state, for all interaction strengths smaller than the critical value. Increasing the interaction further, a nearly homogeneous Mott insulating state is stabilized.

20 pages

References in corpus (27)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• 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
• The numerical renormalization group method for quantum impurity systems
• 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
• Nonlocal edge state transport in the quantum spin Hall state
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Quantum Spin Hall Effect and Enhanced Magnetic Response by Spin-Orbit Coupling
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• Finite size effects of helical edge states in HgTe/CdTe quantum wells
• Multichannel Generalization of Kitaev's Majorana End States and a Practical Route to Realize Them in Thin Films
• Mott Physics and Topological Phase Transition in Correlated Dirac Fermions
• Quantum phase transitions in the Kane-Mele-Hubbard model
• Corner Junction as a Probe of Helical Edge States
• Mott transition of fermionic atoms in a three-dimensional optical trap
• Tunneling between edge states in a quantum spin Hall system
• Band insulator to Mott insulator transition in a bilayer Hubbard model
• Kondo proximity effect: How does a metal penetrate into a Mott insulator?
• Correlation effects on a topological insulator at finite temperatures
• Mott Physics on Helical Edges of 2D Topological Insulators
• Néel transition of lattice fermions in a harmonic trap: a real-space DMFT study
• Dynamical mean-field theory and numerical renormalization group study of superconductivity in the attractive Hubbard model
• Supersolid state of ultracold fermions in an optical lattice
• Luttinger Liquid Physics and Spin-Flip Scattering on Helical Edges
• Supersolid state in fermionic optical lattice systems
• Quasiparticle excitations and dynamic susceptibilities in the BCS-BEC crossover

Cited by in corpus (57)

• Topological Insulator Materials
• Interacting topological insulators: a review
• Non-Hermitian perspective of the band structure in heavy-fermion systems
• Correlation effects in two-dimensional topological insulators
• Exploring Interacting Topological Insulators with Ultracold Atoms: the Synthetic Creutz-Hubbard Model
• Many-Body Quantum Electrodynamics Networks: Non-Equilibrium Condensed Matter Physics with Light
• Characterization of a topological Mott insulator in one dimension
• Higher-order Topological Mott Insulators
• Fluctuation driven topological Hund insulators
• Fluctuation-induced Topological Quantum Phase Transitions in Quantum Spin Hall and Quantum Anomalous Hall Insulators
• Chiral-symmetry protected exceptional torus in correlated nodal-line semi-metals
• Topological antiferromagnetic phase in a correlated Bernevig-Hughes-Zhang model
• Topological phase transition in a generalized Kane-Mele-Hubbard model: A combined Quantum Monte Carlo and Green's function study
• Entanglement spectra between coupled Tomonaga-Luttinger liquids: Applications to ladder systems and topological phases
• Exceptional band touching for strongly correlated systems in equilibrium
• Edge states reconstruction from strong correlations in quantum spin Hall insulators
• Spin Density Waves in the Hubbard model - A DMFT approach
• Strong Correlation Effects on Topological Quantum Phase Transitions in Three Dimensions
• Coexistence of light and heavy surface states in a topological multi-band Kondo insulator
• Valence Fluctuations and Electric Reconstruction in the Extended Anderson Model on the Two-Dimensional Penrose Lattice
• ${\mathbb{Z}}_N$ gauge theories coupled to topological fermions: QED${}_2$ with a quantum-mechanical $\theta$ angle
• Local Electron Correlations in a Two-dimensional Hubbard Model on the Penrose Lattice
• 1/4 is the new 1/2 when topology is intertwined with Mottness
• Quantum cluster approach to the spinful Haldane-Hubbard model
• Antiferromagnetic topological insulator state in the correlated Bernevig-Hughes-Zhang model
• Topological Mott insulators of ultracold atomic mixtures induced by interactions in one-dimensional optical superlattices
• Coexistence of metallic edge states and anti-ferromagnetic ordering in correlated topological insulators
• Stability of Multinode Dirac Semimetals against Strong Long-Range Correlations
• Magnetic states in a three-dimensional topological Kondo insulator
• The Mott transition as a topological phase transition
• Topological edge Mott insulating state in two dimensions at finite temperatures -bulk and edge analysis-
• Higher-Order Topological Mott Insulator on the Pyrochlore Lattice
• Dynamical Mean-Field Theory of Strongly Correlated Electron Systems
• Topological phase in a two-dimensional metallic heavy-fermion system
• Quantum metric on the Brillouin Zone in correlated electron systems and its relation to topology for Chern insulators
• Rashba coupling and magnetic order in correlated helical liquids
• Characterization of a correlated topological Kondo insulator in one dimension
• Kane-Mele-Hubbard model on the $\pi$-flux honeycomb lattice
• Kane-Mele Hubbard model on a zigzag ribbon: stability of the topological edge states and quantum phase transitions
• Proximity effects in a topological-insulator/Mott-insulator heterostructure
• Quantum phase transitions of topological insulators without gap closing
• Flat-band ferromagnetism and spin waves in the Haldane-Hubbard model
• Valence Fluctuations in the Extended Anderson Lattice Model with Quasiperiodicity
• Quasiparticle excitations in a one-dimensional interacting topological insulator: Application for dopant-based quantum simulation
• Quasiparticle Berry curvature and Chern numbers in spin-orbit coupled bosonic Mott insulators
• Local vs non-local correlation effects in interacting quantum spin Hall insulators
• Quantum cluster approach to the topological invariants in correlated Chern insulators
• Effects of correlations on phase diagrams of the two-dimensional Su-Schrieffer-Heeger model with the longer-range hoppings
• Intersite electron correlations in a Hubbard model on inhomogeneous lattices
• Buried topological edge state associated with interface between topological band insulator and Mott insulator
• Topological properties of magnetically ordered heavy-fermion systems in the presence of mirror symmetry
• Topological and magnetic properties of the interacting Bernevig-Hughes-Zhang model
• Interaction-induced phases in the half-filled Bernevig-Hughes-Zhang model in one dimension
• Mott transition and magnetism in a fragile topological insulator
• Topological charge excitations and Green's function zeros in paramagnetic Mott insulators
• First and second-order metal-insulator phase transitions and topological aspects of a Hubbard-Rashba system
• Analytic density of states of two-dimensional Chern insulator