Photovoltaic and rectification currents in quantum dots

We investigate theoretically and experimentally the statistical properties of dc current through an open quantum dot subject to ac excitation of a shape-defining gate. The symmetries of rectification current and photovoltaic current with respect to applied magnetic field are examined. Theory and experiment are found to be in good agreement throughout a broad range of frequency and ac power, ranging from adiabatic to nonadiabatic regimes.

Figure 1

(Color online) Symmetry factor $S_k=⟨\overline{\delta G_k^{+\Phi }}\overline{\delta G_k^{-\Phi }}⟩∕⟨{\left(\overline{\delta G_k^{\Phi }}\right)}^2⟩$ as a function of frequency $\omega$ for $k=0$ (upper panel) and $k=1$ (lower panel) at two values of temperature $T$ and power $C_0$ of the ac excitation. Inset: micrograph of the device and a schematic picture of applied voltages.

Figure 2

(Color online) Upper panel: Variance of the conductance as a function of the ac excitation power $P=P_0{C}_0∕{\gamma }_{\mathrm{e}}$ at $\omega ∕2\pi =5.56\mathrm{GHz}(\hslash \omega =7.2{\gamma }_{\mathrm{e}})$ and the theoretical result of Eq. (7) with $k=0$. We use $P_0=9\times {10}^{-8}\mathrm{W}$ and $k_{B}T=5.4{\gamma }_{\mathrm{e}}$. Lower panel: Symmetric (solid triangles) and antisymmetric (open triangles) current correlators as a function of ac excitation strength $C_0$. The solid line shows the variance of the photovoltaic current Eq. (6) with parameters fixed by the fit in the upper panel. The dashed and dotted lines show the symmetric and antisymmetric correlators of the rectification current Eq. (8) with ${\alpha }_{\omega }=0.45\hslash \omega ∕e$ and ${\phi }_1=0$.

Figure 3

(Color online) Symmetric (solid triangles) and antisymmetric (open triangles) current correlators at $\omega ∕2\pi =2.4\mathrm{GHz}$ as a function of power $P=P_0{C}_0∕{\gamma }_{\mathrm{e}}$, with $P_0=2.5\times {10}^{-7}\mathrm{W}$. The solid line shows the variance of the photovoltaic current Eq. (6) at temperature $T=5.4{\gamma }_{\mathrm{e}}∕k_{\mathrm{B}}$ and frequency $\omega =3.1{\gamma }_{\mathrm{e}}∕\hslash$. The dashed and dotted lines show the symmetric and antisymmetric correlators of the rectification current Eq. (8) with ${\alpha }_{\omega }=4.7\hslash \omega ∕e$ and ${\phi }_1=0$.