The Floquet formalism describes the response of a system subject to a periodic time-dependent perturbation.
If the system's Hamiltonian H(t)=H(t+T) is periodic in time with T=2π/Ω, new energy levels (Floquet replica levels) spaced by ±nħΩ (n integer) from the original level may emerge. When we consider solids, the Floquet folding of the electronic states along the energy axis is analogous to the momentum-periodicity of the band structure described by the Bloch theorem. For this reason, new states in solids induced by a time-dependent perturbation are usually called Floquet-Bloch states. The folding of the electronic bands along the energy axis may be a powerful tool to engineer the electronic properties of materials: not only can particular electronic states hybridize and gap, but Floquet engineering can reshape the local topology leading to the emergence of topologically-protected transient states and/or controlling electron interactions [1-3].
To date, light-induced Floquet-Bloch replica bands have been directly observed solely in the Dirac cone of topological insulators via time-resolved photoemission (TR-ARPES) [4-5]. The TR-ARPES endstation at ALLS meets all technical requirements to investigate Floquet engineering to control the electronic properties of quantum materials in an ultrafast fashion.
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