Half quantum spin Hall effect on the surface of weak topological insulators

Abstract

We investigate interaction effects in three dimensional weak topological insulators (TI) with an even number of Dirac cones on the surface. We find that the surface states can be gapped by a surface charge density wave (CDW) order without breaking the time-reversal symmetry. In this sense, time reversal symmetry alone can not robustly protect the weak TI state in the presence of interactions. If the translational symmetry is additionally imposed in the bulk, a topologically non-trivial weak TI state can be obtained with helical edge states on the CDW domain walls. In other words, a CDW domain wall on the surface is topologically equivalent to the edge of a two-dimensional quantum spin Hall insulator. Therefore, the surface state of a weak topological insulator with translation symmetry breaking on the surface has a "half quantum spin Hall effect", in the same way that the surface state of a strong topological insulator with time-reversal symmetry breaking on the surface has a "half quantum Hall effect". The on-site and nearest neighbor interactions are investigated in the mean field level and the phase diagram for the surface states of weak topological insulators is obtained.

6 pages and 4 figures

References in corpus (17)

• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• 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
• Topological Field Theory of Time-Reversal Invariant Insulators
• 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
• Topological Mott Insulators
• Helical Metal Inside a Topological Band Insulator
• Direct Evidence for the Dirac-Cone Topological Surface States in Ternary Chalcogenide TlBiSe2
• Observation of Single Dirac Cone Topological Surface State in Compounds TlBiTe2 and TlBiSe2 from a New Topological Insulator Family
• Helical edge and surface states in HgTe quantum wells and bulk insulators
• Single-Dirac-Cone topological surface states in TlBiSe2 class of Topological Insulators
• Weak topological insulator with protected gapless helical states
• Quantum spin Hall effect induced by non-magnetic and magnetic staggered potentials
• Three-dimensional topological insulators in the octahedron-decorated cubic lattice

Cited by in corpus (42)

• Classification of topological quantum matter with symmetries
• Topological Crystalline Insulators in the SnTe Material Class
• Dirac Semimetals in Two Dimensions
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• Interacting topological insulators: a review
• Chiral anomaly, Charge Density Waves, and Axion Strings from Weyl Semimetals
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Topological Materials Discovery from Crystal Symmetry
• Quantum interference and Aharonov-Bohm oscillations in topological insulators
• Topology, Delocalization via Average Symmetry and the Symplectic Anderson Transition
• Discovery of switchable weak topological insulator state in quasi-one-dimensional bismuth iodide
• Statistical Topological Insulators
• Prediction of weak topological insulators in layered semiconductors
• Classification of stable Dirac and Weyl semimetals with reflection and rotational symmetry
• Statistical translation invariance protects a topological insulator from interactions
• Spin-Resolved Topology and Partial Axion Angles in Three-Dimensional Insulators
• Weak topological insulators induced by the inter-layer coupling: A first-principles study of stacked Bi2TeI
• Weak Topological Insulators in PbTe/SnTe Superlattices
• From an array of quantum wires to three-dimensional fractional topological insulators
• Topological Zero-Dimensional Defect and Flux States in Three-Dimensional Insulators
• Eightfold Fermionic Excitation in a Charge Density Wave Compound
• Anatomy of Topological Surface States: Exact Solutions from Destructive Interference on Frustrated Lattices
• Z2 phase diagram of three-dimensional disordered topological insulator via scattering matrix approach
• Spin-directed network model for the surface states of weak three-dimensional ${\mathbb{Z}}_2^{}$ topological insulators
• Stability of surface states of weak ${\mathbb{Z}}_2$ topological insulators and superconductors
• The fundamental differences between Quantum Spin Hall edge-states at zig-zag and armchair terminations of honeycomb and ruby nets
• Boundaries of boundaries: a systematic approach to lattice models with solvable boundary states of arbitrary codimension
• The Z2-anomaly and boundaries of topological insulators
• Characterizing the weak topological properties: Berry phase point of view
• Dynamical Piezomagnetic Effect in Time-Reversal Invariant Weyl Semimetals with Axionic Charge-Density Waves
• Interacting and fractional topological insulators via the ${\mathbb{Z}}_2$ chiral anomaly
• Cataloging topological phases of $N$-stacked Su-Schrieffer-Heeger chains by a systematic breaking of symmetries
• One-dimensional Dirac electrons on the surface of weak topological insulators
• Delocalization of surface Dirac electrons in disordered weak topological insulators
• Effective model for massless Dirac electrons on a surface of weak topological insulators
• Manipulating quantum channels in weak topological insulator nanoarchitectures
• Hedgehog spin texture and competing orders associated with strains on the surface of a topological crystalline insulator
• Layer dependent topological phases and transitions in TaRhTe${}_4$: From monolayer and bilayer to bulk
• Engineering Dirac electrons emergent on the surface of a topological insulator
• Gapless Topological Peierls-like instabilities in more than one dimension
• Weak topological insulators with step edges: Subband engineering and its effect on electron transport
• Landau levels on a surface of weak topological insulators