Bifurcation phenomena in a semiconductor superlattice subject to a tilted magnetic field

Two-dimensional collective electron magnetotransport, oscillations, and chaos in a semiconductor superlattice

“…Numerical simulations of the ETF based 1D drift-Poisson (Kroemer) model indicate that quasiperiodic and chaotic oscillations appear only for superimposed dc and ac voltage biases [22]. Apparently, and unlike our results based on 2D calculations, spontaneous chaos under dc voltage bias was not observed in 1D simulations [22], although one period doubling bubble was found in [23]. Note that period doubling bubbles and the Feigenbaum route to chaos have been found in simulations of weakly coupled superlattices [24,25].…”

“…In contrast with ours, previous theory extends the Esaki-Tsu formula to the 2D configuration resulting from a tilted magnetic field and finds a multipeaked drift velocity [4,5,7,9,22,23]. Assuming that the electric field is directed along the superlattice growth direction (which is not the case, as shown in Appendix B), the obtained drift velocity is then inserted in a 1D drift-Poisson Kroemer model.…”

Mechanism of resonant enhancement of electron drift in nanometer semiconductor superlattices subjected to electric and inclined magnetic fields

“…This study revealed a remarkable feature of the evolution: as the temperature increases, the ET peak quickly decreases, while the main (1st-order) resonant peak decays much more slowly so that, at moderate temperatures (∼ 100 − 400K), the resonant peak becomes a strongly dominating feature in the drift velocity vs. the electric field. However, no explanation was offered 30,31,36,38 , and no effort was made to study either how generic this feature is, or what characteristic types of resonant peak evolution may arise. We now address these important issues.…”

“…The other motivation was to extend the earlier arguments in favour of the non-chaotic mechanism 37 . Need for the latter arose because some researchers seemed to remain unpersuaded by the arguments in the Letter 37 and had been explicitly 38,71,72 or implicitly 39,41 continuing to refer to the original conjecture 19,21 of chaotic diffusion as the mechanism underlying the resonant enhancement of electron transport. It also seems that a huge number of references to this exciting-sounding but incorrect idea done before the publication of the Letter 37 and its continued promulgation 38,39,41,71,72 after it keep misleading researchers in other areas [73][74][75][76][77][78][79] , who still mention the resonant enhancement of electron drift 19,21,26 as a manifestation of "chaotic dynamics in semiconductor SLs" 73,75,76,78,79 or as the ability of non-KAM chaos to "enhance electronic transport in semiconductor superlattices" 74,77 .…”

Amplification of electromagnetic radiation in a superlattice placed in a tilted magnetic field

“…That makes possible to achieve amplification of radiation without formation of space-charge wave instabilities. If the superlattice is placed in a tilted magnetic field, then the ballistic electron dynamics becomes more complicated and exhibits chaotic behavior [17][18][19][20]. This chaos manifests itself with the appearance of bifurcation points in the parameter space of the system.…”