Classical ratchet effects in heterostructures with a lateral periodic potential

We study terahertz radiation induced ratchet currents in low dimensional semiconductor structures with a superimposed one-dimensional lateral periodic potential. The periodic potential is produced by etching a grating into the sample surface or depositing metal stripes periodically on the sample top. Microscopically, the photocurrent generation is based on the combined action of the lateral periodic potential, verified by transport measurements, and the in-plane modulated pumping caused by the lateral superlattice. We show that a substantial part of the total current is caused by the polarization-independent Seebeck ratchet effect. In addition, polarization-dependent photocurrents occur, which we interpret in terms of their underlying microscopical mechanisms. As a result, the class of ratchet systems needs to be extended by linear and circular ratchets, sensitive to linear and circular polarizations of the driving electromagnetic force.

Figure 1

Sample design. (a) Blanter and Büttiker’s geometry. (b) The experimental geometry of the first set of samples (type 1, ST1) with an asymmetric groove profile. (c) The geometry of the second set of samples (type 2, ST2) with supercells $\mathit{ABCABC}\dots$ of metallic stripes on top of the sample. (d) Electron micrograph of the first set of samples (ST1). (e) Electron micrograph of the second set of samples (ST2). Here, the widths of the patterns $A$, $B$, and $C$ are 1, 0.6, and 0.3 $\mu$m, respectively.

Figure 2

Circular photogalvanic current $J_C=[J(\phi ={45}^{°})-J(\phi ={135}^{°})]/2$ measured as a function of the angle of incidence ${\theta }_0$ in a (001)-oriented GaAs$/$Al${}_{0.25}$Ga${}_{0.75}$ reference QW sample R1 without a lateral structure. The current is measured at room temperature in the direction normal to the light propagation. The photocurrent is excited by radiation with the wavelength $\lambda$ $=$ 280 $\mu$m and power $P\approx 2$ kW. The inset (bottom, left) shows the dependence of the total photocurrent $J$ on the angle $\phi$ measured for angles of incidence ${\theta }_0=\pm {35}^{°}$. Two other insets (right panels) show, respectively, the experimental geometry and the quarter-wave plate which varies the radiation helicity according to $P_{\mathrm{circ}}=\sin 2\phi$. Full lines are fits to the phenomenological theory for $C$${}_{2v}$ symmetry relevant for (001)-grown unstructured III–V QWs and given by Eq. (34); see Ref. 19.

Figure 3

Photocurrent measured as a function of the angle $\phi$ at normal incidence (${\theta }_0=0^{°}$) in sample ST1 with the asymmetric lateral structure prepared along the [100] cubic axis. The current is measured at room temperature and $T=10$ K, excited by radiation with the wavelength $\lambda$ $=$ 280 $\mu$m and power $P\approx 2$ kW. Full lines are fits to Eq. (35), see also Eq. (29). The inset shows the experimental geometry. The ellipses on top illustrate the state of polarization for various angles $\phi$.

Figure 4

Photocurrent measured as a function of the angle $\phi$ at various angles of incidence ${\theta }_0$ in sample ST1 with an asymmetric lateral structure prepared along the [100] cubic axis. The data for ${\theta }_0\ne 0$ are shifted by $\pm 5$ $\mu$A for each $\pm 5^{°}$ step in ${\theta }_0$. The current is measured at room temperature, excited by radiation with the wavelength $\lambda$ equals; 280 $\mu$m and power $P\approx 2$ kW. Full lines are fits to Eq. (35) [see also Eq. (29)]. The inset shows the experimental geometry.

Figure 5

Angle of incidence dependence of the photocurrent. $•$ and $○$: current $J_{\mathrm{circ}}$ measured in sample ST1 and the reference sample R1, respectively.$\square$, $\blacksquare$, and $▴$ are current contributions proportional to $J_3$, $J_2$, and $J_1$. Dotted line is the fit after Eq. (38), solid and dashed lines to Eq. (36).

Figure 6

Photocurrent $J$ measured as a function of the azimuth angle $\alpha$ under normal incidence at room temperature and $T=10$ K in sample ST1 with the asymmetric lateral structure along the [100] axis. The photocurrent is excited by linearly polarized radiation with the wavelength $\lambda$ $=$ 280 $\mu$m and power $P\approx 2$ kW. Full lines are fits to Eq. (37); see also Eq. (29). We used for fitting the same values of $J_j$ as in the experiments with elliptically polarized radiation; see Fig. 3. Left inset shows the experimental geometry, and right inset defines the angle $\alpha$. Arrows on top indicate the polarization corresponding to various values of $\alpha$.

Figure 7

Photocurrent $J_x$ measured at sample ST2 as a function of the azimuth angle $\alpha$ at normal incidence and a wavelength of $\lambda$ $=$ 280 $\mu$m and power $P\approx 9$ kW. The dependences for both parts with and without asymmetric stripes are shown. The current induced in the structured part by linearly polarized radiation is well fitted by Eq. (39); see also Eq. (29). The inset displays the design of the Hall bar with the structured and the unpatterned part. Arrows on top indicate the polarization corresponding to various values of $\alpha$.

Figure 8

Shubnikov–de Haas oscillations measured at $100$ mK in the unpatterned reference section of the ST2 sample.

Figure 9

Longitudinal resistance ${\rho }_{\mathit{xx}}$ in the modulated part of the Hall bar sample ST2. At low $B$, $1/B$ periodic commensurability oscillation indicate the presence of a weak periodic potential. The $1/B$ periodicity of the low-field oscillations is evident from the inset where the oscillation index ${\lambda }_C$ is plotted vs the resistance minima position $1/B$.