Cyclotron-Resonance Harmonics in the ac Response of a 2D Electron Gas with Smooth Disorder

Abstract

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 ...

Microwave photoconductivity of a modulated two-dimensional electron gas due to intra-Landau-level transitions

“…A second contribution to the photoconductivity arises from the microwave-induced change in the electronic distribution function. 4,13,14 It turns out that typically, this distribution-function mechanism (DF) tends to dominate the magnetooscillations of the photoconductivity in realistic samples, 14 although there are exceptions to this. 17 Zero-resistance states are expected to occur once the microwave-induced oscillations become so strong that the microscopic longitudinal conductivity is negative within certain magnetic-field regions.…”

“…6,7,8,9,10,11,12,13,14,15,16,17,18 One mechanism is based on the observation that disorderassisted microwave absorption is accompanied by a realspace displacement which depending on the magnetic field, is preferentially along or against the applied dc electric field. 8,9,10,11,12 We refer to this mechanism as displacement mechanism (DP).…”

Zero‐resistance states induced by bichromatic microwaves

“…Despite the large amount of theoretical work 4,5,6,7,8,9,12 the origin of ZRS remains elusive. Nevertheless most theories agree that some mechanism produces negative-resistance states (NRS) that rapidly drive the system into a ZRS due to Andreev's instabilities 12 .…”

Oscillatory nonlinear differential magnetoresistance of highly mobile 2D electrons in high Landau levels

“…These resistance oscillations always occur at low temperatures and are related to magnetotransport of 2D electrons occupying high Landau levels (LLs). Among them the microwave-induced magnetoresistance oscillations and the related zero-resistance states were the central focus of most experimental 1,2,3,4,5,6,7,8,9,10 and theoretical 11,12,13,14,15,16,17,18,19,20,21 studies. Recently, the oscillatory behavior in the nonlinear magnetotransport has attracted much attention: in a 2D system even without irradiation, a relatively weak current can induce drastic suppression and strong oscillations of the differential magnetoresistance, and may result in a state of zero-differential resistance.…”

“…For nonlinear transport Eq. (15) shows that the SdHO term, which diminishes when temperature T e ≫ ω c /2π 2 , is modulated with an oscillatory factor S(2πǫ j ) by the finite current density through the dimensionless parameter ǫ j . Furthermore, the non-SdHO part (17) and its approximate expression (19) and (21) for small and large argument z = 2πǫj .…”