Mailman 3 March 2023 - Kwant-discuss

Re: How does the grid spacing in kwant.continuum.discretize effect the system?
by Clarke, Isobel March 22, 2023

March 22, 2023

Dear Christoph, Thank you so much for your reply. I've had a look at the Kwant tutorial about the discretization. However, the response I am seeing isn't consistent with the idea of an energy limit being reached. It appears that as I change the number of lattice points, therefore the grid spacing, the response of the system changes as shown in the attached image. The graphs show the state being evolved in Tkwant with the expectation values of the Pauli spin matrices plotted. For 20, 40 and 120 lattice points the graphs show an expected and similar response. For 60, 70 and 100 the graphs show no evolving of the state or an unphysical response. It appears to be very inconsistent with the grid spacing value. Could there be another cause of this result, for example how the system is built rather than a continuum limit? Thank you for any more help with this. Best wishes, Isobel ________________________________ From: Christoph Groth Sent: Thursday, March 16, 2023 15:05 To: Clarke, Isobel Cc: kwant-discuss(a)python.org Subject: Re: [Kwant] How does the grid spacing in kwant.continuum.discretize effect the system? Hi Isobel, As you decrease the discretization grid spacing you should approach the continuum limit. For example, the band structure should become more and more accurate also for larger momenta. Did you check the Kwant tutorial on the discretizer? In particular the example comparing a=1.0 and a=0.25: https://kwant-project.org/doc/1/tutorial/discretize#limitations-of-discreti… Tkwant should not really matter here. I suggest that you first check whether your discretization behaves as it should without even using tkwant, for example by looking at the band structure. Cheers Christoph

2 1

How to add magnetic field (Peierls substitution) for the continuum model
by dielectric_hjzhao＠126.com March 16, 2023

March 16, 2023

Dear kwanters, I am using kwant for handle a k.p Hamiltonian, for the conductance calculations. I start from a k.p model, and transform it to a tight-binding model using kwant.continuum tools [procedures listed here https://kwant-project.org/doc/1/tutorial/discretize]. Now I want to study the conductance of the system under magnetic field. I try to do Peierls substitution for hoppings between site i and site j (i-j being parallel to the lead). However, I find that using the kwant.continuum scheme, there are no information regarding the lattice information such as "lat = kwant.lattice.honeycomb() ". This prevents the application of Peierls substitution by the following way: _____________________________ def hopx(site1, site2, B): y = site1.pos[1] return - np.exp(-1j * B * y) syst[kwant.builder.HoppingKind((1, 0), lat.a, lat.b)] = hopx ____________________________ My question is how to add magnetic field during the calculations for the systems generated from a continuum model by kwant.continuum? Thank you very much!

3 5

Question about template
by Alejandro Alvarez Chico March 16, 2023

March 16, 2023

Im studying a small circular wafer with a set hamiltonian. The problem comes when i try to introduce disorder in the onsite parameter. I first use the discretize function on the hamiltonian to get the discretized template, then modify the onsite function to my needs while maintaining the hoppings the same, but I can't seem to use the template in my code so that it builds my system. Im currently using the modified output of the print(template), and embedding it in a new function called def template2(): to then use it in the fill function. What am I doing wrong here?

2 1

How does the grid spacing in kwant.continuum.discretize effect the system?
by Clarke, Isobel March 16, 2023

March 16, 2023

Dear Kwant developers, I am currently simulating a carbon nanotube system by defining a 1D scattering region as: def kwant_shape(site): (z,) = pos return (-total_length / 2 <= z < total_length/ 2) I then build the system by discretizing a continuous Hamiltonian onto the grid region, as shown in the function below: def make_system(): lattice_size = total_length / number_of_lattices template = kwant.continuum.discretize(hamiltonian, grid=lattice_size) syst = kwant.Builder() # add the nanotube to the system syst.fill(template, kwant_shape, (0,)) syst = syst.finalized() return syst The lowest eigenvector of the Hamiltonian system is calculated and evolved over time using Tkwant. However, by changing the parameter 'number_of_lattices', hence using a different size grid spacing, the response of the system is very different. Sometimes the resulting graph shows a changing density of the wavefunction (which is expected), however for certain lattice points there is no change in the graph, suggesting that the system does not evolve. For example, for 40 lattice points I get the expected response however for 60 lattice points I do not. I was wondering why changing the grid spacing might affect the response of the state being evolved by Tkwant? Could it be due to the symmetry of the system or how the system is defined? Thank you for any help with this!

2 1