Microwave response of interacting oxide two-dimensional electron systems

We present an experimental study on microwave illuminated high mobility MgZnO/ZnO based two-dimensional electron systems with different electron densities and, hence, varying Coulomb interaction strength. The photoresponse of the low-temperature dc resistance in perpendicular magnetic field is examined in low and high density samples over a broad range of illumination frequencies. In low density samples a response due to cyclotron resonance (CR) absorption dominates, while high-density samples exhibit pronounced microwave-induced resistance oscillations (MIRO). Microwave transmission experiments serve as a complementary means of detecting the CR over the entire range of electron densities and as a reference for the band mass unrenormalized by interactions. Both CR and MIRO-associated features in the resistance permit extraction of the effective mass of electrons but yield two distinct values. The conventional cyclotron mass representing center-of-mass dynamics exhibits no change with density and coincides with the band electron mass of bulk ZnO, while MIRO mass reveals a systematic increase with lowering electron density consistent with renormalization expected in interacting Fermi liquids.

Figure 1

(a) Sketch of the experimental setup. (b) Magnetotransmission data [negated $\delta R_{\mathrm{t}}\left(B\right)$ reflecting the $B$-dependence of the transmittance, $T_{\mathrm{s}}\left(B\right)$, solid lines] and photoresistance $\delta R_{xx}\left(B\right)$ (dashed lines) for three microwave frequencies (as marked) obtained at $T=1.4$ K on a sample with density $n=2.05$ $\times {10}^{11}{\mathrm{cm}}^{-2}$. Curves are shifted vertically for clarity. Linear scales are used. (c) Positions of the minima in the magnetotransmission traces obtained for a number of available microwave frequencies on the sample in panel (b) (open squares). A linear fit crossing the origin for data points corresponding to $f\ge 75$ GHz (solid line) gives the value of the effective mass $m_{\text{CR}}^{*}=(0.31\pm 0.005)m_0$ associated with the CR in transmission.

Figure 2

Representative examples for the recorded variation of the longitudinal dc resistance, $\delta R_{xx}$, induced by incident radiation with a frequency $f=96$ GHz at $T=1.4$ K. The response differs in samples with low [$n=2.3$ $\times {10}^{11}{\mathrm{cm}}^{-2}$, panel (a)] and high electron density [$n=7.5$ $\times {10}^{11}{\mathrm{cm}}^{-2}$, panel (b)] plotted on a linear scale. (c) Position of the maxima in $\delta R_{xx}$ for the low-density sample shown in panel (a) in the frequency vs. magnetic field plane (open squares) together with a linear fit passing through the origin (solid line). (d) Position of selected MIRO extrema as marked in panel (b) extracted from data obtained at different microwave frequencies. Solid lines are linear fits to the data points using the equation $f=(N\pm 1/4)eB/2\pi m_{\mathrm{MIRO}}^{*}$, with $N=1,2,3$, and 4. This yields an average value of $m_{\mathrm{MIRO}}^{*}$ equal to $0.335m_0$. (e) Temperature dependence of the dark resistance $R_{xx}$ at $B=0$ for the structures in panels (a) and (b).

Figure 3

Microwave-induced change $\delta R_{xx}$ of the longitudinal resistance recorded on a sample with $n=4.3$ $\times {10}^{11}{\mathrm{cm}}^{-2}$ for different levels of the output power $P_{\text{out}}$ (as marked) of the $f=95$ GHz microwave radiation. The same data are plotted against $B$ in panel (a) and against $\epsilon =\omega /{\omega }_{\mathrm{c}}$ in panel (b), where $\epsilon$ is calculated using the MIRO mass $m_{\mathrm{MIRO}}^{*}=0.375$. Linear scales are used.

Figure 4

The values of effective mass extracted using MIRO period (squares), magnetotransmission (diamonds), CR peak in $\delta R_{xx}$ (triangles), and SdHO (circles) versus the carrier density $n$. Dashed line represents the band mass $m_{\mathrm{b}}\approx 0.3m_0$ of bulk ZnO, solid lines are guides for the eye.

Figure 5

(a) Photoresponse $\delta R_{xx}$ for a sample with $n=7.5$ $\times {10}^{11}{\mathrm{cm}}^{-2}$ at microwave frequency $f=84$ GHz. (b) The inverted $B$-positions of MIRO maxima and minima for the data in panel (a) plotted against $N-1/4$ and $N+1/4$, respectively. Here, $N$ is an integer. All points fall on a straight line hitting the coordinate origin. Fitting the slope yields the quasiparticle (MIRO) mass $m_{\text{MIRO}}^{*}=(0.335\pm 0.006)m_0$. In panel (c) the measured microwave-induced change of resistivity $\delta R_{xx}$ [multiplied by $exp(a/B)$ with $a=0.4$ T for better visibility of high harmonics] is plotted against the inverse of magnetic field which is rescaled to $\epsilon$ using the obtained value of $m_{\text{MIRO}}^{*}$. Linear scales are used.

Figure 6

Power dependence of the MIRO amplitude [panel (a), sample with $n=7.5$ $\times {10}^{11}{\mathrm{cm}}^{-2}$] and of the amplitude of the CR peak [panel (b), sample with $n=2.3$ $\times {10}^{11}{\mathrm{cm}}^{-2}$]. Solid lines in panel (a) are a guide for the eye illustrating a linear and square-root power dependence. The analysis suggests a transition from a linear to a sublinear regime of MIRO at the output power between 1 and 2 mW. The magnitude of the CR peak in panel (b) shows a monotonic sublinear dependence across the entire power range within which such a signal could be clearly identified.

Figure 7

The magnetic field values $B$ where a photoresistance peak is detected for different microwave frequencies $f$ on a sample with $n=2.3$ $\times {10}^{11}{\mathrm{cm}}^{-2}$. The data points are plotted using quadratic scales ($f^2$ vs. $B^2$). The main panel presents data for the entire frequency set, while the inset only includes data for $f<30$ GHz. Dashed line in the main plot is a linear fit to the data for $f>75$ GHz with the additional constraint that it passes through the origin. This corresponds to the CR relationship between frequency and field, $f=1/T_c$, with $m_{\mathrm{CR}}^{*}=0.32m_0$. The dashed line in the inset is a linear fit with a nonzero offset, as in Eq. (C1). It yields the plasmon frequency $f_{\text{p}}=11.8$ GHz.