Scheme to Equilibrate the Quantized Hall Response of Topological Systems from Coherent Dynamics

Abstract

Two-dimensional topologically distinct insulators are separated by topological gapless points, which exist as Weyl points in three-dimensional momentum space. Slowly varying parameters in the two-dimensional Hamiltonian across two distinct phases therefore necessarily experiences the gap closing process, which prevents the intrinsic physical observable, the Hall response, from equilibrating. To equilibrate the Hall response, engineered laser noises were introduced at the price of destroying the quantum coherence. Here we demonstrate a new scheme to equilibrate the quantized Hall response from pure coherent dynamics as the Hamiltonian is slowly tuned from the topologically trivial to nontrivial regimes. We show the elements that affect the process of equilibration including the sequence when the electric field is switched on, its strength and the band dispersion of the final Hamiltonian. We further apply our method to Weyl semimetals in three dimensions and find the equilibrated Hall response despite the underlying gapless band structure. Our finding not only lays the theoretical foundation for observing the two-dimensional topological phase transition but also for observing and controlling Weyl semimetals in ultracold atomic gases.

7 pages including SMs, 3 figures

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Cited by in corpus (6)

• Ideal Weyl semimetal with 3D spin-orbit coupled ultracold quantum gas
• Type-II quadrupole topological insulators
• Topological Gapless Matters in Three-dimensional Ultracold Atomic Gases
• Non-Hermitian Absorption Spectroscopy
• Quench Dynamics and Hall Response of Interacting Chern Insulators
• Universal Landau-Zener regimes in dynamical topological phase transitions