Chiral topological insulator on Nambu 3-algebraic geometry

Abstract Chiral topological insulator (AIII-class) with Landau levels is constructed based on the Nambu 3-algebraic geometry. We clarify the geometric origin of the chiral symmetry of the AIII-class topological insulator in the context of non-commutative geometry of 4D quantum Hall effect. The many-body groundstate wavefunction is explicitly derived as a ( l , l , l − 1 ) Laughlin–Halperin type wavefunction with unique K -matrix structure. Fundamental excitation is identified with anyonic string-like object with fractional charge 1 / ( 2 ( l − 1 ) 2 + 1 ) . The Hall effect of the chiral topological insulators turns out be a color version of Hall effect, which exhibits a dual property of the Hall and spin-Hall effects.

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