Abstract
The family of solutions to the Dirac equation for an electron moving in an electromagnetic lattice with the chiral structure created by counterpropagating circularly polarized plane electromagnetic waves is obtained. At any nonzero quasimomentum, the dispersion equation has two solutions which specify bispinor wave functions describing electron states with different energies and mean values of momentum and spin operators. The inversion of the quasimomentum results in two other linearly independent solutions. These four basic wave functions are uniquely defined by eight complex scalar functions (structural functions), which serve as convenient building blocks of the relations describing the electron properties. These properties are illustrated in graphical form over a wide range of quasimomentums. The superpositions of two basic wave functions describing different spin states and corresponding to (i) the same quasimomentum (unidirectional electron states with the spin precession) and (ii) the two equal-in-magnitude but oppositely directed quasimomentums (bidirectional electron states) are also treated.
Highlights
The motion of electrons in natural crystals is described by the Schrodinger equation with a periodic electrostatic scalar potential
Electromagnetic fields with periodic dependence on space-time coordinates can be treated by analogy with the crystals of solid-state physics, so it is natural to refer to these field lattices as electromagnetic space-time crystals (ESTCs) [1,2,3,4,5,6]
The bispinor functions Ψj(q±) are uniquely defined by eight complex scalar functions zjk(j = 1, 2; k = 1, 2, 3, 4), which serve as convenient building blocks of the relations describing the electron properties
Summary
The motion of electrons in natural crystals is described by the Schrodinger equation with a periodic electrostatic scalar potential. Electromagnetic fields with periodic dependence on space-time coordinates can be treated by analogy with the crystals of solid-state physics, so it is natural to refer to these field lattices as electromagnetic space-time crystals (ESTCs) [1,2,3,4,5,6] In this context, the idea of a space-time crystal was first presented in [1] and the electron wave functions for the ESTC, created by two linearly polarized plane waves, were calculated by using the first-order perturbation theory for the SchrodingerStueckelberg equation. The new technique presented in [2,3,4,5,6] is applied in [5]
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