Chaotic behavior of the electrons in graphene superlattice

Dynamic chaotisation of the electronic subsystem in a graphene superlattice subjected to the electromagnetic radiation

“…Below we investigate the possibility of dynamic chaotisation in a GSL subjected to EM radiation and find the conditions for the amplitude and frequency of such radiation when the chaotic behaviour of electrons takes place. The d'Alembert equation in this case differs from that of [44,45]; therefore, the results obtained below are new. Moreover, unlike the SL based on AlGaAs/GaAs [30], the nonadditivity of the GSL electron spectrum allows the possibility of dynamic chaotisation in the case when the vector potential of incident EM wave A ext is perpendicular to the GSL axis.…”

“…The results obtained in [12,37,40,43] are valid if the frequency of the EM radiation ω is much more than the plasma frequency. However, there is another requirement for frequency ω, which is related to the chaotic behaviour of nonlinear systems [41,[44][45][46][47][48][49][50]. Such a phenomenon should be taken into account in the process of the stabilisation of nonlinear and solitary EM waves.…”

“…Such a phenomenon should be taken into account in the process of the stabilisation of nonlinear and solitary EM waves. The chaotic dynamics of the charge carriers induced by the set alternate current in GSL with dissipation was suggested in [44,45].…”

Possibility of propagation of dissipative solitons in ac-driven superlattice

“…However, there is another requirement for frequency ω which is related to the chaotic behavior of the electron subsystem of SL [30,31]. In this section, we investigate the conditions for the HF-field amplitude a and frequency ω under which dynamic chaotization of the electronic subsystem in the ac-driven model (5) occurs.…”

Fractal structure of the soliton scattering for the graphene superlattice equation

“…S. V. Kryuchkov and E. I. Kukhar' [2] showed that the sine-Gordon equation governed the propagation of nonlinear solitary electromagnetic waves in Ratnikov's graphene superlattice subjected to sinusoidal electromagnetic radiation if radiation frequency is much larger than the plasma frequency and the overlap of the wave functions of neighboring wells is very small. The relaxation of the last condition results in a generalized sine-Gordon equation, here on referred to as the graphene superlattice equation [3]; this equation can be either approximated by a double sine-Gordon equation [4] or further generalized to an integro-differential Klein-Gordon equation for electromagnetic waves in the terahertz regime [5]. The study of the solitary wave solutions of the graphene superlattice equation and their interactions could be useful for the development of new technological applications.…”