Dynamical electron localization and self-induced transparency in semiconductor superlattices

Electron Bloch oscillations and electromagnetic transparency of semiconductor superlattices in multi-frequency electric fields

“…In the strong time-periodic electric field with fundamental frequency ω (without the static component), Bragg reflections give rise to nonlinear periodic oscillations with the period of this field and to corresponding quasienergetic minibands [5][6][7][8][9][10][11]. We call these oscillations "ac BOs" to differ from usual BOs occurring in the static field.…”

“…cos( ) ( α α α α δ ω α , arbitrary initial phases δ α , and amplitudes E α , determined by the conditions J 0 (αg α ) = 0, where g α =eE α d/hω α [8]. It should be noted that in this case ac BOs are not periodic and the average electron velocity vanishes (i.e.…”

“…in the nearest-neighbor approximation). In the SLs with more complicated miniband dispersion law, the DL and the miniband collapse can occur in the multi-frequency electric fields only [6,8,10,11]. In particular, if the electric field is a set of rectangular pulses with the magnitude E c and the period T n = 4πn/Ω с , (n = 1,2,..), it occurs for any arbitrary miniband dispersion law [6,11].…”

“…It should be noted that in this case ac BOs are not periodic and the average electron velocity vanishes (i.e. the DL occurs) only after the averaging over an infinitely large time interval [8].…”

“…Consequently, the DL and the miniband collapse occur in the SLs with sinusoidal miniband only if the ac BOs spectra at E c = 0 do not contain the n-th harmonics. If the high-frequency field is harmonic, this happens at amplitudes determined by the zeros of the n-th order Bessel functions, J n (g) = 0, [8,12] (see the expression for the electron velocity given above). In the opposite case, electrons are delocalized.…”