Abstract
We report the observation of dccurrentbiasinduced Bperiodic Hall resistance oscillations and Hall plateaus in the GaAs/AlGaAs 2D system under combined microwave radiation and dc bias excitation at liquid helium temperatures. The Hall resistance oscillations and plateaus appear together with concomitant oscillations also in the diagonal magnetoresistance. The periods of Hall and diagonal resistance oscillations are nearly identical, and source power (P) dependent measurements demonstrate sublinear relationship of the oscillation amplitude with P over the span 0 < P ≤ 20 mW.
Introduction
Magnetotransport studies of twodimensional electron systems (2DES) subjected to microwave, mmwave, and terahertz photoexcitation have revealed many interesting phenomena including the radiationinduced zeroresistance states and associated radiationinduced magnetoresistance oscillations, which have drawn attention from both experiment and theory^{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48}. It is by now wellknown that the above mentioned radiationinduced magnetotransport effect consists of 1/4cycle phaseshifted 1/Bperiodic oscillations, where the oscillatory minima emerge in the vicinity of B = [4/(4j + 1)]B_{ f }, where B_{ f } = 2πfm^{*}/e, f is the microwave frequency, m^{*} is the effective electron mass and j = 1, 2, 3…. Such oscillatory magnetoresistance is mostly observed, at modest radiationintensity, in the regime of approximately 2πf > ω_{ c }, where ω_{ c } is the cyclotron frequency. It turns out that, in addition to the above mentioned 1/B periodic photoexcited magnetotransport effects, there are also Bperiodic oscillatory photoexcited magnetooscillations in both the diagonal resistance, R_{ xx }, and the photovoltage V_{ p }. In contrast to 1/B periodic photoexcited magnetotransport effects which occur approximately when 2πf > ω_{ c }, these Bperiodic magnetooscillations in the R_{ xx } and V_{ p } are typically observed at 2πf < ω_{ c }, i.e., B > B_{ f }^{49,50,51,52} Further, initial reports^{49,50} proposed that the oscillation period, ΔB, follows ΔB∝n_{ e }/ωL, where n_{ e } is electron density and L is the distance between potential probes along the Hall bar. Such oscillations in R_{ xx } and V_{ p } were attributed to the interference of coherently excited edge magnetoplasmons (EMP) at contacts along the periphery of the sample^{49,50,53,54}. In their study, Stone et al.^{52} confirmed the existence of such Bperiodic oscillations in the regime 2πf < ω_{ c }, in specimens where both the 1/B periodic and the B periodic photoexcited magneto oscillations occur together. However, they found that the period ΔB is independent of L, the spacing between adjacent contacts^{52}, which suggested a reduced role for the interference between edge magnetoplasmons excited at adjacent contacts, and generally pointed to effects within a contact.
Here, we report the observation of Bperiodic oscillations, ΔR_{ xy }, in the Hall resistance, R_{ xy }, which go together, remarkably, with plateaulike features in the Hall resistance trace, and examine the correlation of these ΔR_{ xy } oscillations with Bperiodic diagonal magnetoresistance oscillations, ΔR_{ xx }, induced by microwave photoexcitation. Critically, it turns out that the realization of such Bperiodic oscillations in both R_{ xy } and R_{ xx } in our specimens requires the injection of a supplemental dccurrent, I_{ dc }, into the specimen. The observed Bperiodic oscillations in ΔR_{ xy } and ΔR_{ xx } appear very similar, although the ΔR_{ xy } oscillations are larger in magnitude, their amplitudes increase sublinearly with the microwave power, and the period ΔB decreases with increasing microwave frequency, f. The necessity of a supplemental dccurrent for the observability of this effect suggests a role for heating in this observed 2DES effect.
