Thin crystals in circularly polarized laser fields

THIN CRYSTALS IN CIRCULARLY POLARIZED LASER FIELDS 

Let us consider a thin crystal (e.g., a 2D sheet of graphite also referred to as graphene) possessing the reflection and rotation symmetries. Without lost of generality, the one-particle, field-free Hamiltonian can be written as 

Upon shining the thin crystal with (monochromatic) circularly polarized laser field, propagating in parallel to its rotation axes, the corresponding Roquet Hamiltonian is given hy 

Note that 7i r, t) is periodic both in time and space hence, it is referred to as a Roquet-Bloch (TO) Hamiltonian. In other words, the Roquet states can be expressed as FB eigenstates. 

The energy bands (EBs) E(k) of the field-free Hamiltonian have transformed into the QEBs fi(k). It is, therefore, natural to inquire what are the symmetries of the QEBs and what is the relation between these symmetries and those of the field-free EBs. The answer lies in the application of the DS operators Pjv and on the FB eigenstates e(k),k(r, t) which gives 

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Thin crystals in circularly polarized laser fields 397... 

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