Non-adiabatic extension of the Zak phase and charge pumping in the Rice--Mele model

Abstract

In this study, the Landau--Zener (LZ) transition method is applied to investigate a weak non-adiabatic effect on the Zak phase and the topological charge pumping in the Rice--Mele model. The non-adiabatic effect is formulated using the LZ transfer matrix. The effective lower band wave function picks up the Stokes phase as well as the usual dynamical phase through two avoided crossings appearing in the two band instantaneous energy spectrum. The interference effect from the upper band has a decisive influence on the decay behavior of the lower band population. A non-adiabatic extension of the Zak phase can then be formulated, corresponding to the center of mass of the lower band Wannier function. Furthermore, we estimate the validity of the LZ formalism and verify the breakdown of the quantization of the topological charge pumping by changing the sweeping speed.

8 pages, 4 figures, accepted in EPJB

References in corpus (11)

• Many-Body Physics with Ultracold Gases
• Bulk-boundary correspondence from the inter-cellular Zak phase
• Non-adiabatic breaking of topological pumping
• Topological pumping of photons in nonlinear resonator arrays
• Topological charge pumping in the interacting bosonic Rice-Mele model
• Quantum Transport of Bosonic Cold Atoms in Double Well Optical Lattices
• Breakdown of topological Thouless pumping in the strongly interacting regime
• Fractional charge pumping of interacting bosons in one-dimensional superlattice
• Interband Coherence Induced Correction to Adiabatic Pumping in Periodically Driven Systems
• Various Topological Mott insulators in strongly-interacting boson system in one-dimensional superlattice
• Interband coherence induced correction to Thouless pumping: possible observation in cold-atom systems

Cited by in corpus (7)

• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• Effect of disorder on topological charge pumping in the Rice-Mele model
• Splitting of topological charge pumping in an interacting two-component fermionic Rice-Mele Hubbard model
• First-Principles Demonstration of Non-adiabatic Thouless Pumping of Electrons in A Molecular System
• An ideal rapid-cycle Thouless pump
• Molecular Control of Floquet Topological Phase in Non-adiabatic Thouless Pumping
• Topological states constructed by two different trivial quantum wires