Microwave induced magnetoresistance oscillations at the subharmonics of the cyclotron resonance

Abstract

The magnetoresistance oscillations, which occur in a two-dimensional electron system exposed to strong microwave radiation when the microwave frequency ω coincides with the n-th subharmonic of the cyclotron frequency ωc have been investigated for n = 2, 3 and 4. It is shown that these subharmonic features can be explained within a non-equilibrium energy distribution function picture without invoking multi-photon absorption processes. The existence of a frequency threshold above which such oscillations disappear lends further support to this explanation. PACS numbers: 72.20.Fr, 72.20.My, 73.40.Kp The observation of microwave induced magnetoresistance oscillations (MIMO) with some minima saturating near zero in state-of-the-art two-dimensional electron systems [1,2,3] has attracted great interest. The effect is governed by the ratio of the microwave frequency to the cyclotron frequency: ω/ω c . At the magnetic field close to an integer ratio, the magnetoresistance remains unaffected by the microwave radiation (zero-response node). At slightly larger values of ω/ω c , the microwaves cause a drop of resistance, while at smaller values they produce a positive contribution to the resistance. The two mainstream approaches to explain these oscillations are based on scattering assisted indirect optical transitions [4,5] and on the creation of a non-equilibrium electron energy distribution function [6,7]. Already in early experiments [2, 6, 8], additional oscillations were detected near ω = ω c /2 as well as close to other fractional values of ω/ω c such as 3/2, 5/2, and 2/3. In a recent article [9], these 'fractional' oscillations were tentatively ascribed to multi-photon processes involving the simultaneous absorption of n photons. Here, n = 2 or 3 and corresponds to the denominator of the fractional value. This interpretation was supported on a qualitative level within the model of microwave induced indirect transitions when multi-photon absorption is included [10,11,12].In this paper, we report on the observation of MIMO when ω = ω c /n with n = 2, 3 and 4 and in particular we investigate the frequency range where these additional oscillations are observed. We find that they only occur at microwave frequencies below a certain threshold value. If interpreted in terms of indirect optical transitions our data would imply the involvement of two-, three-and four-photon absorption processes. However within this framework, it is difficult to account for the frequency threshold. We show that all important properties of these additional oscillations, including the frequency threshold, are captured by the non-equilibrium electron distribution function picture when only single photon absorption processes are considered.Our investigations were carried on a double-sided modulation doped GaAs/AlGaAs quantum well with an elec-tron density of n s = 2.7 × 10 11 cm −2 and a mobility µ = 17 × 10 6 cm 2 /V s. Hall bar geometries were prepared with a width W of 400 µm and with potential probes spaced a distance L = 800 µm apart. The sam...

Nonequilibrium phenomena in high Landau levels

“…Similar fractional MIRO (fMIRO) for other fractions in the n = 1 series ǫ ac = 1/m were reported for m = 3, 4 (Dorozhkin et al, 2007b;Wiedmann et al, 2009a) andm = 5, 6, 7, 8 (Wiedmann et al, 2009a). Fractions that have been observed in the fMIRO series with n = 2 (apart from the even denominator fractions coinciding with the members of the n = 1 series) are represented by m = 3 (Dorozhkin et al, 2007b;Wiedmann et al, 2009a;Zudov, 2004;Zudov et al, 2006a) and m = 5, 7 (Wiedmann et al, 2009a). Note that the fMIRO series with n = 1, 2 belong to the high-B side of the CR and thus do not overlap with the integer MIRO which occur at ǫ ac > 1.…”

“…The data were obtained at T ≃ 1.0 K in a sample with ne ≃ 3.6 × 10 11 cm −2 and µ ≃ 2 × 10 7 cm 2 /V s. From Zudov et al (2006b). (b) Similar data for f = 17 GHz at T ≃ 1.4 K in a sample with ne ≃ 2.7 × 10 11 cm −2 and µ ≃ 1.7 × 10 7 cm 2 /V s. From Dorozhkin et al (2007b).…”

“…35). The oscillatory feature at ǫ ac = 1/2 was observed by Dorozhkin (2003); Dorozhkin et al (2007bDorozhkin et al ( , 2005; Wiedmann et al (2009a); Willett et al (2004) [in retrospective, the first signature of the halfinteger MIRO can be recognized already in early experiments on moderate-mobility samples (Zudov et al, 2001a), see a weak oscillation at B ≃ 2 kG in the f = 45 GHz trace there]. Similar fractional MIRO (fMIRO) for other fractions in the n = 1 series ǫ ac = 1/m were reported for m = 3, 4 (Dorozhkin et al, 2007b;Wiedmann et al, 2009a) andm = 5, 6, 7, 8 (Wiedmann et al, 2009a).…”

“…. .. For given n, therefore, there exists a finite range of ω and ω c within which m = n photons can bridge the gap between n LLs via real intermediate states, which leads to the emergence of an additional mechanism of fMIRO (Dorozhkin et al, 2007b;Pechenezhskii et al, 2007). fMIRO induced by this mechanism of sequential single-photon absorption are specific to the crossover between the regimes of overlapping and well-separated LLs and disappear altogether for 2∆ g > ω c .…”

Multiphoton processes at cyclotron resonance subharmonics in a two-dimensional electron system under dc and microwave excitation

“…For large microwave intensity, MIROs can occur at rational fractions of ǫ ac , with ǫ ac = 1/m the most readily obtainable experimental series [18][19][20][21][22][23] . These fractional MIROs are a result of multiphoton processes.…”