Microwave photoconductivity of a two-dimensional electron gas: Mechanisms and their interplay at high radiation power

We develop a systematic theory of microwave-induced oscillations in the magnetoresistivity of a two-dimensional electron gas, focusing on the regime of strongly overlapping Landau levels. At linear order in microwave power, two mechanisms of the oscillations (“quadrupole” and “photovoltaic”) are identified, distinctly different from those studied before (“displacement” and “inelastic”). The quadrupole and photovoltaic mechanisms are shown to be the only ones that give rise to oscillations in the nondiagonal part of the photoconductivity tensor. In the diagonal part, the inelastic contribution dominates at moderate microwave power, while at elevated power the other mechanisms become relevant. We demonstrate the crucial role of feedback effects, which lead to a strong interplay of the four mechanisms in the nonlinear photoresponse and yield, in particular, a nonmonotonic power dependence of the photoconductivity, narrowing of the magnetoresonances, and a nontrivial structure of the Hall photoresponse. At ultrahigh power, all effects related to the Landau quantization decay due to a combination of the feedback and multiphoton effects, restoring the classical Drude conductivity.

Figure 1

All possible contributions to the photoconductivity at minimal order $O\left(E_{dc}{E}_{\omega }^2\right)$ are illustrated as graphs in $(\nu ,n)$ space of angular and temporal harmonics of the distribution function $F_{\nu n}$, according to Eqs. (3.4, 3.8). The arrows denote coupling of the harmonics $F_{\nu n}$ by the impurity collision integral ${\mathrm{St}}_{\mathrm{im}}$ [Eq. (2.10)]. The filled circles denote the action of the propagator ${\mathcal{L}}^{-1}$ in the resulting state. More precisely, ${\mathrm{St}}_{\mathrm{im}}^{(j,1,2)}$ (which is of third order in the electric fields) is denoted by the thick line in diagram (A), while the first-order collision integrals ${\mathrm{St}}_{\mathrm{im}}^{(j,1,0)}$ and ${\mathrm{St}}_{\mathrm{im}}^{(j,0,1)}$ in diagrams (B)-(F) are denoted by the thin lines. The double-line arrows in diagrams (B)–(F) correspond to the second-order integrals ${\mathrm{St}}_{\mathrm{im}}^{(\perp ,1,1)}$ and ${\mathrm{St}}_{\mathrm{im}}^{(\perp ,0,2)}$.

Figure 2

Evolution of the contribution $F_{3d}\left(Q\right)$, Eq. (7.25), to the photoconductivity (7.18) with increasing effective microwave power $Q$, Eq. (7.7), for $\alpha =1$, 10, and 30, and $\beta =0.3$ [Eq. (7.11)]. Dashed curve: the displacement contribution to $F_{3d}\left(Q\right)$, given by the first two terms in Eq. (7.24).

Figure 3

(a) Contribution $F_{2d}\left(Q\right)$, Eq. (7.25), to the photoconductivity (7.18) for $\alpha =1$, 10, and 30, and $\beta =0.3$. (b) “Nonphotovoltaic” (positive) and photovoltaic (negative) contributions to $F_{2d}\left(Q\right)$ for $\alpha =1$ and 10.

Figure 4

(a) Contribution $F_{1d}\left(Q\right)$, Eq. (7.25), to the photoconductivity (7.18) for $\alpha =1$, 10, and 30, and $\beta =0.3$. (b) Contributions to $F_{1d}\left(Q\right)$ [Eq. (7.19)] for $\alpha =1$ and 10: Dashed line: Displacement contribution [third term in Eq. (7.24)]; solid line in the upper half-plane: nonphotovoltaic contribution [second term in Eq. (7.19)]; and solid line in the lower half-plane: photovoltaic contribution [third term in Eq. (7.19)].

Figure 5

Hall contributions (7.26) to the photoconductivity (7.18) for $\alpha =1$, 10, and 30, and $\beta =0.3$: (a) $F_{1h}\left(Q\right)$; (b) $F_{2h}\left(Q\right)$; and (c) $F_{3h}\left(Q\right)$.

Figure 6

Diagonal, $d_s$, and Hall, $h_a$, parts of the magnetoresistivity tensor (8.3) at moderate microwave power $P=0.01$ [Eq. (8.2)] vs ${\omega }_c∕\omega$. Solid lines: the functions $-d_s$ [panels (a) and (c)] and $h_a$ [panels (b) and (d)]; (a) and (b) correspond to ${\alpha }_{1∕2}=1$, while (c) and (d) to ${\alpha }_{1∕2}=10$. Dashed lines: the linear-in-$P$ asymptotes $d_s^{\left(B\right)}+d_s^{\left(D\right)}$ and $h_a^{\left(D\right)}$ [Eqs. (5.15, 5.16, 5.21)].

Figure 7

Solid lines: same as in Fig. 6 for $P=0.1$. Dashed lines: the asymptote for $h_a$ in the SIC regime [Eq. (8.7)]. Dotted lines: the saturated inelastic contribution [Eq. (6.6)].

Figure 8

Solid lines: same as in Fig. 7 for $P=1$. Dashed lines: the asymptotes for $d_s$ and $h_a$ in the SIC regime [Eqs. (8.5, 8.7)]. Dotted lines: the saturated inelastic contribution [Eq. (6.6)].

Figure 9

Same as in Fig. 8 for $P=10$.

Figure 10

Isotropic part of the distribution function at three levels of the microwave power: $P=0$, $P⪡P_{\star }$, and $P\sim P_{\star }$.