Magneto-phonon resonance in two-dimensional electron systems (2DES) was studied a long time ago [1,2]. Experiments revealed that resistance oscillates with ωLO/ωc, where ωLO is the frequency of longitudinal optical phonon and ωc = eB/m (m is the effective mass) is the cyclotron frequency. This effect requires high temperatures T ≈ 102 K and high magnetic fields B ≈ 102 kG.
A few years ago another class of resistance oscillations was discovered in 2DES at much lower T ≈ 1 K and B ≈ 1 kG. These oscillations were attributed to resonant interaction with acoustic phonons which, for brevity, will be termed phonon-induced resistance oscillations (PIRO) [3]. Resonant interaction of electrons with acoustic phonons is made possible in high Landau levels by virtue of a selection rule which favors electron backscattering. Each backscattering event corresponds to a jump of the electron guiding center Δy by a maximum distance, Δy ≈ 2Rc, where Rc is the cyclotron radius. This largest jump is accompanied by the largest momentum transfer Δqx = 2kF (kF is Fermi wavenumber), which can be supplied by an acoustic phonon. Such an acoustic phonon has a well defined frequency ωs ≈ 2kFs (s is the sound velocity) and thus can be "resonantly" absorbed (emitted) by an electron jumping to a higher (lower) Landau level. Therefore, PIRO originate from indirect inter-Landau level transitions and are governed by the ratio of the 2kF-phonon frequency to the cyclotron frequency:
PIRO peaks are believed to occur near integral values of εph:
Similar to MIRO and HIRO, PIRO extend to magnetic fields an order of magnitude lower than the onset of the Shubnikov-de Haas oscillations, but their amplitude usually remains welll below 10%. Also, while MIRO and HIRO are best observed at T≈1 K, PIRO rely on thermal excitation of 2kF-phonons and require elevated T, typically T ≈ 5-10 K.
More recent experiments in higher mobility 2DES showed up to eight oscillations persisting down to T < 2 K [3]. This allowed detailed study of the temperature dependence over a wide temperature range which revealed that higher B oscillations fully develop at progressively higher temperatures. The temperature at which a particular oscillation reaches its maximum amplitude was found to scale with B½ suggesting that PIRO, unlike SdHO, decay at higher temperature due to electron-electron interactions modifying the quantum lifetime entering the Dingle factor. There exist several outstanding issues that warrant further investigation of resonant interactions between electrons and acoustic phonons. First, existing experiments report a variety of sound velocities ranging from ~ 3 km/s [3-5] to ~ 6 km/s [6,7]. Second, it is still unclear whether PIRO are caused by interface [4,8] or bulk [5,9] phonons. Finally, little is known about the contributions from different phonon modes and the relevance of multi-phonon processes.
[1] V.L. Gurevich and Y. Firsov, Sov. Phys. JETP 13, 137 (1961)
[2] D.C. Tsui, T. Englert, A.Y. Cho, and A.C. Gossard, “Observation of Magnetophonon Resonances in a Two-Dimensional Electronic System”, Phys. Rev. Lett. 44, 341 (1980) [abstract] [full text]
[3] A. T. Hatke, M. A. Zudov, L. N. Pfeiffer and K. W. West, “Phonon-induced resistance oscillations in 2D systems with a very high electron mobility”, Physical Review Letters 102, 086808 (2009) [abstract] [full text]
[4] M.A. Zudov, I.V. Ponomarev, A.L. Efros, R.R. Du, J.A. Simmons, and J.L. Reno, “New Class of Magnetoresistance Oscillations: Interaction of a Two-Dimensional Electron Gas with Leaky Interface Phonons”, Physical Review Letters 86, 3614 (2001) [abstract] [full text]
[5] J. Zhang, S.K. Lyo, R.R. Du, J.A. Simmons, and J.L. Reno, “Oscillatory Magnetothermopower and Resonant Phonon Drag in a High-Mobility 2D Electron Gas”, Phys. Rev. Lett. 92, 156802 (2004)[abstract] [full text]
[6] A.A. Bykov, A.K. Kalagin, and A.K. Bakarov, “Magnetophonon Resonance in a GaAs Quantum Well with AlAs/GaAs Superlattice Barriers at High Filling Factors”, JETP Lett. 81, 523 (2005) [abstract] [full text]
[7] W. Zhang, M. A. Zudov, L. N. Pfeiffer and K. W. West, “Resonant Phonon Scattering in Quantum Hall Systems Driven by dc Electric Fields”, Physical Review Letters 100, 036805 (2008) [abstract] [full text]
[8] I.V. Ponomarev and A.L. Efros, “Leaky interface phonons in Al[sub x]Ga[sub 1 - x]As/GaAs structures”, Physical Review B 63, 165305 (2001) [abstract] [full text]
[9] X. L. Lei, “Low temperature electron-phonon resonance in dc-current-biased two-dimensional electron systems&rdquo:, Physical Review B 77, 205309 (2008) [abstract] [full text]