kwant.continuum.discretize scale factors?
Hello, Happy holidays to the happy Kwanters! Due to the holiday break, I finally found some time and trying to go over the 2020 quantum transport mini-workshop materials available at https://virtualscienceforum.org/quantum-transport-workshop/ <https://virtualscienceforum.org/quantum-transport-workshop/>. I noticed that one of the energy band plots for the Majorana wire (in Anton’s lecture) differs in the continuum version from that of the discretized version, by some scale factors in both x- and y- axes. I have attached the notebook (grabbed from above web site) here. Before executing any cells in the notebook, I would’ve expected the plots in cells #5 and #7 to look identical? Am I wrong? Does kwant.continuum.discretize introduce any additional scale factors, e.g. k_x ==> 2*k_x, intentionally or otherwise? I suppose I could go into the code and examine it myself, but I thought I should ask folks here first, as someone may have figured it out already. Thanks! Chagaan Baatar
Hi Chagaan, kwant.continuum.discretize doesn't change the scale. Indeed, plotting the two dispersions on the same plot shows that they agree quite well. To confirm, try adding the code below after cell 7. As a note here, the Fermi momentum is around pi/2a, which is rather high, and if one wanted to make a more accurate approximation, reducing the lattice constant would be the way to go. Best, Anton from matplotlib import pyplot as plt params = dict( B_x=0, mu=1, alpha=0.5, Delta=0 ) fig, ax = plt.subplots(figsize=(8, 6)) kwant.plotter.spectrum(h_cont, ('k_x', momenta), params=params, show=False, ax=ax) kwant.plotter.spectrum( infinite_wire, ('k_x', np.linspace(-np.pi, np.pi, 301)), params=params, ax=ax )
participants (2)
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Anton Akhmerov -
Chagaan Baatar