High-Dimensional Topological Insulators with Quaternionic Analytic Landau Levels

Abstract

We study the 3D topological insulators in the continuum by coupling spin-1/2 fermions to the Aharonov-Casher SU(2) gauge field. They exhibit flat Landau levels in which orbital angular momentum and spin are coupled with a fixed helicity. The 3D lowest Landau level wavefunctions exhibit the quaternionic analyticity as a generalization of the complex analyticity of the 2D case. Each Landau level contributes one branch of gapless helical Dirac modes to the surface spectra, whose topological properties belong to the Z2-class. The flat Landau levels can be generalized to an arbitrary dimension. Interaction effects and experimental realizations are also studied.

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• The 6D quantum Hall effect and 3D topological pumps
• Measurement of Chern numbers through center-of-mass responses
• Topological phases of quantized light
• Higher Dimensional Quantum Hall Effect as A-Class Topological Insulator
• Topological insulators with SU(2) Landau levels
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• Chiral Topological Insulator on Nambu 3-Algebraic Geometry
• Systematic Construction of tight-binding Hamiltonians for Topological Insulators and Superconductors
• Four-dimensional topological lattices through connectivity
• Relativistic Landau Models and Generation of Fuzzy Spheres
• Higher (Odd) Dimensional Quantum Hall Effect and Extended Dimensional Hierarchy
• $SO(4)$ Landau Models and Matrix Geometry
• Unification of valley and anomalous Hall effects in a strained lattice
• Time-reversal Invariant SU(2) Hofstadter Problem in Three Dimensional Lattices
• Ideal flat and resolved SU(3) Landau levels in three dimensions
• Quantum Hall Effect on Odd Spheres
• Exact Solutions of D-dimensional Klein-Gordon Oscillator with Snyder-de Sitter Algebra
• ADHM and the 4d Quantum Hall Effect
• $SO(5)$ Landau Model and 4D Quantum Hall Effect in The $SO(4)$ Monopole Background
• Topological spinor vortex matter on spherical surface induced by non-Abelian spin-orbital-angular-momentum coupling
• Noncompact dynamical symmetry of a spin-orbit coupled oscillator
• Extended Dynamical Symmetries of Landau Levels in Higher Dimensions
• Non-Abelian geometric potentials and spin-orbit coupling for periodically driven systems