Macroscopic Channel-Size Effect of Nonequilibrium Electron Distributions in Quantum Hall Conductors

We have studied the channel-size dependence of nonequilibrium electrons excited into higher Landau levels in a quantum Hall conductor, by mapping cyclotron emission in Hall bars of different sizes. The images obtained reveal that the spatial evolution of the nonequilibrium electrons with current density significantly depends on the channel width of the Hall bar on a macroscopic scale of several hundred $\mu \mathrm{ms}$. This observation provides clear evidence of a macroscopic channel-size effect, which can be reasonably understood as originating from a very long equilibrium length of the excited electrons.

Figure 1

Schematic of the scanning THz microscope for imaging CE.

Figure 2

$R_{xx}$ as a function of magnetic field $B$ for $j=0.15$ (solid line), 0.4 (broken line), and $1.5\mathrm{A}/\mathrm{m}$ (dot-dashed line) for the three samples. The insets represent the samples. From $I\mathrm{\text{−}}V$ characteristic measurements at $\nu =2$ ($B=5.26\mathrm{T}$), we obtain $j_{\mathrm{c}}=1.4$, 0.34, and $0.15\mathrm{A}/\mathrm{m}$ for $W=20$, 300, and $1200\mu \mathrm{m}$, respectively.

Figure 3

Imaging plots of CE at three current densities $j=0.15$, 0.4, and $1.5\mathrm{A}/\mathrm{m}$ and for the three samples ($W=20$, 300, and $1200\mu \mathrm{m}$ from the top to the bottom). The white solid lines denote the 2DEG boundaries of the samples. The polarities of $B$ and $I$ are the same as those indicated in the insets of Fig. 2. For clarity, the signals are magnified by factors of 1300 (20, 0.15), 360 (20, 0.4), 23 (20, 1.5), 70 (300, 0.15), 18 (300, 0.4), 3 (300, 1.5), 14 (1200, 0.15), and 5 (1200, 0.4), respectively, compared to that for (1200, 1.5), where $(A,B)$ represents ($W$ in mm, $j$ in $\mathrm{A}/\mathrm{m}$).

Figure 4

Schematic representation of trajectories of excited electrons in the QHE breakdown regime ($j\ge j_{\mathrm{c}}$) for a narrow Hall bar with $W\ll L_{\mathrm{eq}}$ (upper panel) and a wide Hall bar with $W\gg L_{\mathrm{eq}}$ (lower panel).