Symmetry breaking and Landau quantization in topological crystalline insulators

Abstract

In the recently discovered topological crystalline insulators SnTe and Pb_{1-x}Sn_{x}(Te,Se), crystal symmetry and electronic topology intertwine to create topological surface states with many interesting features including Lifshitz transition, Van-Hove singularity and fermion mass generation. These surface states are protected by mirror symmetry with respect to the (110) plane. In this work we present a comprehensive study of the effects of different mirror-symmetry-breaking perturbations on the (001) surface band structure. Pristine (001) surface states have four branches of Dirac fermions at low-energy. We show that ferroelectric-type structural distortion generates a mass and gaps out some or all of these Dirac points, while strain shifts Dirac points in the Brillouin zone. An in-plane magnetic field leaves surface state gapless, but introduces asymmetry between Dirac points. Finally, an out-of-plane magnetic field leads to discrete Landau levels. We show that the Landau level spectrum has an unusual pattern of degeneracy and interesting features due to the unique underlying band structure. This suggests that Landau level spectroscopy can detect and distinguish between different mechanisms of symmetry breaking in topological crystalline insulators.

10 pages, 5 figures, main results are summarized in Table I; (v2) minor corrections

References in corpus (5)

• Topological Crystalline Insulators
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• Antiferromagnetic topological insulators
• New Dirac points and multiple Landau level crossings in biased trilayer graphene

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