Dear Henrique,


I suspect that this is not a Kwant question but a physics one.

There are three relevant length scales in this problem: the width of the sample,

the magnetic length and the Fermi wave length. You can get them from simple analytical calculations.

I suspect (from the fact that the energy is very close to -4 in your plot, hence to the bottom of the band) that these

three length scales are of the same order of magnitude, hence you're in a crossover regime. To get to the 

"standard" QHE regime, you want the number of open channels = (width)/(Fermi wave length) to be relatively

large.


Best regards,

Xavier



De : Henrique Veiga <up201805202@edu.fc.up.pt>
Envoyé : jeudi 15 août 2024 17:13:11
À : kwant-discuss@python.org
Objet : [Kwant] Fwd: Query on Conductance Quantization in Kwant Simulations within the Integer Quantum Hall effect
 
Dear Kwant community,

I have been studying the integer quantum Hall effect using the Kwant
software, through which I computed the longitudinal and transverse
conductance of a central sample (without disorder) in a four-terminal setup.

I model the central device, which is subject to a strong magnetic field,
as a square of lateral length, L. Both the sample and the four ideal
leads are described by a square-lattice tight-binding model with
nearest-neighbor hoppings.

By computing the transverse conductance as a function of the Fermi
energy, so that the first two Landau levels are crossed, I observe the
expected behavior: the conductance appears quantized in integer steps of
e²/h. However, upon zooming in on each of the two plateaus, I notice
that the conductance does not converge immediately to the expected
value. Instead, it exhibits a rippling effect, which seems to be
dependent on the leads' cross-section, L_{Lead}.

This phenomenon is illustrated in the attached .pdf file, and I have
also included the code used to evaluate the conductance.

My question is whether this behavior is a numerical issue, or if it is
expected within the context of charge transport simulations in
four-terminal setups.

Thank you in advance,

Henrique Veiga