Microwave-Induced Resistance Oscillations

When a 2DES is subject to a weak magnetic field B and is illuminated by microwave radiation, the longitudinal resistivity exhibits strong oscillations with magnetic field. These oscillations are known as Microwave-Induced Resistance Oscillations (MIRO) [1,2]. MIRO are periodic in the inverse magnetic field and generally persist to magnetic fields which are well below the onset of the Shubnikov-de Hass (SdH) oscillations. Stepping from inter-Landau level transitions accompanied by microwave absorption, MIRO are governed by the ratio of the microwave frequency ω = 2πf to the cyclotron frequency ωc = eB/m (m is the effective mass of the carrier):

εac = ω/ωc

MIRO maxima and minima of are offset symmetrically from the harmonics of cyclotron resonance:

εac = n ± φac, n=1,2,3,..

In the regime of overlapping Landau levels the MIRO phase φac is close to ¼ but when the levels get separated it becomes considerably smaller decreasing roughly as B-1[3,4]. At integer and half-integer values of εac, photoresistance vanishes and these points are called zero-response nodes. MIRO are best observed at low temperatures and quickly decay when the temperature reaches a few Kelvin.

Theoretical proposals aimed at identifying microscopic mechanisms of MIRO should be able to account for its generic properties, such as oscillatory character and frequency dependence. One group of the microscopic theories is based on radiation-induced impurity-assisted scattering and is commonly referred to as the “displacement” model [5-10]. However, another group of theories argues [11-14], that in realistic samples, where remote impurities dominate electron scattering, the leading contribution originates from the radiation-induced oscillations in the non-equilibrium electron distribution function. This mechanism is usually termed “non-equilibrium” or “inelastic”. When εac >> 1, the correction to the resistivity due to either “displacement” or “inelastic” mechanism can be written as [13]:

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Here, ρD is the Drude resistivity, τtr is the transport scattering time, and Pω is a dimensionless parameter proportional to the microwave power. For a circular polarization of microwave radiation
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where the sign in the denominator should be chosen according to the orientation of magnetic field and sense of microwave polarization. For the “displacement” mechanism ‾τ‾ = 3τim, where τim is the long-range impurity contribution to the quantum (or single particle) lifetime τq. For the “inelastic” mechanism ‾τ‾ = τin ~ EFT -2, where EF is the Fermi energy.

It is reasonable to favor the “inelastic” mechanism over the “displacement” mechanism for two reasons. First, it is expected to dominate the response since, usually, τin >> τim at T ~ 1 K. Second, it offers plausible explanation for the decay of MIRO with increasing temperature [15]. However, more recent studies [16] revealed that the temperature dependence is exponential and originates from the temperature-dependent quantum lifetime entering the square of the Dingle factor. The corresponding correction to the quantum scattering rate was found to obey T 2 dependence, consistent with the electron-electron interaction effects. At the same time no significant temperature dependence of the prefactor in Eq. (1) was identified, suggesting that the “displacement” contribution remains relevant down to temperatures as low as 1 K. Introducing a small amount of short-range impurities into the theory is expected to enhance the “displacement” contribution leading to a better quantitative agreement. At the same time further systematic experiments in samples with different amounts and types of disorder are highly desirable. While the “displacement” and “inelastic” models appear to be the most popular, there exist many other interesting proposals, which discussed MIRO in terms of phonon-assisted effects, non-parabolicity, magneto-plasma oscillations, orbital dynamics and quantum coherence effects, and sliding charge-density waves.

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Fig. 1 This figure shows MIRO in one of our 2DES samples obtained under microwave illumination of frequency f = 81 GHz and temperature T = 1 K.

References

[1] M.A. Zudov, R.R. Du, J.A. Simmons, and J.L. Reno, “Shubnikov-de Haas-like Oscillations in Millimeterwave Photoconductivity in a High-mobility Two-dimensional Electron System”, Physical Review B – Rapid Communications 64, 201311(R) (2001) [abstract] [full text]

[2] P.D. Ye, L.W. Engel, D.C. Tsui, J.A. Simmons, J.R. Wendt, G.A. Vawter, and J.L. Reno, “Giant microwave photoresistance of two-dimensional electron gas”, Applied Physics Letters 79, 2193 (2001) [abstract] [full text]

[3] M.A. Zudov, “The period and the phase of microwave-induced resistance oscillations and zero-resistance states”, Physical Review B – Rapid Communications, 69 041304(R) (2004) [abstract] [full text]

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[5] V. I. Ryzhii, “Photoconductivity characteristics in thin films subjected to crossed electric and magnetic fields”, Soviet Physics Solid State 11, 2078 (1970)

[6] V. I. Ryzhii, R. A. Suris, B. S. Shchamkhalova, “Photoconductivity of a two-dimensional electron gas in a strong magnetic field”, Soviet Physics 20, 1299 (1986)

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[8] X.L. Lei and S.Y. Liu, “Radiation-Induced Magnetoresistance Oscillation in a Two-Dimensional Electron Gas in Faraday Geometry”, Physical Review Letters 91, 226805 (2003) [abstract] [full text]

[9] J. Shi and X. C. Xie, “Radiation-Induced "Zero-Resistance State'' and the Photon-Assisted Transport”, Physical Review Letters 91, 086801 (2003)

[10] M.G. Vavilov and I.L. Aleiner, “Magnetotransport in a two-dimensional electron gas at large filling factors”, Physical Review B 69, 035303 (2004) [abstract] [full text]

[11] I. A. Dmitriev, A. D. Mirlin, and D. G. Polyakov, “Cyclotron-Resonance Harmonics in the ac Response of a 2D Electron Gas with Smooth Disorder”, Physical Review Letters 91, 226802 (2003) [abstract] [full text]

[12] I. A. Dmitriev, M. G. Vavilov, I. L. Aleiner, A. D. Mirlin, and D. G. Polyakov, “Theory of the oscillatory photoconductivity of a two-dimensional electron system”, Physica E 25, 205 (2004) [abstract] [full text]

[13] I.A. Dmitriev, M.G. Vavilov, I.L. Aleiner, A.D. Mirlin, and D.G. Polyakov, “Theory of microwave-induced oscillations in the magnetoconductivity of a two-dimensional electron gas”, Physical Review B 71, 115316 (2005) [abstract] [full text]

[14] I. A. Dmitriev, A. D. Mirlin, and D. G. Polyakov, “ Microwave photoconductivity of a two-dimensional electron gas: Mechanisms and their interplay at high radiation power”, Physical Review B 75, 245320 (2007) [abstract] [full text]

[15] S. A. Studenikin, A. S. Sachrajda, J. A. Gupta, Z. R. Wasilewski, O. M. Fedorych, M. Byszewski, D. K. Maude, M. Potemski, M. Hilke, K. W. West and L. N. Pfeiffer, “Frequency quenching of microwave-induced resistance oscillations in a high-mobility two-dimensional electron gas”, Physical Review B 76, 165321 (2007) [abstract] [full text]

[16] A. T. Hatke, M. A. Zudov, L. N. Pfeiffer and K. W. West, “Temperature Dependence of Microwave Photoresistance in 2D Electron Systems”, Physical Review Letters 102, 066804 (2009) [abstract] [full text]