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

Abstract

AbstractThe 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)