A treatment of edge magnetoplasmons (EMP), based on a microscopic evaluation of the local contributions to the current density, is presented. It is valid in the quantum Hall regime for filling factor ν = 1 or 2 and low temperatures when the dissipation is localized near the edge. The confining potential, flat in the interior of the channel, is assumed smooth on the magnetic length ℓ0 scale but sufficiently steep at the edges that the density profile is sharp and the dissipation considered results only from electron intraedge-intralevel transitions due to scattering by piezoelectrical phonons. For wide channels there exist independent EMP modes spatially symmetric and antisymmetric with respect to the edge. Certain of these modes can propagate nearly undamoped even when the dissipation is strong and are thus termed edge helicons. In contrast with well-known results for a spatially homogeneous dissipation within the channel, we obtain that the damping of the fundamental EMP is not quantized and varies as T 3 or T −3 , where T is the temperature, in the high-and low-frequency limits, respectively. The characteristic length of the resulting dispersion relation and of the charge density distortion is ℓ0. The screening of the metallic gates, when present, is taken into account. PACS 73.20.Dx, 73.40.Hm

Based on a microscopic evaluation of the local current density, a treatment of edge magnetoplasmons (EMP) is presented for confining potentials that allow Landau level (LL) flattening to be neglected. Mode damping due to electron-phonon interaction is evaluated. For ν = 1, 2 there exist independent modes spatially symmetric or antisymmetric with respect to the edge. Certain modes, changing shape during propagation, are nearly undamped even for very strong dissipation and are termed edge helicons. For ν > 2 inter-LL Coulomb coupling leads to a strong repulsion of the decoupled LL fundamental modes. The theory agrees well with recent experiments. PACS numbers:The essentially classical treatments [1]-[2] of lowfrequency collective excitations, propagating along the edges of a two-dimensional electron gas (2DEG) subject to a normal magnetic field B, termed in Ref. [3] edge magnetoplasmons (EMP), account for some important characteristics of EMP, e.g., the gapless spectrum of these excitations [1] and the acoustic modes [2], [4]. However, the results of Refs.[1] and [2] are valid, respectively, for infinitely sharp and smooth density profiles that are independent of the filling factor ν. As contrasted in Fig. 1 with our calculated density profile for one or two LLs occupied and a smooth , on the magnetic length ℓ 0 = h/|e|B scale, parabolic confining potential these assumed profiles miss an important quantum mechanicall aspect, the LL structure. This inadequacy was manifested in the observed [4] plateau structure of the transit times reflecting that of the quantum Hall effect (QHE) plateaus and not accounted for in Ref. [2]. In addition, for a spatially homogeneous dissipation within the channel, the damping is found quantized and independent of temperature [1] [7] at the edge of a rotating "shallow" sea with chirality determined by the Coriolis parameter which corresponds to the cyclotron frequency ω c = |e|B/m * . In these mostly classical models the position of the edge does not vary but the charge density profile at the edge does.In another distinctly different and fully quantummechanical edge wave mechanism [8][9][10] only the edge position, for ν = 1, of an incompressible 2DEG varies; with respect to that the density profile is that of the undisturbed 2DEG. This approach is limited to the subspace of the lowest LL wave functions, neglects LL mixing and dissipation, and results in a single chiral EMP with dispersion law similar to that in [1].Both previous classes of models are oversimplifications. In this Letter we present a quasi-microscopic treatment of EMPs for integer ν, which takes into account LL structure, LL mixing, dissipation (related to LL mixing essentially), and the inhomogeneity of the current density near the edges treated recently [11]. It is valid for bare confining potentials sufficiently steep that LL flattening and the formation of compressible and incompressible strips [12] can be neglected [13] ; in this case the dissipation is essential only within a distance < ∼ ℓ 0 from the edges [11]. ...

Heating of carriers in an intrinsic graphene under dc electric field is considered taking into account the intraband energy relaxation due to acoustic phonon scattering and the interband generationrecombination transitions due to thermal radiation. The distribution of nonequilibrium carriers is obtained for the cases when the intercarrier scattering is unessential and when the carrier-carrier Coulomb scattering effectively establishes the quasiequilibrium distribution with the temperature and the density of carriers that are determined by the balance equations. Because of an interplay between weak energy relaxation and generation-recombination processes a very low threshold of nonlinear response takes place. The nonlinear current-voltage characteristics are calculated for the case of the momentum relaxation caused by the elastic scattering. Obtained current-voltage characteristics show low threshold of nonlinear behavior and appearance of the second ohmic region, for strong fields.

A self-consistent treatment of exchange and correlation interactions in a quantum wire (QW) subject to a strong perpendicular magnetic field is presented using a modified local-density approximation (MLDA). The influence of many-body interactions on the spin-splitting between the two lowest Landau levels (LLs) is calculated within the screened Hartree-Fock approxima-Recently the effects of electron-electron interactions on the edge state properties of a channel [1]− [5] and on the subband structure of QWs [6]− [8], [4] have attracted significant attention. One consensus of the theoretical work is that it is important to include the Coulomb interactions self-consistently. In the present work we introduce a realistic model of a QW in a strong magnetic field B and self-consistently treat mainly the case when the lowest, spin-polarized, LL is occupied, i.e., when ν = 1 in the interior part of a channel and, in the assumed integral QHE regime, the formation of a dipolar strip [1] at the channel edges is impossible. Moreover, we consider submicron width channels with rather steep confining potential that prevents the flattening of edge states [2], [4], [7] in the vicinity of the Fermi level that was suggested in Ref. [1]. To date we are aware of only the Hartree [7], [4] and Hartree-Fock [6] treatments of LLs in a QW, at a strong B field, that are similar to the edge-state studies of a wide channel [1]− [4] . Here we show that, if we include correlations in the Coulomb interaction in a QW, the spatial behavior of the LLs is strongly modified.We use the SHFA [9] to take into account exchange and correlation effects in calculating the LL single-particle energies and assessing the spatial dependence of the spin-splitting.Including correlations leads to strong changes in the spin-splitting between the two lowest LLs. These changes differ essentially between the middle of the channel and the region near the edges. The most essential role played by correlations is related with screening by the edge states which in turn depends strongly on their (group) velocity v g . The correlationscan restore a smooth, on the scale of the magnetic length ℓ 0 = (h/m * ω c ) 1/2 , dispersion of the single-particle energy as a function of the oscillator center y 0 ≈ k x ℓ 2 0 where ω c is the cyclotron frequency. It is assumed that the confining potential without many-body interactions is smooth on the ℓ 0 scale and, hence, leads to a rather small v H g ; notice that in this case the exchange interaction leads to an infinite (logarithmically divergent) v g . Because in typical experimental situations the strong magnetic field limit condition, r 0 = e 2 /(εℓ 0h ω c ) ≪ 1, is not satisfied, we propose a modified local-density approximation (MLDA) to self-consistently