Results
Figure 1(a) shows the dark and photoexcited R_{ xy } (left ordinate) and R_{ xx } (right ordinate) vs. the magnetic field B to B = 2 Tesla. Here, the supplemental dccurrent bias, I_{ dc } = 0, and the frequency of microwave excitation for the photoexcited trace is f = 58 GHz. Note that the dark R_{ xy } has been offset with respect to the photo excited R_{ xy } trace for the sake of clarity. The Fig. 1(a) shows that the dark and photoexcited traces are nearly the same. Indeeed, subtracting the photoexcited data from the dark data for both R_{ xy } and R_{ xx } shows a vanishing residual. These residuals shown as \({\rm{\Delta }}{R}_{xy}={R}_{xy}^{(photoexcited)}{R}_{xy}^{(dark)}\) and \({\rm{\Delta }}{R}_{xx}={R}_{xx}^{(photoexcited)}{R}_{xx}^{(dark)}\) in Fig. 1(b) are vanishingly small in comparison to the ascollected signals. Thus, at first sight it looks like there is hardly a difference between the photoexcited and dark curves in the absence of a dccurrent bias, although a close examination shows small Shubnikovde Haas (SdH) in the residue since the SdH oscillations are slightly suppressed by the microwaves. The characteristic field for cyclotron resonance is labeled as B_{ f } = 2πfm^{*}/e, where f is microwave frequency, m^{*} is effective mass, e is the electron charge, and it is indicated by the dotted vertical line. Figure 1(c,d) show the transport results when a supplemental dccurrent bias is applied to the sample. Here, when I_{ dc } = 30 μA, the photoexcited R_{ xy } shows evidence for Hall oscillations with plateau like features in comparison to dark R_{ xy } for B ≥ 0.5 Tesla, see Fig. 1(c). Again, the dark R_{ xy } has been offset with respect to the photoexcited R_{ xy } for the sake of clarity. Concurrently, the R_{ xx } trace shows strong Bperiodic oscillations on top of the SdH oscillations, which were evident in R_{ xx } of Fig. 1(a). [Such behavior is also observable in Fig. 2(a,d), which also suggest some harmonic distortion in the SdH oscillations under these experimental conditions]. The background subtracted ΔR_{ xy } and ΔR_{ xx } extracted from Fig. 1(c) have been plotted in Fig. 1(d). This figure demonstrates strong Bperiodic oscillations in both R_{ xy } and R_{ xx } induced by the application of the I_{ dc } in the presence of microwave photoexcitation for B > 0.25 Tesla. The maxima (minima) of ΔR_{ xy } oscillations align with the minima (maxima) of ΔR_{ xx } oscillations. An observable beat in the Bperiodic oscillations, which did not show an obvious dependence on f, occurs for B ≈ 1.3 Tesla. This feature suggests the possibility of interference between two harmonic terms closely spaced frequency, and differing in frequency by ≤ 10%. Note that ΔR_{ xy } and ΔR_{ xx } oscillations are observed for B > B_{ f }.
Similar results are shown in Fig. 2 at other f. Figure 2(a,c) exhibit photoexcited and dark R_{ xy } and R_{ xx } curves at I_{ dc } = 30 μA and f = 31 and 46 GHz respectively. As in Fig. 1(c), additional small Bperiodic oscillations become evident on the R_{ xy } and R_{ xx } under the combined application of both the current bias and the microwave photoexcitation. The additional Bperiodic features on the photoexcited R_{ xy } in Fig. 2(a,c) have a distinct plateaulike appearance to them. Figure 2(b,d) show ΔR_{ xy } and ΔR_{ xx } at f = 31 and 46 GHz respectively. In both Fig. 2(b,d), Bperiodic oscillations appear in ΔR_{ xy } and ΔR_{ xx } above B_{ f }. Note that the period of the these microwave and currentbiasinduced oscillations decreases with increasing microwave frequency.
Figure 3 examines the microwave source power, P, dependence of ΔR_{ xy }, in panel (a), and ΔR_{ xx }, in panel (b), vs. B at f = 58 GHz. From Fig. 3(a,b), it is apparent that both ΔR_{ xy } and ΔR_{ xx } oscillation amplitudes are enhanced by increasing P. A closer investigation suggests that the B positions of oscillatory extrema move toward high B as P increases. Panel (c) and (d) exhibit the amplitudes of specified oscillatory maximum (labeled with an asterisk) of ΔR_{ xy } and ΔR_{ xx } as a function of P at f = 58 GHz. The data illustrate a sublinear relation between the amplitude and P. A power law function, ΔR ∝ P^{α}, has been applied to the experimental data to extract α characterizing the increase in the amplitude with P. The preliminary results indicate that α ≈ 0.55 ± 0.1, which suggests that the oscillation amplitude could be sensitive to the magnitude of the microwave electric field, E, since E∝P^{0.5} ^{19}.
