Mailman 3 May 2024 - Kwant-discuss

[kwant] How to make a finite lead?
by 김봉수 12 Jun '24

12 Jun '24

Dear kwant users, I am trying to reproduce the paper following. https://arxiv.org/abs/1110.4280 (in this paper, fig5, 6 will help to understand my questions.) What I’m struggling with now is to build a finite(not infinite, and not having any translational symmetry) lead as below. I wonder 1. I think "kwant.builder.SelfEnergyLead()” function might be proper thing to build a finite lead without any translational symmetry. Is it correct? 2. If it's right, when I run this code using SelfEnergyLead(), the following error occurs. How can I solve it? ------------------------------------------------------------------------------------------------ lat = kwant.lattice.chain(norbs=1) syst = kwant.Builder() syst[(lat(i) for i in range(4))] = 4 syst[lat.neighbors()] = -1 def self_energy(energy, args=(), *, params=None): return -1j left_lead = kwant.builder.SelfEnergyLead(self_energy, interface=[lat(0)], parameters = []) right_lead = kwant.builder.SelfEnergyLead(self_energy, interface=[lat(3)], parameters = []) syst.leads.append(left_lead) syst.leads.append(right_lead) syst = syst.finalized() H = syst.leads[0].kwant.hamiltonian_submatrix kwant.plot(syst) ------------------------------------------------------------------------------------------------ AttributeError: 'SelfEnergyLead' object has no attribute ‘kwant' Any help is appreciated! Best, Bongsu Kim

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Leads self-energy matrix elements not ordered as system's hamiltonian_submatrix?
by wilson2048＠outlook.com 03 Jun '24

03 Jun '24

Dear kwant community: I am investigating the `kwant.greens_function`。 I would like to get the lead self-energies and add to the original system Hamiltonian and then inverse it, thus obtaining the retarded green's function. I tested, but the resulted green's function is not identical to the one kwant calculated. I want to know the reason. Is it because what I describe in the title? Below is a minimal code example: ``` lat = kwant.lattice.square() def make_system(r=20, t=-1): def circle(pos): x, y = pos return x**2 + y**2 < r**2 syst = kwant.Builder() syst[lat.shape(circle, (0, 0))] = 0 syst[lat.neighbors()] = t syst.eradicate_dangling() def lead_shape(pos): return -12 < pos[0] < 12 lead = kwant.Builder( kwant.TranslationalSymmetry((0, 1))) lead[lat.shape(lead_shape, (0, 0))] = 0 lead[lat.neighbors()] = -t syst.attach_lead(lead) return syst syst = make_system() fsyst = syst.finalized() kwant.plot(fsyst) greens_function=kwant.greens_function(fsyst) Hc = fsyst.hamiltonian_submatrix(sparse=False) index = fsyst.lead_interfaces[0] Hc[np.ix_(index, index)] += greens_function.lead_info[0] Gr = np.linalg.inv(-Hc) Gr[np.ix_(index, index)]-greens_function.submatrix(0, 0) # should be a zero matrix ``` Bests, Wilson

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Questions About Magnetic Field Units in Landau_level.py for Landau Level Calculations
by ac76888＠sjtu.edu.cn 30 May '24

30 May '24

Dear Kwant Community, I am writing to seek assistance with two issues I have encountered while using Kwant for solving transport problems. Your guidance would be greatly appreciated. 1. I am trying to calculate the Landau levels of monolayer graphene using the following Hamiltonian (python): ``` hamiltonian = """ + hbar_vF * (k_x * kron(sigma_0, sigma_x) + k_y * kron(sigma_0, sigma_y)) """ params = dict(hbar_vF=6.582) ``` In the documentation for the `discretize_landau` function, it is stated that "The units of magnetic field are :math:`ϕ₀ / 2 π a²` with :math:`ϕ₀ = h/e` the magnetic flux quantum and :math:`a` the unit length." Is a^2 here the area (A) of a primitive cell of graphene (A = 5.24 Å²)? How can I convert this unit into Tesla? 2. Can I use this code to calculate the Landau levels of multilayer stacking graphene with a sequences of hoppings ? Are there specific considerations or modifications I should be aware of when extending the calculation to multilayer graphene? Thank you in advance for your help. Best regards, ac76888

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Current density for given lead currents
by X.-X. Zhang 15 May '24

15 May '24

Hello Kwant community, I am considering a 6-terminal sample with 0,1,2,3 the voltage leads and 4,5 the current lead. Normally, with the conductance_matrix M found by kwant I can calculate transport properties (the voltages in vector V) as per the linear equation I = M V, given I = [0,0,0,0,1,-1]. Now I want to plot the current density corresponding to this transport state, but not sure how to do it. For instance, with wf = kwant.wave_function(sys, energy), I can have all scattering wavefunctions wf(4) incoming from the current lead 4. But how to (or is it necessary to) reflect the above current configuration vector I we specified? I presume the current density may vary with different I vectors. Or maybe I misunderstand some basics? Thank you!

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wave function amplitude square meaning in kwant setting
by YIGITHAN GEDIZ 14 May '24

14 May '24

Hi all, I have a scattering region, where for a given energy E, there is a single propagating mode. (kwant.wave_function(sys, E).shape[0] == 1) When I increase the energy a little bit without leaving the same band and plot the wavefunction again, I observe the same pattern in the scattering region, but the amplitudes are different. First one's maximum amplitude square is 6, whereas the other one's is 4, for instance. I observe that this is somehow related to the density of states at given energies, such that higher maximum amplitude corresponds to higher DOS, but I did not understand why. What does wave function's amplitude square mean in kwant? I tried to investigate the source code but I failed. Thank you very much for your time

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About the Warning "Hamiltonian breaks Conservation law, ignoring the symmetry in the computation.."
by GUIDO MENICHETTI 04 May '24

04 May '24

Dear developers, dear all, I am Guido Menichetti, a Post-Doc at the University of Pisa. I am currently working on computing the Andreev reflection in a 3D hexagonal lattice system, incorporating the spin degree of freedom and utilizing wraparound techniques. To facilitate this, I have been following the Kwant tutorial available at https://kwant-project.org/doc/1.0/tutorial/tutorial5. In my approach, I define a "conservation law" to decompose the transmission function into four blocks: two for the spin degree of freedom and two for the electron-hole degree of freedom. Initially, I successfully ran calculations in a 2D system with periodic boundary conditions, perpendicular to the transport direction, without encountering any warning messages. However, when attempting the same calculations in a 3D system with periodic boundary conditions in the perpendicular directions, I encountered a warning message: "[...] |envs\Kwant-env\lib\site-packages\kwant\system.py:316: UserWarning: Hamiltonian breaks Conservation law, ignoring the symmetry in the computation warnings.warn('Hamiltonian breaks ' + name +". This warning disappears when I set the superconductor gap Delta (as defined in https://kwant-project.org/doc/1.0/tutorial/tutorial5) to 0 (Delta = 0). The superconducting part is located in the right lead. I believe the issue does not stem from the Hamiltonian of the scattering region. However, I am puzzled by the origin of this warning and its potential impact on the results. Could this problem be related to the "wraparound" technique in the 3D system? The only difference between the 2D and 3D systems is the lattice: the 2D system lives on a square lattice, while the full 3D system is a hexagonal lattice. Your insights and guidance on resolving this issue would be greatly appreciated. Best regards, Guido Menichetti University of Pisa

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