Quantum lifetime of two-dimensional electrons in a magnetic field

Positive magnetoresistance of two-dimensional (2D) electrons in GaAs quantum wells placed in weak quantizing magnetic fields is observed. From comparison of the magnetoresistance with theory, the quantum lifetime of 2D electrons is determined in a broad range of temperatures from 0.3 to 20 K. The temperature variation of the inverse electron lifetime is in good agreement with the conventional theory of electron-electron scattering and correlates with the rate of energy relaxation of 2D electrons.

Figure 1

Resistance vs magnetic field at different temperatures: from bottom to top, 2.25, 2.98, 3.75, 4.71, 5.94, 6.95, 7.96, 8.85, 9.80, 10.73, 11.75, 12.66, and 13.70 K.

Figure 2

Comparison between experiment (solid lines) and theory (open circles) at different temperatures as labeled. Inset shows the data plotted vs inverse magnetic field $1/B$, indicating exponential growth of the magnetoresistance at small magnetic fields.

Figure 3

Temperature dependence of the quantum scattering rate $1/{\tau }_q$ (open circles) plotted vs $T^2$. Dashed line presents a linear fit of the temperature dependence at $T<15$ K. Solid line presents expected temperature dependence due to electron-electron scattering [see Eq. (4)]. Inset shows parameters $R_0\left(T\right)$ (open circles) and $R_D=27$ $\Omega$ (black squares), which are used to compare data shown in Fig. 1 with Eq. (2).

Figure 4

Temperature dependence of transport scattering time ${\tau }_{\text{tr}}$.

Figure 5

Thin curve (1) shows contributions of correlated disorder and scattering to magnetoresistance. Curve 1 is plotted in accordance with Eq. (5). Curve 2 presents experimental data for the magnetoresistance at $T=4.72$ K. Curve 3 is a difference between curves 2 and 1.