Compressibility of a two-dimensional electron gas under microwave radiation

Microwave irradiation of a two-dimensional electron gas (2DEG) produces a non-equilibrium distribution of electrons, and leads to oscillations in the dissipative part of the conductivity. We show that the same non-equilibrium electron distribution induces strong oscillations in the 2DEG compressibility, measured by local probes. Local probe measurements of the compressibility are expected to provide information about the domain structure of the zero resistance state of a 2DEG under microwave radiation.

Figure 1

The microwave-induced correction to the compressibility (solid line) of a 2DEG as a function of ${\omega }_{\mathrm{c}}∕\omega$ at fixed $\omega {\tau }_q=2\pi$ and microwave power ${\phantom{\mid }\mathcal{P}\mid }_{{\omega }_c=0}=1$. In the zero resistance state (ZRS), the electric field inside domains ${\mathcal{E}}_{\mathrm{dc}}^{*}$ fixes the compressibility at the level of $\delta \chi *$ shown by a dashed line [see Eq. (9)]. Inside the domain wall, the electric field ${\mathcal{E}}_{\mathrm{dc}}$ is smaller than ${\mathcal{E}}_{\mathrm{dc}}^{*}$ and the compressibility depends on the local field as shown in the inset (for ${\omega }_{\mathrm{c}}∕\omega =0.45$, this ratio is indicated by the arrow).