Lowest Landau Level Resistance Quantization

[fatman101]

For a 2D system of N electrons in the presence of a perpen B field and parallel E field
the resistance comes out quantized proportional to h/e. And I know this result can be obtained by finding the probablity current for the lowest Landua level wavefunction. But isn't the resistance quanitization a result of electron interaction between Landau levels? i.e. once the lowest level has 'filled up' (paulis exclusion) the electrons have to jump the E gap to the next level. So how can quanitized resistance come out of the lowest wavefunction?

 

[eljose79]

Thank you for bringing up this interesting topic. I would like to provide some insights into the quantization of resistance in a 2D system of N electrons in the presence of a perpendicular magnetic field and parallel electric field.

Firstly, let me clarify that the quantization of resistance in this system is a result of both electron interactions between Landau levels and the probability current for the lowest Landau level wavefunction. This can be explained by the concept of the quantum Hall effect.

In a 2D system, when a magnetic field is applied perpendicular to the plane, the electrons will begin to move in circular orbits, forming Landau levels. The energy of these levels is quantized and the spacing between them is proportional to the strength of the magnetic field.

Now, when an electric field is applied parallel to the plane, the electrons will experience a Lorentz force which causes them to move in a helical path. This leads to a build-up of charge at the edges of the sample, resulting in a potential difference across the sample. This potential difference can be measured as a voltage, and the current flowing through the sample can be measured as well.

In the lowest Landau level, the electrons are confined to a small region near the center of the sample and are not able to move freely. However, when the electric field is applied, the electrons can tunnel through the energy gap to the next Landau level. This results in a quantized increase in the current and a corresponding quantized decrease in the resistance.

Therefore, the quantization of resistance in this system is a result of both the electron interactions between Landau levels and the probability current for the lowest Landau level wavefunction. Both of these factors play a crucial role in understanding the quantum Hall effect and the resulting quantization of resistance.

I hope this explanation helps to clarify any confusion regarding the quantization of resistance in a 2D system of N electrons in the presence of a perpendicular magnetic field and parallel electric field. Thank you for your interest in this topic and for promoting discussions in the scientific community.