To determine the periodicity of the Bperiodic oscillations, the oscillatory maxima of R_{ xy } and R_{ xx } were assigned to integer values and the oscillatory minima to halfinteger values. The plots of the oscillation index, N as a function of the extremal Bvalue for the oscillatory R_{ xy } and R_{ xx } for f = 31, 40, 46, and 58 GHz are exhibited in Fig. 4(a,b); these plots confirm a linear relationship indicating that the R_{ xy } and R_{ xx } oscillations are periodicinB. The period, ΔB, of the R_{ xy } and R_{ xx } oscillations as a function of f are plotted in Fig. 4(c), while the inset shows a plot of 1/ΔB vs. f. Since data points are shown at only four frequencies in Fig. 4(c), it is difficult to clarify the functional dependence of the oscillatory effect on the microwave frequency from these measurements. Studies at higher frequencies appear necessary to further investigate the relationship between the period of oscillations and microwave frequency.
Discussion
Plasmons are collective excitations of electronic system that arise upon displacing electrons from their equilibrium positions with respect to the background positive charge^{54}. A GaAs/AlGaAs 2DES is expected to exhibit a collective plasmon response in the absence of a magnetic field, i.e., B = 0, following the dispersion \({\omega }_{p}^{2}=n{e}^{2}k\mathrm{/2}{\varepsilon }_{eff}{\varepsilon }_{0}{m}^{\ast }\), where ω_{ p } is the plasmon frequency, n is the electron density, e is the electron charge, k is the plasmon wave vector, m^{*} is the effective mass, and for the GaAs/AlGaAs 2DES, ε_{ eff } = (ε_{ GaAs } + ε_{ vac })/2, with ε_{ GaAs } = 12.8, and ε_{ vac } = 1^{55}. The application of a transverse magnetic field leads to a hybridization of cyclotron resonance with this plasmon, producing the (bulk) magnetoplasmon which follows \({\omega }_{mp}^{2}={\omega }_{p}^{2}+{\omega }_{C}^{2}\)^{54}. In a strip or Hall bar geometry, the length scale established by the boundary helps to determine the quantization condition or allowed values for the plasmon wavevector, k. Vasiliadou et al. investigated the transport signature of this phenomenon in Hall bars and found that their data could be described by k = π/W, where W is the width of the device^{55}. This suggests that the finite sized specimen should exhibit the magnetoplasmon or plasmon shifted cyclotron resonance (hf = ħω_{ mp }) in place of the bare cyclotron resonance (hf = ħω_{ C }). In addition to the lowest mode, it is possible to also have additional allowed plasmon modes at wave vectors k, i.e., k = nπ/W, with n = 2, 3, 4…. Then, one expects additional magnetoplasmon branches to also leave behind a signature in transport. However, all these magnetoplasmon resonances would be expected to occur at magnetic fields below the bare cyclotron resonance magnetic field at a fixed frequency, f, for photoexcitation, i.e., B ≤ B_{ f } = 2πfm^{*}/e.
