Microwave photoconductivity of a periodically modulated two-dimensional electron system: Striped states and overlapping Landau levels

We study the dc response of the striped state under microwave irradiation. The striped state can be modeled by a two-dimensional electron system under the influence of a unidirectional periodic modulation potential, which was examined in J. Dietel et al. [Phys. Rev. B 71, 045329 (2005)]. We further extend our study of the periodically modulated system to the case of strongly overlapping Landau levels and calculate the dark and photoconductivities. The strength of the modulation potential serves as an additional parameter which allows us to vary the overlap of the Landau levels independently of the filling fraction.

Figure 1

The functions $A_i(\Delta \omega ∕2V_N,0)$ (solid line) given by (10, 13) and $B_i(\Delta \omega ∕2V_N,0)$ (dashed line) given by (17, 20) describing the dependence of the conductivities on the microwave frequency for the upper Landau level half filled system $\Delta \mu =0$.

Figure 2

The oscillatory part of the density of states $\Sigma (V_N∕{\omega }_{\mathrm{c}},ϵ∕{\omega }_{\mathrm{c}}-1∕2)$ (60) where ${(V_N∕{\omega }_{\mathrm{c}})}_1≔(V_N∕{\omega }_{\mathrm{c}})\mathrm{mod}1$. The values where ${(ϵ∕{\omega }_{\mathrm{c}})}_1-1∕2=0$ correspond to the center of the Landau bands.

Figure 3

The frequency dependent scaling ${\sigma }_{xx}^{\mathrm{DP},\mathrm{DF}}$, ${\sigma }_{yy}^{\mathrm{DF}}\sim C(\omega ∕{\omega }_{\mathrm{c}})$ (solid line) and of ${\sigma }_{yy}^{\mathrm{DP}}\sim D(\omega ∕{\omega }_{\mathrm{c}})$ (dashed line). The scaling functions $C$ and $D$ (75) are the exact frequency dependent prefactors of the photoconductivities in the case of a circular polarized microwave field derived in Sec. 7 ($\alpha =\pi ∕4$ and $\beta =-\pi ∕4$).