Magnetic-field antisymmetry of photovoltaic voltage in evanescent microwave fields as seen in a semiconductor Hall bar

A two-dimensional electron system without spatial inversion symmetry develops a sample specific dc voltage when exposed to a microwave radiation at low temperature. We investigate this photovoltaic (PV) effect in the case where spatial symmetry is broken by an evanescent high-frequency potential. We measure the induced PV voltage in a $\text{GaAs}/{\text{Ga}}_{1-x}{\text{Al}}_x\text{As}$ Hall bar at magnetic fields in the tesla range. We find that in this regime the induced PV voltage is antisymmetric with magnetic field and exhibits regular Shubnikov–de Haas-type oscillations. Our experimental results can be understood from a simple model, which describes the effect of stationary orbital currents caused by microwave driving.

Figure 1

(Color online) Magnetotransport properties of the Hall bar. The dashed and neighbor curves represent respectively the Hall resistances $R_{H,2}=R_{14,35}$ and $R_{H,1}=R_{14,26}$ (see text). The oscillating curve represents the longitudinal resistance $R_{xx}=R_{14,23}$. The data were acquired with a 100 nA excitation and lock-in detection at frequency 67 Hz at a temperature of 300 mK. The inset is an optical image of the sample, the leads (1)–(6) form the contacts of the Hall bar, while the electrodes $\left[S\right]$ and $\left[C\right]$ are local gates connected to a high-frequency $50\Omega$ transmission line. The (orange) copper shield on top of the Hall bar can be used as a top gate to change the carrier density in the 2DEG. The black scale bar corresponds to $10\mu \text{m}$.

Figure 2

(Color online) Left panel: magnetic-field dependence of the photovoltaic voltage $V_{\text{PV}}$ for different microwave powers, namely, 0.08, 0.42, 1.45, and 2.63 nW in the direction of increasing oscillation amplitude. Right panel: dependence of the photovoltage amplitude $V_{\text{PV}}$ as a function of microwave power for different values of the magnetic field (the symbols correspond to different magnetic fields and are indicated on both the right and left panels). The dashed line represents the dependence $V_{\text{PV}}\propto P$. Temperature is 300 mK, and frequency $f=2.5\text{GHz}$.

Figure 3

(Color online) Left panel: comparison of the PV voltage $V_{\text{PV}}$ as a function of inverse magnetic field for positive and negative magnetic fields. Frequency was $f=2.5\text{GHz}$ and injected microwave power of 1 nW. On the right panel, a color/grayscale diagram showing the PV voltage as a function of both top-gate voltage and applied magnetic field.

Figure 4

(Color online) Comparison of the PV voltage $V_{\text{PV}}$ as a function of inverse magnetic field for positive and negative magnetic fields. For the continuous curves microwave irradiation was sent using an external 3-mm-long antenna terminating a $50\Omega$ cryogenic coaxial cable. The dashed curves reproduce for comparison our data of Fig. 3 obtained by applying a high-frequency potential directly on the local split gate. In both cases frequency was $f=2.5\text{GHz}$. The continuous curves are shifted for clarity by $2\mu \text{V}$.

Figure 5

(Color online) Comparison between the behavior of $R_{xx}$ $\left(\text{k}\Omega \right)$ (green/gray curve), $V_{\text{PV}}$ $\left(\mu \text{V}\right)$ (blue/black curve), and $\int V_{\text{PV}}\left(H^{-1}\right)d{H}^{-1}$ (red dashed curve). The inset shows a simplified sample geometry with schematic of induced stationary currents, $i_{\text{dc}}$, and density modulation (colored/grayscale semidisks). Frequency is $f=2.5\text{GHz}$ and $P=1\text{nW}$.

Figure 6

(Color online) Dependence of the photovoltage on temperature for several magnetic fields in semilogarithmic scale. The data for different magnetic fields can be rescaled on a single linear curve as predicted by Eq. (4). The inset shows the photovoltage dependence on inverse magnetic fields for different temperatures for $f=2.5\text{GHz}$ and $P=1\text{nW}$.