In addition to bulk plasmons, there exist edge plasmons that occur in bounded specimens. In contrast to the bulk plasmons, the mode frequencies of edge magnetoplasmons decrease with increasing magnetic field and follow the relation \({\omega }_{emp}={\mathrm{((2}}^{\mathrm{1/2}}\mathrm{/3)(3}{\omega }_{p}^{2}+{\omega }_{C}^{2}{)}^{\mathrm{1/2}}{\omega }_{c}) \sim {\omega }_{p}^{2}/{\omega }_{c}\)^{54}. As with bulk magnetoplasmons, many edge magnetoplasmon modes are possible, one for each allowed value for k in the bounded specimen
As mentioned, our study reveals strong Bperiodic oscillations in the Hall resistance that go together with the R_{ xx } oscillations. Remarkably, the features in the R_{ xy } trace even have a plateau like appearance associated with them, see Fig. 2(a,c). Such Bperiodic oscillations in the Hall resistance have not been reported before, to our knowledge. On the other hand, the B periodic oscillations in R_{ xx } appearing in this study under microwave excitations are similar to the Bperiodic oscillations in R_{ xx } discussed in ref.^{49}. Further, in our study, it appears vitally important to apply a supplementary current, i.e., a dccurrent bias, to realize the Bperiodic oscillations. It is the moderate microwave excitation in the presence of the dccurrent bias that helps to bring out the Bperiodic oscillations in both R_{ xy } and R_{ xx }. Although such data from our study have not been shown here, the period of observed Bperiodic oscillations in the R_{ xx } did not depend on the spacing of the voltage contacts, as in the work of Stone et al.^{52}. Early work claimed an edge magnetoplasmon origin for such Bperiodic R_{ xx } oscillations based on the dependence of the period on microwave frequency, electron density, and distance between potential contacts. As mentioned, such oscillations were attributed to the interference of coherently excited edge magnetoplasmons (EMP) at adjacent diagonal voltage contacts along the periphery of the sample^{49,50,53}. Yet, the independence of the period on the potential probe distance^{52} seems to be, at first sight, in variance with expectations based on the edge magnetoplasmon model. ref.^{52} suggested, however, that, given the long decay length of edge magnetoplasmon modes, such can propagate along the whole edge around the sample as a consequence of the high sample mobility. We note that even in the high mobility sample, thermal dissipation at the source and drain contacts may not support the propagation of edge magnetoplasmons across current contacts. That is, the EMP’s on opposite edges of the sample, on either side of the line connecting the source and the drain, are most likely decoupled. In this situation, it is difficult to understand the observed similarity between the magnetooscillations in the R_{ xx } and R_{ xy } in our measurements since the R_{ xy } contacts lie on opposite edges while the R_{ xx } contacts lie on the same edge. The requirement of a dcbias for the observability of the effect, together with the improved observability of the effect at higher bath temperatures, T ≈ 4 K, suggests that the dcbias serves to heat the electron system, and the current heating helps to bring about the obervability of the effect. Certainly, the observed effects are fascinating and further measurements are being carried out to understand their origin, and the role of the dcbias in the electronic system^{30,31}.
In summary, we have observed a dc current bias induced B  periodic Halloscillations that go together with longitudinal magnetoresistance oscillations in the GaAs/AlGaAs 2D electron systems under combined microwave and dc bias excitation. As noted, these Bperiodic oscillations in R_{ xy } go together with remarkable plateaulike features in the Hall resistance trace. The Hall and longitudinal magnetoresistance oscillations reveal similar period at given microwave frequency as their amplitude increases sublinearly with the microwave power. The dependence of the observed effect to the dc– bias current offers a new method to study the Bperiodic magnetooscillations with an easily controlled experimental parameter in a given specimen.
Methods
Sample Preparation
GaAs/AlGaAs heterojunctions were grown by molecular beam epitaxy and 200μmwide Hall bars were fabricated by optical lithography, and they included alloyed goldgermanium contacts. The specimen’s carrier density and mobility were n_{ e } ≈ 2.4 × 10^{11} cm^{−2} and μ ≈ 11.6 × 10^{6} cm^{2}⋅V^{−1}⋅s^{−1} at 1.5 K respectively.
Measurement Configuration
A Hall bar was mounted at the end of a 0.5′′diameter stainless steel waveguide sample holder. The sample holder was immersed into pumped liquid helium. The temperature of the sample was controlled over the span 1.5 ≤ T ≤ 4 K by controlling the helium vapor pressure. The magnetic field, produced by a superconducting solenoid, was aligned along waveguide axis and perpendicularly to the sample. Microwaves were generated by a synthesizer over the frequency range 30 ≤ f ≤ 50 GHz at a source power 0.1 ≤ P ≤ 10 mW and a millimeter wave IMPATT diode source at f = 58 GHz with a maximal source power 20 mW. The TE_{10} mode microwaves excited by a probecoupled antenna launcher was transported through the waveguide onto the sample and the electric field was oriented along the Hall bar long axis. The Hall voltage, V_{ xy }, and diagonal voltage, V_{ xx }, were collected using a fourterminal lockin technique with an lowfrequency ac current, I_{ ac }, flowing along the Hall bar; as indicated in Fig. 1 inset. A supplemental dc current, I_{ dc }, was applied along with I_{ ac } for a portion of the measurements.
