Appearance of flat surface bands in three-dimensional topological insulators in a ferromagnetic exchange field

Abstract

We study the properties of the surface states in three-dimensional topological insulators in the presence of a ferromagnetic exchange field. We demonstrate that for layered materials like Bi${}_2$Se${}_3$ the surface states on the top surface behave qualitatively different than the surface states at the side surfaces. We show that the group velocity of the surface states can be tuned by the direction and strength of the exchange field. If the exchange field becomes larger than the bulk gap of the material, a phase transition into a topologically nontrivial semimetallic state occurs. In particular, the material becomes a Weyl semimetal, if the exchange field possesses a non-zero component perpendicular to the layers. Associated with the Weyl semimetallic state we show that Fermi arcs appear at the surface. Under certain circumstances either one-dimensional or even two-dimensional surface flat bands can appear. We show that the appearence of these flat bands is related to chiral symmetries of the system and can be understood in terms of topological winding numbers. In contrast to previous systems that have been suggested to possess surface flat bands, the present system has a much larger energy scale, allowing the observation of surface flat bands at room temperature. The flat bands are tunable in the sense that they can be turned on or off by rotation of the ferromagnetic exchange field. Our findings are supported by both numerical results on a finite system as well as approximate analytical results.

45 pages, 17 figures

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Cited by in corpus (8)

• Double Weyl points and Fermi arcs of topological semimetals in non-Abelian gauge potentials
• Edge states of a three-dimensional topological insulator
• Pure spin current devices based on ferromagnetic topological insulators
• Tunneling magnetoresistance devices based on topological insulators: Ferromagnet/insulator/topological-insulator junctions employing Bi${}_2$Se${}_3$
• Low-energy behaviour of strongly-interacting bosons on a flat-banded lattice above the critical filling factor
• Topological flat bands in optical checkerboard-like lattices
• Anomalous Diffusion, Prethermalization, and Particle Binding in an Interacting Flat Band System
• Determination of Out-of-plane Spin Polarization of Topological Surface States by Spin Hall Effect Tunneling Spectroscopy