Highly nonlinear phenomena of self‐organization of quasi‐two‐dimensional electron gas in high magnetic and electric fields

Abstract

The transverse electric field Ey that appears in lateral superlattices (2SLs) under Hall‐measurement conditions, i.e. in the presence of a longitudinal applied electric field Ex and applied magnetic field H normal to the SL plane (H ∥ OZ) is calculated. In contrast to previous works devoted to this problem both applied electric and magnetic fields are treated as control parameters. By introducing the generalized function of entropy production (the synergetic potential) the kinetic behavior of a quasi‐two‐dimensional nonequilibrium electron gas is investigated from the viewpoint of self‐organization and catastrophe theory. The field Ey contains both the Hall field and the spontaneous transverse electric field that exists without H. The magnetoresistance caused by the appearance of a spontaneous transverse EMF is investigated. Spontaneous transverse EMF, current–voltage characteristics and magnetoresistance are multivalued and sign‐changing functions of applied electric and magnetic fields. From the model computer simulations the observed multistability exhibits a large difference in the behavior of the system in high magnetic fields as compared to low one. The novel nonlinear effects such as first‐order nonequilibrium phase transitions and hysteresis, induced by magnetic field are predicted. As the magnetic field is increased the nonlinear behaviors show self‐organized hierarchical complexity, which manifests itself in fractalization of bifurcation set, whose self‐similar fine structure leading to fractal‐like folds of critical manifold sheets, resulting in fuzzy bifurcations, was discovered. Complex nonlinear behaviors including macrostate crisis and chaotic‐looking intermittency of Hall‐effect characteristics were discovered in limited narrow ranges of the control parameter space. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Effects of a Perpendicularly Applied Magnetic Field on Harmonically Driven Quasi-two-dimensional Electron Gas: the Static Macrostates Symmetry Breaking and Generation of Even Harmonics in System Output

“…where the summation is made within the first Brillouin zone. Substituting (2.4) into (2.7), we finally get [8,9] j(E, H, t, E, H))e −t dt, (…”

“…The artificially grown quasi-two-dimensional structure -the lateral superlattice (2SL) [4,5] may serve as a rather suitable model system for investigation of self-organization of quasi-twodimensional electron gas [6][7][8] and nonlinear signal transfer [9,10] in complex nonlinear systems.…”

Weak Signals Amplification Through Controlled Bifurcations in Quasi-Two-Dimensional Electron Gas

“…When the external electric field (E x ) is applied to 2SL sample, it gives rise to a transverse field E y [10,11] which is treated as an order parameter. This order parameter defines the output signal U AB (t) = LE y -the response of the system, where L is the sample length in the OY direction.…”

“…Here the angular brackets mean the averaging over the equilibrium carrier distribution. In the following we consider the electron gas nondegenerate, then [10,11]…”

“…here the value of R cp has the sense of sample resistance in weak electric fields. Define the potential function Φ -the synergetic potential (the generalized function of entropy production [10,11]) whose meaning is discussed in [9] Φ…”