Planck's quantum-driven integer quantum Hall effect in chaos

Abstract

The integer quantum Hall effect (IQHE) and chaos are commonly conceived as being unrelated. Contrary to common wisdoms, we find in a canonical chaotic system, the kicked spin-$1/2$ rotor, a Planck's quantum($h_e$)-driven phenomenon bearing a firm analogy to IQHE but of chaos origin. Specifically, the rotor's energy growth is unbounded ('metallic' phase) for a discrete set of critical $h_e$-values, but otherwise bounded ('insulating' phase). The latter phase is topological in nature and characterized by a quantum number ('quantized Hall conductance'). The number jumps by unity whenever $h_e$ decreases passing through each critical value. Our findings, within the reach of cold-atom experiments, indicate that rich topological quantum phenomena may emerge from chaos.

Fig. 1 and 2 modified

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Cited by in corpus (26)

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• Quantum Walk in Momentum Space with a Bose-Einstein Condensate
• Floquet topological phases in a spin-1/2 double kicked rotor
• Recipe for creating an arbitrary number of Floquet chiral edge states
• Non-Hermitian Floquet topological phases in the double-kicked rotor
• Non-Hermitian Floquet Topological Matter -- A Review
• Dynamical Localization of Coupled Relativistic Kicked Rotors
• Quantum simulation of disordered systems with cold atoms
• Experimental realization of a momentum-space quantum walk
• Interband Coherence Induced Correction to Adiabatic Pumping in Periodically Driven Systems
• Floquet topological phases with fourfold-degenerate edge modes in a driven spin-1/2 Creutz ladder
• Emergence of integer quantum Hall effect from chaos
• Experimental observation of time singularity in classical-to-quantum chaos transition
• Torsional Topological Invariants
• Topological edge states at Floquet quantum criticality
• Entanglement spectrum and entropy in Floquet topological matter
• Route towards Localization for Quantum Anomalous Hall Systems with Chern Number 2
• Lecture Notes on Quantum Electrical Circuits
• Floquet higher-order topological phases in momentum space
• Pseudoclassical dynamics of the kicked top
• Coexistence of directed momentum current and ballistic energy diffusion in coupled non-Hermitian kicked rotors
• Self-duality triggered dynamical transition
• Localization Trajectory and Chern-Simons axion coupling for Bilayer Quantum Anomalous Hall Systems
• Quantum geometry and geometric entanglement entropy of one-dimensional Floquet topological matter
• Symmetry and dynamics universality of supermetal in quantum chaos
• Transport through Quantum Anomalous Hall Bilayers with Lattice Mismatch