The Floquet Engineer's Handbook

Abstract

We provide a pedagogical technical guide to many of the key theoretical tools and ideas that underlie work in the field of Floquet engineering. We hope that this document will serve as a useful resource for new researchers aiming to enter the field, as well as experienced researchers who wish to gain new insight into familiar or possibly unfamiliar methods. This guide was developed out of supplementary material as a companion to our recent review, "Band structure engineering and non-equilibrium dynamics in Floquet topological insulators," Nature Reviews Physics 2, 229 (2020). The primary focus is on analytical techniques relevant for Floquet-Bloch band engineering and related many-body dynamics. We will continue to update this document over time to include additional content, and welcome suggestions for further topics to consider.

This is a significantly expanded version of supplementary information originally included in arXiv:1909.02008, now upgraded to a stand-alone, living document. Suggestions for further sections are welcome. v2: Updated with references and link to published version of the companion review, Nature Reviews Physics 2, 229 (2020)

References in corpus (16)

• Photovoltaic Hall effect in graphene
• Topological characterization of periodically-driven quantum systems
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Driven quantum transport on the nanoscale
• Irradiated graphene as a tunable Floquet topological insulator
• Multiterminal Conductance of a Floquet Topological Insulator
• Out of equilibrium electrons and the Hall conductance of a Floquet topological insulator
• Correlated electron systems periodically driven out of equilibrium: Floquet + DMFT formalism
• Dissipative Floquet Topological Systems
• Scattering Theory for Floquet-Bloch States
• Occupation of topological Floquet bands in open systems
• Floquet engineering of long-range p-wave superconductivity
• Floquet Topological Order in Interacting Systems of Bosons and Fermions
• Floquet Edge States with Ultracold Atoms
• Optical Control of Topological Quantum Transport in Semiconductors
• Floquet Majorana zero and $\pi$ modes in planar Josephson junctions

Cited by in corpus (16)

• Quantum Floquet engineering with an exactly solvable tight-binding chain in a cavity
• Fermi's golden rule for heating in strongly driven Floquet systems
• Floquet engineering bulk odd-frequency superconducting pairs
• Light-driven Lifshitz transitions in non-Hermitian multi-Weyl semimetals
• Hexagonally warped exceptional physics in multi-Weyl semimetals
• Prethermalization and entanglement dynamics in interacting topological pumps
• Electronic Floquet Liquid Crystals
• Topological phase transition in commensurate multi-frequency Floquet Su-Schrieffer-Heeger model
• Floquet Graphene Antidot Lattices
• Symmetry-driven Phononic Metamaterials
• Holographic Floquet states in low dimensions (I)
• Beyond-adiabatic Quantum Admittance of a Semiconductor Quantum Dot at High Frequencies: Rethinking Reflectometry as Polaron Dynamics
• A Floquet analysis perspective of driven light-matter interaction models
• Simulating a Chern Insulator with C = $\pm$2 on Synthetic Floquet Lattice
• The Rabi problem with elliptic polarization
• Floquet Gauge Pumps as Sensors for Spectral Degeneracies Protected by Symmetry or Topology