Scaling of thermoelectric voltage induced by microwave radiation at the boundary between two-dimensional electron systems

We report measurements of the rectification of microwave radiation ($0.7$-$20$ GHz) at the boundary between two- dimensional electron systems created by a narrow gap split gate on a silicon surface for different temperatures, electron densities and microwave power. For frequencies above $4$ GHz and different temperatures, the rectified voltage $V_{dc}$ as a function of microwave power $P$ can be collapsed onto a single universal curve $V_{dc}^{*}=f^*(P^{*})$ using two scaling parameters. The scaled voltage, $V_{dc}^{*}$, is a linear function of power, $P^{*}$, for small power and proportional to $(P^*)^{1/2}$ at higher power. A theory is developed which attributes the observed voltage to the thermoelectric response associated with local heating by the microwave radiation of adjacent two-dimensional electron systems with different densities $n_1$ and $n_2$. Excellent quantitative agreement is obtained between theory and experiment. *The work at the City College of New York was supported by DOE grant DOE-FG02-84-ER45153. The work at International Center of Condensed Matter Physics, Brasilia, was supported by IBEM fund from Brazilian Ministry of Science and Technology.