Reply to “Comment on ‘Theory of microwave-induced zero-resistance states in two-dimensional electron systems’ and on ‘Microwave-induced zero-resistance states and second-harmonic generation in an ultraclean two-dimensional electron gas’ ”

Abstract

We show that all questions raised in the Comment can be easily answered within the theory formulated in the commented papers. It is also shown that the bulk theory promoted by the commenter fails to explain the most important fundamental features of the discussed phenomenon. In the Comment1 Zudov claims that our theory 2,3does not explain the microwave induced resistance oscillations/zero resistance states (MIRO/ZRS) and that MIRO/ZRS is a bulk phenomenon. In this Reply we show that, focusing his attention on only a few very specific aspects of the effect, Zudov does not notice a number of global, fundamental problems of MIRO/ZRS, which could be understood only after assuming that this phenomenon has a near-contact origin 2,3 . The MIZRS phenomenon 4,5 has demonstrated at least five mysterious features which seemed to contradict both the previously known physics and common sense:1. The MIZRS effect is huge. The photoresistance maxima were found to be 7 − 10 times larger than the dark resistance values. The photoresistance is a nonlinear phenomenon: the dc current is proportional to the dc electric field E 0 and the squared microwave field E ω , j ∝ E dc E 2 ω . As known, substantial nonlinear effects can be observed only if the corresponding electric field parameter exceeds unity:Physically F is the additional momentum ∼ eE ω /ω (energy ∼ eE ω v F /ω), acquired by an electron during one oscillation period, normalized to its average momentum p F (energy E F ); here ω is the microwave frequency, p F , v F , E F are the Fermi momentum, velocity and energy, and n s is the density of two-dimensional (2D) electrons. The condition (1) can be rewritten in terms of the microwave power density P required for the observation of such a huge MIZRS effect:For typical MIZRS parameters (f ≃ 100 GHz, n s ≃ 3 × 10 11 cm −2 ) the required nonlinear power density (2) isIn real MIZRS experiments the microwave power density was about six orders of magnitude smaller ( 1 mW/cm 2 , Refs. 4,5 ). The first MIZRS puzzle was thus: How such a huge effect can be observed at so low microwave powers?2. The MIRO/ZRS effect demonstrates strong oscillations not only around the fundamental cyclotron frequency ω = ω c but also around harmonics ω = nω c , n = 2, 3, 4, 5, . . .. It is well known that in the uniform external ac electric field the transitions between Landau levels E N = ω c (N + 1/2) are forbidden if ∆N = ±1. In order to violate this selection rule the microwave field should be strongly inhomogeneous on the cyclotron radius (r c ) scale: the nonlocal bulk conductivity of the 2D electron gas in the magnetic field B has the formwhere X = qv F /ω c = qr c is the non-locality parameter, q is the wave-vector of the external wave and J n are Bessel functions. In the MIRO/ZRS experiments the radiation wavelength (≃ 3 mm) and the sample dimensions (≃ 0.2 − 1 mm) were much larger than the cyclotron radius (r c ≃ 1 − 5 µm). As seen from (4), the amplitude of the n-th resonance (at ω = nω c ) scales at qr c ≪ 1 as A n ∝ [n(qr c /2) n−1 ] 2

Plasmon–terahertz photon interaction in high-electron-mobility heterostructures

“…Important plasma phenomena, which have not been addressed either in [3] or in our paper are microwave-induced resistance oscillations (MIRO) [4] and zero resistance states [5]. These issues have been discussed in detail in a recent review [6] which should be, however, supplemented with an interesting scientific discussion between Zudov and Mikhailov [7,8] and the recently proposed explanation put forward by Beltukov and Dyakonov [9]. Both approaches presented in [8] and [9] share the point of view that MIRO is a classical effect, but despite this fact, these two models are totally different.…”

“…These issues have been discussed in detail in a recent review [6] which should be, however, supplemented with an interesting scientific discussion between Zudov and Mikhailov [7,8] and the recently proposed explanation put forward by Beltukov and Dyakonov [9]. Both approaches presented in [8] and [9] share the point of view that MIRO is a classical effect, but despite this fact, these two models are totally different. The former points at the role of strong nonuniform oscillating fields at the borders of metallic parts of samples (gates and ohmic contacts) and a high ponderomotive potential thereby created.…”

Dressed Photons Induced Resistance Oscillation and Zero Resistance in Arrayed Simple Harmonic Oscillators with No Impurity

“…According to experimental data12678910111213141516171819, the magneto-resistance of the two-dimensional semiconductor shows peculiar oscillation with the irradiation of microwave on the sample. Many theories have been proposed for the MIZR and MIRO in 2DEG620212223242526272829303132333435363738394041424344454647484950515253545556. Among these researches, the displacement model of the photon assisted impurity and phonon scatterings has been studied in many works, and several accomplishments have been achieved in these theories.…”