Global and Local Topological Quantized Responses from Geometry, Light and Time

• URL: http://arxiv.org/abs/2106.15665v3
• Date: Wed, 20 Oct 2021 18:31:28 GMT
• Title: Global and Local Topological Quantized Responses from Geometry, Light and Time
• Authors: Karyn Le Hur
• Abstract summary: We describe a spin-$frac12$ particle on the Bloch sphere with a radial magnetic field and topological states of matter from the reciprocal space. For the Haldane model on the honeycomb lattice, this $C2$ can be measured from the Dirac points through circularly polarized light related to the high-symmetry $M$ point(s) We address a relation with a spin pump and the quantum spin Hall conductance.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: To describe a spin-$\frac{1}{2}$ particle on the Bloch sphere with a radial magnetic field and topological states of matter from the reciprocal space, we introduce $C$ square ($C^2$) as a local formulation of the global topological invariant. For the Haldane model on the honeycomb lattice, this $C^2$ can be measured from the Dirac points through circularly polarized light related to the high-symmetry $M$ point(s). For the quantum spin Hall effect and the Kane-Mele model, the $\mathbb{Z}_2$ topological number robust to interactions can be measured locally from a correspondence between the pfaffian and light. We address a relation with a spin pump and the quantum spin Hall conductance. The analogy between light and magnetic nuclear resonance may be applied for imaging, among other applications.

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