References
 1.
Mani, R. G. et al. Zeroresistance states induced by electromagneticwave excitation in GaAs/AlGaAs heterostructures. Nature (London) 420, 646 (2002).
 2.
Zudov, M. A., Du, R. R., Pfeiffer, L. N. & West, K. W. Evidence for a new dissipationless effect in 2D electronic transport. Phys. Rev. Lett. 90, 046807 (2003).
 3.
Mani, R. G. et al. Demonstration of a 1/4cycle phase shift in the radiationinduced oscillatory magnetoresistance in GaAs/AlGaAs devices. Phys. Rev. Lett. 92, 146801 (2004).
 4.
Mani, R. G. et al. Radiation induced oscillatory Hall effect in high mobility GaAs/AlGaAs devices. Phys. Rev. B 69, 16130614 (2004).
 5.
Mani, R. G. et al. Radiation induced zeroresistance states in GaAs/AlGaAs heterostructures: Voltagecurrent characteristics and intensity dependence at the resistance minima. Phys. Rev. B 70, 15531015 (2004).
 6.
Mani, R. G. et al. Radiationinduced oscillatory magnetoresistance as a sensitive probe of the zerofield spin splitting in highmobility GaAs/AlGaAs devices. Phys. Rev. B 69, 193304–14 (2004).
 7.
Mani, R. G. Zeroresistance states induced by electromagneticwave excitation in GaAs/AlGaAs heterostructures. Physica E (Amsterdam) 22, 1–6 (2004).
 8.
Mani, R. G. Radiationinduced zeroresistance states with resolved Landau levels. Appl. Phys. Lett. 85, 4962–4964 (2004).
 9.
Smet, J. H. et al. Circularpolarizationdependent study of the microwave photoconductivity in a twodimensional electron system. Phys. Rev. Lett. 95, 116804 (2005).
 10.
Mani, R. G. Radiationinduced oscillatory magnetoresistance in a tilted magnetic field in GaAs/AlGaAs devices. Phys. Rev. B 72, 075327–15 (2005).
 11.
Mani, R. G. Photoexcited zeroresistance states in quasitwodimensional GaAs/AlGaAs devices. Sol. St. Comm. 144, 409–412 (2004).
 12.
Zhang, W., Zudov, M. A., Pfeiffer, L. N. & West, K. W. Resistance oscillations in twodimensional electron systems induced by both ac and dc fields. Phys. Rev. Lett. 98, 106804 (2007).
 13.
Studenikin, S. A. et al. Frequency quenching of microwaveinduced resistance oscillations in a highmobility twodimensional electron gas. Phys. Rev. B 76, 165321 (2007).
 14.
Mani, R. G. Radiationinduced decay of Shubnikovde Haas oscillations in the regime of the radiationinduced zeroresistance states. Appl. Phys. Lett. 91, 132103–13 (2007).
 15.
Raichev, O. E. Magnetic oscillations of resistivity and absorption of radiation in quantum wells with two populated subbands. Phys. Rev. B 78, 125304 (2008).
 16.
Mani, R. G., Johnson, W. B., Umansky, V., Narayanamurti, V. & Ploog, K. Phase study of oscillatory resistances in microwaveirradiated and darkGaAs/AlGaAs devices: Indications of an unfamiliar class of the integral quantum Hall effect. Phys. Rev. B 79, 205320 (2009).
 17.
Fedorych, O. M. et al. Quantum oscillations in the microwave magnetoabsorption of a twodimensional electron gas. Phys. Rev. B 81, 201302(R) (2010).
 18.
Wiedmann, S., Gusev, G. M., Raichev, O. E., Bakarov, A. K. & Portal, J. C. Microwave zeroresistance states in a bilayer electron system. Phys. Rev. Lett. 105, 026804 (2010).
 19.
Mani, R. G., Gerl, C., Schmult, S., Wegscheider, W. & Umansky, V. Nonlinear growth in the amplitude of radiationinduced magnetoresistance oscillations. Phys. Rev. B 81, 125320 (2010).
 20.
Mani, R. G., Ramanayaka, A. N. & Wegscheider, W. Observation of linearpolarizationsensitivity in the microwaveradiationinduced magnetoresistance oscillations. Phys. Rev. B 84, 085308 (2011).
