Quantum Response at Finite Fields and Breakdown of Chern Numbers

Abstract

We show that the response to an electric field, in models of the Integral Quantum Hall effect, is analytic in the field and has isolated essential singularity at zero field. We also study the breakdown of Chern numbers associated with the response of Floquet states. We argue, and give evidence, that the breakdown of Chern numbers in Floquet states is a discontinuous transition at zero field. This follows from an observation, of independent interest, that Chern numbers for finite dimensional Floquet operators are generically zero. These results rule out the possibility that the breakdown of the Hall conductance is a phase transition at finite fields for a large class of models.

16 pages, 8 eps figures, LaTeX2e with IOP style. Many changes, including new material

References in corpus (1)

• Floquet Energies and Quantum Hall Effect in a Periodic Potential

Cited by in corpus (10)

• Thouless pumping and topology
• Observation of topological transport quantization by dissipation in fast Thouless pumps
• Non-adiabatic breaking of topological pumping
• Localization, topology and quantized transport in disordered Floquet systems
• Quantum response theory for open systems and its application to Hall conductance
• Dynamics of the (spin-) Hall effect in topological insulators and graphene
• Floquet resonances close to the adiabatic limit and the effect of dissipation
• On the quantization of the Hall conductivity in the Harper-Hofstadter model
• An integral-free representation of the Dyson series using divided differences
• Absence of disordered Thouless pumps at finite frequency