Resonant Magneto-phonon Emission by Supersonic Electrons in Ultra-high Mobility Two-dimensional System

TL;DR

This work probes resonant acoustic phonon scattering in a ultra-high mobility GaAs/AlGaAs 2DEG under non-equilibrium DC drive, reaching supersonic drift ($v_{drift}>s$) conditions. By background-subtracting the differential resistivity and comparing to the Dmitriev et al. theory, the authors extract an electron-phonon coupling constant $g^{2}\approx 0.0016$ and a quantum lifetime $\tau_q\approx 6.3$ ps, finding qualitative agreement in the subsonic and supersonic PIRO behavior and a robust saturation of PIRO amplitude in the supersonic regime. The data reveal a predicted $\pi/2$ phase change across the sound barrier and show that crossing this barrier fundamentally alters phonon emission pathways, with Landau level quantization sharpening resonant phonon emission under a magnetic field. The results illuminate electron-phonon coupling in high-murity 2D systems, test non-equilibrium PIRO theory, and hint at practical avenues toward magneto-phonon lasers in ultra-high mobility 2DEGs.

Abstract

We investigate resonant acoustic phonon scattering in the magneto-resistivity of an ultra-high mobility two-dimensional electron gas system subject to DC current in the temperature range 10 mK to 3.9 K. For a DC current density of $\sim$1.1 A/m, the induced carrier drift velocity $v_{drift}$ becomes equal to the speed of sound $s \sim$ 3 km/s. When $v_{drift} \gtrsim s$ very strong resonant features with only weak temperature dependence are observed and identified as phonon-induced resistance oscillations at and above the "sound barrier". Their behavior contrasts with that in the subsonic regime ($v_{drift} < s$) where resonant acoustic phonon scattering is strongly suppressed when the temperature is reduced unless amplified with quasi-elastic inter-Landau-level scattering. Our observations are compared to recent theoretical predictions from which we can extract a dimensionless electron-phonon coupling constant of $g^{2}$=0.0016 for the strong non-linear transport regime. We find evidence for a predicted oscillation phase change ' effect on traversing the "sound barrier". Crossing the "sound barrier" fundamentally alters the resulting phonon emission processes, and the applied magnetic field results in pronounced and sharp resonant phonon emission due to Landau level quantization.

Figures (10)

• Figure 1: $\rho^{*}_{xx}(B,I_{DC})$ at (a) 10 mK for $-B$, and (b) 3.9 K for $+B$. See Fig. \ref{['fig:bigfig']} for full plots of $\rho^{*}_{xx}$ at 10 mK and 3.9 K and Appendix C for data measured at intermediate temperature 1.2 K. The characteristic $B$-field $B_{q} =$ 60 mT for the onset of PIROs is marked in (b)- see discussion in SM supplemental Sec. S4. Plots showing expected path of HIROs (black lines) and PIROs (red lines) at (c) 10 mK for $-B$, and (d) 3.9 K for $+B$, and their expected relative amplitude: solid (dashed) lines indicate HIRO and PIRO features anticipated to be observable (weak or absent). See SM supplemental Sec. S2 (Sec. S3) for details of how the black HIRO (red PIRO) lines are calculated. HIRO lines with order $M=\pm$1, $\pm$2, $\pm$3, $\pm$4, $\pm$5 are shown. PIRO lines converging to points at zero DC current that can give rise to PIRO peaks under equilibrium conditions with index $p= \pm$1, $\pm$2, $\pm$3, $\pm$4, $\pm$5 are shown. See Appendix D for comments related to the sign convention adopted for $M$ and $p$. The "sound barrier" condition $v_{drift} = s$ is indicated by the bold red line. (e) Cartoons of LLs (blue lines indexed $\ldots$, $N-2, N-1, N, N+1, N+2$, $\ldots$) near the Fermi level (black dashed line labeled $E_{F}$) depicting various possible (exemplary) resonant scattering processes involving acoustic phonons that can lead to PIROs (red arrows) and a quasi-elastic scattering process that can lead to HIROs (black arrow). The four cartoons show possible allowed processes at the four points indicated by the colored symbols in (c), all at the same $B$-field. See text, Appendix E and SM supplemental Sec. S3 for full discussion.
• Figure 2: Plots of $\rho^{*}_{xx}$ for (a) 10 mK and (b) 3.9 K. Corresponding plots (c-d) of oscillatory component of PIROs $\rho^{osc}_{xx}$ calculated from model in dmitriev2010. See discussion in text and SM supplemental Sec. S4 regarding parameters used in the calculations. For data in (a), the resonant lines radiating out from the origin in the subsonic regime ($|I_{DC}|<15.9$ µ A) are HIROs. Quasi-elastic inter-LL scattering responsible for HIROs is not incorporated in the model described in dmitriev2010. For reference, we have added the black dashed lines in the subsonic regime in (c) that track the calculated position of the HIRO features extracted from the data in (a)- see SM supplemental Sec. S2.
• Figure 3: $\rho^{*}_{xx}$ at (ai) 10 mK for $-B$, and (aii) 3.9 K for $+B$, plotted as a function of $\epsilon_{ph}$ and $\epsilon_{DC}$ following dmitriev2010. The subsonic and supersonic regimes separated by the "sound barrier" for $s=3.0$ km/s are identified. Some black diagonal and anti-diagonal lines with integer value of $\epsilon_{DC}-\epsilon_{ph}$ acting as guide lines for anticipated PIRO line features are included above the "sound barrier" in (ai) and either side of the "sound barrier" in (aii). Dashed white lines for $\epsilon_{DC}= \pm1, \pm2, \pm3$ highlight HIROs up to third order in the 10 mK data in (ai). Corresponding plots (bi) and (bii) of $\rho^{osc}_{xx}$ calculated from the model dmitriev2010. See SM supplemental Sec. S5 for full discussion regarding interpretation of transformed data and predicted $\pi/2$ phase change effect on transitioning from the subsonic to the supersonic regime dmitriev2010. Compare theoretical red trace (Theo) with experimental blue trace (Exp) in (c) as evidence for the effect: see the PIRO peak in the supersonic [subsonic] regime located near $\epsilon_{DC}-\epsilon_{ph}= +1$$[= -(1 + \frac{1}{4})]$.
• Figure 4: $\rho^{*}_{xx}$ versus B traces for $\epsilon_{DC} =$ 0 (black dashed), $\epsilon_{DC}=$$-3/2$ (blue) and $\epsilon_{DC}=$$-2$ (red), at (a) 10 mK, (b) 1.2 K and (c) 3.9 K. Points are taken from data in the $+I_{DC}$ and $-B$ quadrant. (d) Position of successive extrema of oscillations in (a)-(c) for $\epsilon_{DC}=$$-2$, $-3/2$ plotted versus 1/B. The y-axis index-label 1, 2, 3 (0.5, 1.5, 2.5) for the maxima (minima) here effectively corresponding to $\epsilon_{ph}$. Note that for $\epsilon_{DC}=$ 0 (zero DC current), even at 3.9 K, PIROs extrema are not clearly resolved. The weak oscillations that develop with $B$ in the 10 mK and 1.2 K traces are SdH oscillations.
• Figure 5: (a) Plot of $\rho^{*}_{xx}$ data for 1.2 K, and (b) corresponding plot of oscillatory component of PIROs $\rho^{osc}_{xx}$ calculated from model in dmitriev2010. See discussion in main text regarding Fig. \ref{['fig:bigfig']}.