We develop a theory of magnetooscillations in the photoconductivity of a two-dimensional electron gas observed in recent experiments. The effect is governed by a change of the electron distribution function induced by the microwave radiation. We analyze a nonlinearity with respect to both the dc field and the microwave power, as well as the temperature dependence determined by the inelastic relaxation rate.
Developments in the physics of 2D electron systems during the last decade revealed a new class of nonequilibrium phenomena in the presence of a moderately strong magnetic field. The hallmark of these phenomena is magnetoresistance oscillations generated by the external forces that drive the electron system out of equilibrium. The rich set of dramatic phenomena of this kind, discovered in high mobility semiconductor nanostructures, includes, in particular, microwave radiation-induced resistance oscillations and zero-resistance states, as well as Hall field-induced resistance oscillations and associated zero-differential resistance states. The experimental manifestations of these phenomena and the unified theoretical framework for describing them in terms of a quantum kinetic equation are reviewed. This survey also contains a thorough discussion of the magnetotransport properties of 2D electrons in the linear-response regime, as well as an outlook on future directions, including related nonequilibrium phenomena in other 2D electron systems.
The frequency-dependent conductivity σxx(ω) of 2D electrons subjected to a transverse magnetic field and smooth disorder is calculated. The interplay of Landau quantization and disorder scattering gives rise to an oscillatory structure that survives in the high-temperature limit. The relation to recent experiments on photoconductivity by 76.40.+b The magnetotransport properties of a high-mobility 2D electron gas (2DEG) in semiconductor heterostructures are of great importance from the point of view of both fundamental physics and applications. Important information about the dynamical and spectral properties of the system is provided by its response to a microwave field. Within the quasiclassical Boltzmann theory, the dissipative ac conductivity σ xx (ω) = σ + (ω) + σ − (ω) of a non-interacting 2DEG in a magnetic field B is given by the Drude formula (we neglect spin for simplicity),where v F is the Fermi velocity, ν 0 = m/2π (withh = 1) the density of states (DOS), τ tr,0 the transport relaxation time at B = 0, ω c = eB/mc the cyclotron frequency, and m is the electron effective mass. For a sufficiently clean sample, ωτ tr,0 ≫ 1, Eq.(1) predicts a sharp cyclotron resonance (CR) peak at ω c = ω. It has been shown by Ando [1,2] that the Landau quantization of the orbital electron motion leads, in combination with disorder, to the emergence of harmonics of the CR at ω = nω c , n = 2, 3, . . .. Indeed, such a structure was experimentally observed [3]. The analytical calculations of Ref.[1] were performed, however, only for fully separated Landau levels with point-like scatterers [4].Very recently, great interest in the transport properties of a 2DEG in a microwave field has been caused by experiments on photoconductivity of exceptionally-highmobility samples by Zudov et al. [5] and Mani et al. [6], where oscillations controlled by the ratio ω/ω c were observed. Remarkably, these oscillations persisted down to magnetic fields as low as B ∼ 10 mT, an order of magnitude smaller than the field at which the Shubnikov-de Haas oscillations were damped. The experiments [5,6] triggered an outbreak of theoretical activity. Durst et al. [7] proposed (see also Refs. [8,9]) that the oscillations are governed by the following mechanism: an electron is excited by absorbing a photon with energy ω close to nω c and is scattered by disorder. In view of the oscillatory structure of the DOS, this leads to an extra contribution to the dc conductivity. In fact, a very similar mechanism of oscillatory photoconductivity was proposed long ago [10] for the case of a strong dc electric field.While the proposal of Ref.[7] is very appealing, calculations presented there involve a number of assumptions and approximations, which complicates a comparison with experiment. First, the consideration of Ref. [7] is restricted to the case of white-noise disorder with τ tr,0 = τ s,0 , where τ s,0 is the single-particle relaxation time at B = 0. On the other hand, the experiments are performed on high-mobility samples with smooth disorder, τ tr,0 /τ ...
-Anomalous Hall effect arises in systems with both spin-orbit coupling and magnetization. Generally, there are three mechanisms contributing to anomalous Hall conductivity: intrinsic, side jump, and skew scattering. The standard diagrammatic approach to the anomalous Hall effect is limited to computation of ladder diagrams. We demonstrate that this approach is insufficient. An important additional contribution comes from diagrams with a single pair of intersecting disorder lines. This contribution constitutes an inherent part of skew scattering on pairs of closely located defects and essentially modifies previously obtained results for anomalous Hall conductivity. We argue that this statement is general and applies to all models of anomalous Hall effect. We illustrate it by an explicit calculation for two-dimensional massive Dirac fermions with weak disorder. In this case, inclusion of the diagrams with crossed impurity lines reverses the sign of the skew scattering term and strongly suppresses the total Hall conductivity at high electron concentrations.Many ferromagnetic materials exhibit a finite Hall effect, i.e. transverse voltage in response to a current, without applying external magnetic field. This phenomenon is commonly referred to as the anomalous Hall effect (AHE) [1]. Two important ingredients of AHE are magnetization and spin-orbit interaction. The former breaks timereversal symmetry and exerts a force acting on electron spins while the latter couples the spins to orbital degrees of freedom thus giving rise to the transport effect.AHE can also occur as a result of valley or isospin polarization rather than ordinary ferromagnetism [2]. The spin-orbit coupling can also be of a more general form as it is, e.g. in graphene [3,4] where the role of spin is played by the sublattice index. An important part of the anomalous Hall signal originates in the Berry curvature thus being of a topological origin [5]. It is, therefore, natural that the discovery of materials like graphene and topological insulators [6,7], which are characterized by non-trivial Berry phase of quasiparticles, has considerably broadened the interest to AHE from both theory and experiment [8][9][10][11][12][13][14].Despite the long history [15][16][17] and high experimental relevance of AHE, its theoretical description is a challenging task often leading to confusions. In modern literature, two common approaches based on the Boltzmann kinetic equation and Kubo-Středa diagrammatic formalism are discussed. Boltzmann equation provides an intuitive quasiclassical approach to the effect [1,18] but requires an accurate account of several mechanisms of Hall conductivity: intrinsic, side-jump, and skew-scattering. Intrinsic AHE is attributed to topological properties of the band [19] and is thus independent of disorder. Skew scattering is due to the asymmetry in the impurity scattering crosssection and side jump refers to the transverse displacement of an electron being scattered. An alternative microscopic Kubo-Středa formalism is more...
We present a systematic study of the microwave-induced oscillations in the magnetoresistance of a twodimensional electron gas for mixed disorder including both short-range and long-range components. The obtained photoconductivity tensor contains contributions of four distinct transport mechanisms. We show that the photoresponse depends crucially on the relative weight of the short-range component of disorder. Depending on the properties of disorder, the theory allows one to identify the temperature range within which the photoresponse is dominated by one of the mechanisms analyzed in the paper.
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