Surface States of the Topological Insulator Bi_{1-x}Sb_x

Abstract

We study the electronic surface states of the semiconducting alloy BiSb. Using a phenomenological tight binding model we show that the Fermi surface of the 111 surface states encloses an odd number of time reversal invariant momenta (TRIM) in the surface Brillouin zone confirming that the alloy is a strong topological insulator. We then develop general arguments which show that spatial symmetries lead to additional topological structure, and further constrain the surface band structure. Inversion symmetric crystals have 8 Z_2 "parity invariants", which include the 4 Z_2 invariants due to time reversal. The extra invariants determine the "surface fermion parity", which specifies which surface TRIM are enclosed by an odd number of electron or hole pockets. We provide a simple proof of this result, which provides a direct link between the surface states and the bulk parity eigenvalues. We then make specific predictions for the surface state structure for several faces of BiSb. We next show that mirror invariant band structures are characterized by an integer "mirror Chern number", n_M. The sign of n_M in the topological insulator phase of BiSb is related to a previously unexplored Z_2 parameter in the L point k.p theory of pure Bi, which we refer to as the "mirror chirality", η. The value of ηpredicted by the tight binding model for Bi disagrees with the value predicted by a more fundamental pseudopotential calculation. This explains a subtle disagreement between our tight binding surface state calculation and previous first principles calculations on Bi. This suggests that the tight binding parameters in the Liu Allen model of Bi need to be reconsidered. Implications for existing and future ARPES experiments and spin polarized ARPES experiments will be discussed.

arXiv comment15 pages, 7 figures

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• Topological insulators and geometry of vector bundles
• Topological $d$-wave Superconductivity and Nodal Line-Arc Intersections in Weyl Semimetals
• Edge states of a three dimensional kicked rotor
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• First Principles Prediction of Topological Phases in Thin Films of Pyrochlore Iridates
• Intrinsic chiral topological superconductor thin films
• Local expression of fractional corner charges in obstructed atomic insulators and relationship with the fractional disclination charges
• Engineering Helical Superconductors with Multiple Majorana Kramers Pairs via Higher-Order Rashba Spin-Orbit Coupling
• Ultrafast electronic heat dissipation through surface-to-bulk Coulomb coupling in quantum materials
• Magnetic-field effect on excitonic condensation emergent in extended Falicov-Kimball model
• Long-range permeation of wave function and superficial surface state due to strong quantum size effects in topological Bi/BiSb heterojunctions
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• Exact solutions for topological surface states of three-dimensional lattice models
• Majorana vortex phases in time-reversal invariant higher-order topological insulators and topologically trivial insulators
• Symmetry-protected topological wire in a topological vacuum
• Granular topological insulators
• Crystalline topological states at a topological insulator junction
• Signature of topological crystalline insulating behavior in new B2X2Zn (X=Ir, Rh, Co) compound from first-principles Computation
• Resonantly enhanced photoemission from topological surface states in MnBi${}_6$Te${}_{10}$
• Current induced magneto-optical Kerr effect as a probe of Dirac carriers in Bi${}_{1-x}$Sb${}_x$ alloy
• Double-twisted surface spectrum from hybridized Majorana Kramers pairs and wallpaper fermions
• Reflection-Symmetry Protected Antiferromagnetic Topological Insulator in Three-Dimensional Heavy-Fermion Systems
• One-dimensional topology and topolectrics of nonsymmorphic Kramers degenerate systems
• Classification of topological insulators and superconductors with multiple order-two point group symmetries