 21.
Ramanayaka, A. N., Mani, R. G., Iñarrea, J. & Wegscheider, W. Effect of rotation of the polarization of linearly polarized microwaves on the radiationinduced magnetoresistance oscillations. Phys. Rev. B 85, 205315 (2012).
 22.
Mani, R. G. et al. Terahertz photovoltaic detection of cyclotron resonance in the regime of radiationinduced magnetoresistance oscillations. Phys. Rev. B 87, 245308 (2013).
 23.
Konstantinov, D., Monarkha, Y. & Kono, K. Effect of Coulomb interaction on microwaveinduced magnetoconductivity oscillations of surface electrons on liquid helium. Phys. Rev. Lett. 111, 266802 (2013).
 24.
Mani, R. G., Kriisa, A. & Wegscheider, W. Magnetotransport characteristics of a 2D electron system driven to negative magnetoconductivity by microwave photoexcitation. Sci. Rep. 3, 3478, https://doi.org/10.1038/srep03478 (2013).
 25.
Mani, R. G., Kriisa, A. & Wegscheider, W. Sizedependent giantmagnetoresistance in millimeter scale GaAs/AlGaAs 2D electron devices. Sci. Rep. 3, 2747, https://doi.org/10.1038/02747 (2013).
 26.
Ye, T., Liu, H.C., Wegscheider, W. & Mani, R. G. Combined study of microwavepower/linearpolarization dependence of the microwaveradiationinduced magnetorsistance oscillations in GaAs/AlGaAs devices. Phys. Rev. B 89, 155307 (2014).
 27.
Liu, H.C., Ye, T., Wegscheider, W. & Mani, R. G. Frequencydependent polarizationanglephaseshift in the microwaveinduced magnetoresistance oscillations. J. Appl. Phys. 117, 064306 (2015).
 28.
Ye, T., Liu, H.C., Wang, Z., Wegscheider, W. & Mani, R. G. Comparative study of microwave radiationinduced magnetoresistive oscillations induced by circularly and linearlypolarized photoexcitation. Sci. Rep. 5, 14880 (2015).
 29.
Ye, T., Iñarrea, J., Wegscheider, W. & Mani, R. G. Linear polarization study of microwaveradiationinduced magnetoresistance oscillations: Comparison of power dependence to theory. Phy. Rev. B 94, 035305 (2016).
 30.
Wang, Z., Samaraweera, R. L., Reichl, C., Wegscheider, W. & Mani, R. G. Tunable electron heating induced giant magnetoresistance in the high mobility GaAs/AlGaAs 2D electron system. Sci. Rep. 6, 38516, https://doi.org/10.1038/srep38516 (2016).
 31.
Samaraweera, R. L. et al. Mutual influence between current induced giant magnetoresistance and radiationinduced magnetoresistance oscillations in the GaAs/AlGaAs 2DES. Sci. Rep. 7, 5074 (2017).
 32.
Liu, H.C., Samaraweera, R. L., Mani, R. G., Reichl, C. & Wegscheider, W. Angular phase shift in polarizationangle dependence of microwaveinduced magnetoresistance oscillations. Phy. Rev. B 94, 245312 (2016).
 33.
Gunawardana, B. et al. Millimeter wave radiationinduced magnetoresistance oscillations in the high quality GaAs/AlGaAs 2D electron system under bichromatic excitation. Phy. Rev. B 95, 195304 (2017).
 34.
Durst, A. C., Sachdev, S., Read, N. & Girvin, S. M. Radiationinduced magnetoresistance oscillations in a 2D electron gas. Phys. Rev. Lett. 91, 086803 (2003).
 35.
Lei, X. L. & Liu, S. Y. Radiationinduced magnetoresistance oscillation in a twodimensional electron gas in Faraday geometry. Phys. Rev. Lett. 91, 226805 (2003).
 36.
Koulakov, A. A. & Raikh, M. E. Classical model for the negative dc conductivity of acdriven twodimensional electrons near the cyclotron resonance. Phys. Rev. B 68, 115324 (2003).
 37.
Rivera, P. H. & Schulz, P. A. Radiationinduced zeroresistance states: Possible dressed electronic structure effects. Phys. Rev. B 70, 075314 (2004).
