corresponds to number of LL bands below $E_F$, and $R_{xx}=0$. Whenever $E_F$ passes the center of a LL band, $R_{xy}$ makes a transition between plateaus and $R_{xx}\neq0$ during this transition.

A widely used description of electrical transport in the QHE regime is the edge channel picture [@Halperin1982] and the Landauer-B[ü]{}ttiker formalism [@Buettiker1988]. Within this picture, 1D edge channels are formed at the intersection of $E_F$ with LLs bending at the physical edge of the sample. This can be intuitively understood by treating the exterior of the sample as even higher energy barriers than those which form the QW. As a result, energy levels in the exterior of the sample lie much higher than those inside QW and LLs inside the QW have to smoothly level out to their outside values. The number of edge channels is equal to the number of occupied bulk LLs, and the conductance of each edge channel is $G = \frac{e^2}{h}$, independent of its length. They are also chiral, which means that their direction is determined by the direction of the applied magnetic field.

QHE in semiconductor heterostructures is usually observed at helium temperatures and high magnetic fields when the thermal broadening of LLS is lower 