Magnetically robust topological edge states and flat bands

Abstract

We study thin strips of three dimensional topological insulators in the presence of a spin-splitting Zeeman field. We show that under certain conditions the topological edge states at the sides of a strip remain robust against a time-reversal symmetry breaking Zeeman field. For a particle-hole symmetric system with Zeeman field perpendicular to the strip we strictly proof that the dispersion and the spin-orbital structure of the edge states remains unchanged. When the Zeeman field lies parallel to the strip, the Dirac spectrum becomes flat, but remains intact. Above a critical value of the Zeeman field a topological flat band appears at the edge. We present numerical calculations for a lattice model of Bi${}_2$Se${}_3$. These calculations show that even though particle-hole symmetry is not strictly fulfilled in this system, these special features are still present. The flat band is tunable by the Zeeman field and can be realistically achieved in Bi${}_2$Se${}_3$-ferromagnet heterosystems at room temperature.

5 pages, 5 figures

References in corpus (9)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• 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
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Finite size effects of helical edge states in HgTe/CdTe quantum wells
• Topologically protected flat zero-energy surface bands in non-centrosymmetric superconductors
• Symmetry Protected Topological Order and Spin Susceptibility in Superfluid 3He-B
• Surface spectral function in the superconducting state of a topological insulator

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• Symmetry Protected Topological Superfluid ${}^3$He-B
• Majorana Flat Bands in s-Wave Gapless Topological Superconductors
• 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${}_3$
• Experimental search for one-dimensional edge states at surface steps of the topological insulator Bi${}_2$Se${}_3$: Distinguishing between effects and artifacts
• Topological flat bands in optical checkerboard-like lattices
• Appearance of flat surface bands in three-dimensional topological insulators in a ferromagnetic exchange field
• Topological state transfers in cavity-magnon system
• Three-dimensional symmetry breaking topological matters
• 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