Radiation-induced zero-resistance states in $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ heterostructures: Voltage-current characteristics and intensity dependence at the resistance minima

High mobility two-dimensional electron systems exhibit vanishing resistance over broad magnetic field intervals upon excitation with microwaves, with a characteristic reduction of the resistance with increasing radiation intensity at the resistance minima. Here, we report experimental results examining the voltage-current characteristics, and the resistance at the minima versus the microwave power. The findings indicate that a non-linear $V\text{−}I$ curve in the absence of microwave excitation becomes linearized under irradiation, unlike expectations, and they suggest a similarity between the roles of the radiation intensity and the inverse temperature.

Figure 1

(Color online) (a) The magnetoresistance $R_{xx}$ in a $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ heterostructure device with (w/) and without (w/o) microwave excitation at $119\mathrm{GHz}$. Without radiation, Shubnikov-de Haas (SdH) oscillations are observable in the resistance about $(4∕5)B_f$. Radiation reduces the resistance $R_{xx}$ and eliminates the SdH oscillations in the vicinity of $(4∕5)B_f$ and $(4∕9)B_f$. The star marks the $B$-field at which $V_{xx}$ vs $I$ measurements are reported (see Fig. 2). (b) A plot of the resistance data of (a) versus the normalized inverse magnetic field demonstrates periodicity, with period $\delta$, of the radiation induced oscillations in $B^{-1}∕\delta$. The curves with- and without-radiation intersect in the vicinity of integral and half-integral values of the abscissa. (c) A plot of the dark (w/o radiation) $R_{xx}$ data of (a) versus $B^{-1}∕{\delta }_{\mathrm{SdH}}$ helps to determine the phase of the Shubnikov-de Haas oscillations. Here, ${\delta }_{\mathrm{SdH}}$ is the period of the SdH oscillations. Note that SdH resistance minima occur at integral values of $B^{-1}∕{\delta }_{\mathrm{SdH}}$, suggesting that $R_{xx}$ is proportional to $-\cos (2\pi F_{\mathrm{SdH}}∕B)$, where $F_{\mathrm{SdH}}={\delta }_{\mathrm{SdH}}^{-1}$.

Figure 2

(Color online) (a) The diagonal voltage $\left(V_{xx}\right)$ is shown as a function of the current $\left(I\right)$ for a number of radiation intensities. The measurements were carried out at the $B$-field that is identified by a star in Fig. 1a. At $(-60\mathrm{dB})$, there is a sub-linear increase of $V_{xx}$ vs $I$ above $4\mu \mathrm{A}$. Increasing the radiation intensity, i.e., tuning the attenuation factor toward $0\mathrm{dB}$, reduces the slope and linearizes the $V_{xx}$ vs $I$ curve. (b) The diagonal voltage $V_{xx}$ is shown as a function of $I\text{to}I=80\mu \mathrm{A}$, with $\left(0\mathrm{dB}\right)$ and without $(-60\mathrm{dB})$ microwave excitation. Within experimental resolution, the $V_{xx}$ vs $I$ curve with excitation appears mostly linear to $80\mu \mathrm{A}$. (c) $R_{xx}$ evaluated from the initial slope of the $V_{xx}$ vs $I$ curves of (a) are plotted as a function of the power attenuation factor. Here, $P$ is the attenuated radiation intensity, and $P_0$ is the source intensity. (d) The natural logarithm of $R_{xx}$ is plotted vs $P∕P_0$.

Figure 3

(Color online) (a) Radiation induced resistance oscillations at $f=50\mathrm{GHz}$ are exhibited for a number of source intensities, in units of $\mu \mathrm{W}$. The inset shows the extrema resistance at ${(4∕5)}^{-1}$, ${(4∕7)}^{-1}$, ${(4∕9)}^{-1}$, ${(4∕11)}^{-1}$ vs the logarithm of the power. (b) The logarithm of the extrema resistance vs the logarithm of the power. A comparison with typical activation plots (e.g., see Fig. 3(d) of Ref. 1) suggests that, on the resistance minima, $\log \left(P\right)$ might be analogous to $T^{-1}$.