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 $1/(1+2(l-1{)}^2)$. 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.

6 pages, 1 figure, published version

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• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Probe of Three-Dimensional Chiral Topological Insulators in an Optical Lattice
• Higher Dimensional Quantum Hall Effect as A-Class Topological Insulator
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• Time-reversal Invariant SU(2) Hofstadter Problem in Three Dimensional Lattices
• Quantum Hall Effect on Odd Spheres
• $SO(5)$ Landau Model and 4D Quantum Hall Effect in The $SO(4)$ Monopole Background
• Weyl Semimetal and Nonassociative Nambu Geometry
• Topological Phases for Extended Objects: Semiclassical Phase-Space Approach with Tensorial Coordinates
• A Unified Construction of Skyrme-type Non-linear sigma Models via The Higher Dimensional Landau Models
• Higher bracket structure of density operators in Weyl fermion systems and topological insulators
• Quantum matrix geometry in the lowest Landau level and higher Landau levels
• Deformation of Matrix Geometry via Landau Level Evolution