Demonstration of a $1/4$-Cycle Phase Shift in the Radiation-Induced Oscillatory Magnetoresistance in $\mathrm{GaAs}/\mathrm{AlGaAs}$ Devices

We examine the phase and the period of the radiation-induced oscillatory magnetoresistance in $\mathrm{GaAs}/\mathrm{AlGaAs}$ devices utilizing in situ magnetic field calibration by electron spin resonance of diphenyl-picryl-hydrazal. The results confirm a $f$-independent $1/4$-cycle phase shift with respect to the $hf=j\hslash {\omega }_c$ condition for $j\ge 1$, and they also suggest a small ($\approx 2\%$) reduction in the effective mass ratio, $m^{*}/m$, with respect to the standard value for $\mathrm{GaAs}/\mathrm{AlGaAs}$ devices.

Figure 1

(a) The magnetoresistance $R_{xx}$ is plotted vs the magnetic field $B$ for a $\mathrm{GaAs}/\mathrm{AlGaAs}$ device under photoexcitation at $f=30\mathrm{GHz}$. Also shown is the electron spin resonance (ESR) of diphenyl-picryl-hydrazal (DPPH) at 2.01 GHz, which marks $B_f=2\pi f{m}^{*}/e$. $R_{xx}$ exhibits neither a maximum nor a minimum at $B_f$. A deep $R_{xx}$ minimum between $B_f<B<2B_f$ appears to converge to $2(4/5B_f)=8/5B_f$, suggestive of a two photon effect. (b) $R_{xx}$ and $R_{xy}$ at 50 GHz along with DPPH-ESR field markers for $B_f$, $4/5B_f$, $B_f/2$, and $B_f/2.5$. Note the similarity in the up-sweep and down-sweep $R_{xx}$ curves, and the weak oscillations in $R_{xy}$. The up-sweep curve has been offset to improve clarity.

Figure 2

(a) $R_{xx}$ is shown vs $B^{-1}$ for several radiation intensities at 50 GHz. (b) ESR of DPPH for $f_0=3.21\mathrm{GHz}$ and $f_0/2=1.605\mathrm{GHz}$. Here, $f_0$ marks the first integral fixed point (IFP) in (a). The period of the $R_{xx}$ oscillations, $8.6{\mathrm{T}}^{\mathrm{-}\mathrm{1}}$, appears to be slightly smaller than the spacing of the DPPH-ESR lines. (c) A half-cycle plot of the extrema in (a). A linear fit suggests a $1/4$-cycle phase shift. Fixed points, inserted as open squares, were not used for the fit. (d) The residue in $k$, i.e., $\Delta k=k-k_{\mathrm{FIT}}$, extracted from (c).

Figure 3

(a) (right ordinate) $R_{xx}$ is plotted vs $B^{-1}$ with (w/) and without (w/o) radiation at 103 GHz. (left ordinate) Half-cycle plots of the extrema and the fixed points in the radiation induced resistance oscillations. The slope of the linear fit is proportional to $m^{*}/m$, while the ordinate intercept measures the phase. (b) The phase and the effective mass ratio, $m^{*}/m$, obtained from linear fits of half-cycle plots of extrema [see (a)] as a function of the frequency. (c) The phase and $m^{*}/m$ obtained from linear fits of half-cycle plots of fixed points [see (a)] vs $f$. (d) The residue in the extrema labels, $\Delta k=k-k_{\mathrm{FIT}}$, is shown as a function of $k$, the assigned label, for $f$ shown in (b). (e) For the fixed points, $\Delta k$ is shown vs $k$, for $f$ in (c).

Figure 4

The periodicity of radiation induced $R_{xx}$ oscillations appears insensitive to the electron density, $n$. Here, increasing the slope of $R_{xy}$ vs $B$ corresponds to decreasing $n$.