Geometry induced quantum Hall effect and Hall viscosity
arXiv:1912.09183 · doi:10.1103/PhysRevB.102.155153
Abstract
For a particle confined to the two-dimensional helical surface embedded in four-dimensional (4D) Euclidean space, the effective Hamiltonian is deduced in the thin-layer quantization formalism. We find that the gauge structure of the effective dynamics is determined by torsion, which plays the role of U(1) gauge potential, and find that the topological structure of associated states is defined by orbital spin which originates from 4D space. Strikingly, the response to torsion contributes a quantum Hall effect, and the response to the deformation of torsion contributes Hall viscosity that is perfectly presented as a simultaneous occurrence of multiple channels for the quantum Hall effect. This result directly provides a way to probe Hall viscosity.
arXiv comment10 pages, 4 figures
References in corpus (32)
- Topological Insulators
- Anomalous Hall effect
- Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
- A Four Dimensional Generalization of the Quantum Hall Effect
- Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
- Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
- Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
- Viscosity of Quantum Hall Fluids
- Hall Viscosity and Electromagnetic Response
- Measuring Hall Viscosity of Graphene's Electron Fluid
- Four-Dimensional Quantum Hall Effect in a Two-Dimensional Quasicrystal
- Four-Dimensional Quantum Hall Effect with Ultracold Atoms
- Spin and orbital angular momentum in gauge theories: Nucleon spin structure and multipole radiation revisited
- Reply to the Comment on "Spin and orbital angular momentum in gauge theories: Nucleon spin structure and multipole radiation revisited" [PRL 100:232002 (2008)]
- Spin and orbital angular momentum in gauge theories (II): QCD and nucleon spin structure
- Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
- Fractional Quantum Hall Effect in a Curved Space: Gravitational Anomaly and Electromagnetic Response
- Density-curvature response and gravitational anomaly
- Quantum Mechanics on Manifolds Embedded in Euclidean Space
- Do gluons carry half of the nucleon momentum?
- Boundary effective action for quantum Hall states
- Geometry induced charge separation on a helicoidal ribbon
- 2DEG on a cylindrical shell with a screw dislocation
- Quantum particle confined to a thin-layer volume: Non-uniform convergence toward the curved surface
- Manipulating twisted electron beams
- Dissipative analog of four-dimensional quantum Hall physics
- Geometrically Induced Gauge Structure on Manifolds Embedded in a Higher Dimensional Space
- Quantum Hall-like effect on strips due to geometry
- Four-dimensional topological lattices through connectivity
- Geometric effects resulting from square and circular confinements for a particle constrained to a space curve
- Inner Nonlinear Waves and Inelastic Light Scattering of Fractional Quantum Hall States as Evidence of the Gravitational Anomaly
- Inertial and topological effects on a 2D electron gas