Three Dimensional Topological Insulators with Landau Levels

Physics – Condensed Matter – Strongly Correlated Electrons

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Scientific paper

We study the three dimensional topological insulators of spin-1/2 fermions coupling to the Aharanov-Casher SU(2) gauge field. They exhibit flat Landau levels in which orbital angular momentum and spin are coupled with a fixed helicity. In spite of the intrinsic spatial inhomogeneity, magnetic translations can be defined for the highest weight states of the total angular momentum. Each Landau level contributes one branch of gapless helical Dirac channel to the surface spectra, whose topological properties belong to the $\mathbb{Z}_{2}$-class. The flat Landau levels can be generalized to $N$ dimensions with the fundamental SO(N) spinor fermions coupling to the SO(N) gauge field.

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