The Fermi-Dirac staircase occupation of Floquet bands and current rectification inside the optical gap of metals: a rigorous perspective

Abstract

We consider a model of a Bloch band subjected to an oscillating electric field and coupled to a featureless fermionic heat bath, which can be solved exactly. We demonstrate rigorously that in the limit of vanishing coupling to this bath (so that it acts as an ideal thermodynamic bath) the occupation of the Floquet band is not a simple Fermi-Dirac distribution function of the Floquet energy, but instead it becomes a ``staircase'' version of this distribution. We show that this distribution generically leads to a finite rectified electric current within the optical gap of a metal even in the limit of vanishing carrier relaxation rates, providing a rigorous demonstration that such rectification is generically possible and clarifying previous statements in the optoelectronics literature. We show that this current remains non-zero even up to the leading perturbative second order in the amplitude of electric fields, and that it approaches the standard perturbative expression of the Jerk current obtained from a simpler Boltzmann description within a relaxation time approximation when the frequencies are small compared to the bandwidth.

18 pages, 4 figures

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• The Streda Formula for Floquet Systems: Topological Invariants and Quantized Anomalies from Cesaro Summation
• Asymmetry-induced radiative heat transfer in Floquet systems
• Floquet-Bloch Theory for Nonperturbative Response to a Static Drive
• Ultra-critical Floquet Non-Fermi Liquid
• Light-induced Nonlinear Spin Hall Current in Single-layer WTe${}_2$
• Nonequilibrium electron distribution function in a voltage-biased nanowire: A nonequilibrium Green's function approach
• Time-resolved ARPES and optical transport properties of irradiated twisted bilayer graphene in steady-state
• Dirac Electrons in AC-Magnetic Fields: $\pi$-Landau Levels and Chiral Anomaly-Induced Homodyne Effect
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