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
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
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Henrique Veiga -
WAINTAL Xavier