Shubnikov de haas oscillations, conductance quantization

[Serge87]

Hi all
I'm just studying the QHE and Shubnikov de Haas oscillations. There are two points I find somehow confusing:

1. If you look at ρ_xx (resistance along the direction of applied field), you will find oscillations of this resistance as a function of the external magnetic field. Whenever the Fermi level lies in between 2 landau levels, there is no scattering and therefore ρ_xx is zero. But on the other hand, each edge channel has a finite amount of conductance (2e²/h). So how can it be, that resistance is 0 while conductance is not infinite?

2. The edge channel model is scetched as follows:
http://upload.wikimedia.org/wikipedia/commons/9/9d/Sketch_edge_channels.svg

What I don't get here: Why can you measure a current at all in this situation? I mean, on the left edge the current is running down, while on the right edge current is running up? So from this point of view there is no net current? Or is it, since the Lorentz force is pushing the electrons to one of the two edges, there is an unequal number of edge channels on both sides?

I hope my questions are clear (I'm not native english speaker)

would be great to get some inputs here.
Thanks in advance
cheers
Serge

 

[eljose79]

y

Hi Sergey,

Great questions! Let's address them one by one:

1. The reason for the apparent discrepancy between zero resistance and finite conductance lies in the difference between the macroscopic and microscopic views of the system. From a macroscopic point of view, the resistance is indeed zero when the Fermi level lies between two Landau levels. This is because, as you mentioned, there is no scattering and therefore no energy dissipation in the system. However, from a microscopic point of view, there are still individual edge channels with a finite amount of conductance. This means that while the overall resistance is zero, there is still a finite amount of current flowing through each individual channel. This can be understood by thinking of the edge channels as wires, where each wire has a finite amount of resistance but when connected in parallel, the overall resistance is zero.

2. Your understanding of the edge channel model is correct. The Lorentz force does indeed push the electrons to one of the two edges, creating an unequal number of edge channels on each side. This results in a net current flowing through the system, even though the individual currents on each edge cancel each other out. This is similar to how a river can have a net flow even though the individual water molecules may be moving in different directions.

I hope this helps clarify your questions. If you have any further inquiries, please don't hesitate to ask.