 38.
Mikhailov, S. A. Microwaveinduced magnetotransport phenomena in twodimensional electron system: Importance of electrodynamic effects. Phys. Rev. B 70, 165311 (2004).
 39.
Auerbach, A., Finkler, I., Halperin, B. I. & Yacoby, A. Steady states of a microwaveirradiated quantumHall gas. Phys. Rev. Lett. 94, 196801 (2005).
 40.
Iñarrea, J. & Platero, G. Theoretical approach to microwaveradiationinduced zeroresistance states in 2D electron systems. Phys. Rev. Lett. 94, 016806 (2005).
 41.
Lei, X. L. & Liu, S. Y. Radiationinduced magnetotransport in highmobility twodimensional systems: Role of electron heating. Phys. Rev. B 72, 075345 (2005).
 42.
Dmitriev, I. A., Vavilov, M. G., Aleiner, I. L., Mirlin, A. D. & Polyakov, D. G. Theory of microwaveinduced oscillations in the magnetoconductivity of a twodimensional electron gas. Phys. Rev. B 71, 115316 (2005).
 43.
Iñarrea, J. & Platero, G. Polarization immunity of magnetoresistivity response under microwave excitation. Phys. Rev. B 76, 073311 (2007).
 44.
Wang, S. & Ng, T.K. Circularpolarization independence of microwaveinduced resistance oscillations and the zeroresistance state. Phys. Rev. B 77, 165324 (2008).
 45.
Iñarrea, J. & Platero, G. Microwaveinduced resistance oscillations and zeroresistance states in twodimensional electron systems with two occupied subbands. Phys. Rev. B 84, 075313 (2011).
 46.
Chepelianskii, A. D. et al. Enhancement of edge channel transport by a lowfrequency irradiation. Phys. Rev. B 86, 205108 (2012).
 47.
Lei, X. L. & Liu, S. Y. Linear polarization dependence of microwaveinduced magnetoresistance oscillations in highmobility twodimensional systems. Phys. Rev. B 86, 205303 (2012).
 48.
Zhirov, O. V., Chepelianskii, A. D. & Shepelyansky, D. L. Towards a synchronization theory of microwaveinduced zeroresistance states. Phys. Rev. B 88, 035410 (2013).
 49.
Kukushkin, I. V. et al. New type of Bperiodic magnetooscillations in a twodimensional electron system induced by microwave irradiation. Phys. Rev. Lett. 92, 236803 (2004).
 50.
Kukushkin, I. V., Mikhailov, S. A., Smet, J. H. & von Klitzing, K. Miniature quantumwell microwave spectrometer operating at liquidnitrogen temperatures. Appl. Phys. Lett. 86, 044101 (2005).
 51.
Simovič, B., Ellenberger, C., Ensslin, K., Tranitz, H.P. & Wegscheider, W. Density dependence of microwave induced magnetoresistance oscillations in a twodimensional electron gas. Phys. Rev. B 71, 233303 (2005).
 52.
Stone, K. et al. Photovoltaic oscillations due to edgemagnetoplasmon modes in a very highmobility twodimensional electron gas. Phys. Rev. B 76, 153306 (2007).
 53.
Mikhailov, S. A. Propagation of edge magnetoplasmons in semiconductor quantumwell structures. Appl. Phys. Lett. 89, 042109 (2006).
 54.
Mast, D. B., Dahm, A. J. & Fetter, A. L. Observation of bulk and edge magnetoplasmons in a twodimensional electron fluid. Phys. Rev. Lett. 54, 1706 (1985).
 55.
Vasiladou, E. et al. Collective response in the microwave photoconductivity of Hall bar structures. Phys. Rev. B 48, 17145 (1993).
Acknowledgements
Research has been supported by the NSF ECCS 1710302. The magnetotransport work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Material Science and Engineering Division under DESC0001762. Microwave, mmwave, and terahertz work was supported by the Army Research Office under W911NF1420076 and W911NF1510433.
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Measurements were carried out by H.C.L. Experimental development and manuscript by H.C.L. and R.G.M. High quality GaAs/AlGaAs wafers are due to C.R. and W.W.
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Correspondence to R. G. Mani.
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