The strong side of weak topological insulators

Abstract

Three-dimensional topological insulators are classified into "strong" (STI) and "weak" (WTI) according to the nature of their surface states. While the surface states of the STI are topologically protected from localization, this does not hold for the WTI. In this work we show that the surface states of the WTI are actually protected from any random perturbation that does not break time-reversal symmetry, and does not close the bulk energy gap. Consequently, the conductivity of metallic surfaces in the clean system remains finite even in the presence of strong disorder of this type. In the weak disorder limit the surfaces are found to be perfect metals, and strong surface disorder only acts to push the metallic surfaces inwards. We find that the WTI differs from the STI primarily in its anisotropy, and that the anisotropy is not a sign of its weakness but rather of its richness.

12 pages, 7 figures

References in corpus (15)

• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Weak localisation magnetoresistance and valley symmetry in graphene
• Electron transport in disordered graphene
• Helical Metal Inside a Topological Band Insulator
• Effect of Disorder on Transport in Graphene
• Topological delocalization of two-dimensional massless Dirac fermions
• Tuning phase transition between quantum spin Hall and ordinary insulating phases
• Quantum transport and two-parameter scaling at the surface of a weak topological insulator
• Z2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of Anderson localization
• Two-dimensional spin-filtered chiral network model for the Z_2 quantum spin-Hall effect
• Conductivity of disordered graphene at half filling
• Determining topological order from a local ground state correlation function

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