Mailman 3 April 2025 - Kwant-discuss

Current visualization in 3D nanowire
by Thomas Bredewoud April 28, 2025

April 28, 2025

Dear all, Visualizing current flow in 3D systems is challenging. Kwant provides built-in features for 2D systems, but does not support 3D current visualization. To still gain some insight into the current flow in my 3D nanowire system, I analyze the current on a single 2D facet of the nanowire. However, the resulting current distribution appears inhomogeneous, which is surprising given that the physical system is homogeneous. I have attached a minimal example (current_visualization.py) that demonstrates the issue. Has anyone encountered a similar situation? Could this be a visualization artifact, or might it indicate an issue with how the current is computed in 3D systems? Any suggestions or insights would be greatly appreciated. Best regards, Thomas

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Issue with importing kwant in python
by Li Jingyi April 27, 2025

April 27, 2025

Dear Kwant dev/maintaining group: I was trying to use kwant for setting up a small simulation with many body interaction in tunneling junctions. However the first step I tried importing kwant with ‘import kwant’ I encountered the kernel crushing with the following message : And when i tried to test ```python -c "import kwant; print('Success’)``` it returns ```zsh: abort python -c "import kwant; print('Success’)”````` which suggestes mismatched libraries. I tried other ways such as build from sources but all kind of did not work very well and the kernel keep crushing, and trying to run I am currently using MacBook Apple M1 MacOS 15.3.2 (24D81), I need some further instructions and help on how to proceed to install kwant and use it on my system. Best Jingyi

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Peierls phase convention
by Pericles Philippopoulos April 15, 2025

April 15, 2025

Hello everyone, I am new to KWANT but have been trying to implement a tight-binding model over a (2D) square lattice under the influence of a constant perpendicular magnetic field. This example is explored in section IV B of [Graf, M., & Vogl, P. Electromagnetic fields and dielectric response in empirical tight-binding theory. Physical Review B, 51(8), 4940 (1995)]. My implementation is inspired by the KWANT tutorials. I start with the following function to set up the model: def make_system(a: float=1, eps0: float=4.0, hop: float=1.0, r: float=20): """ Creates a tight-binding model Args: a (float): Lattice constant eps0 (float): On-site energy hop (float): Hopping energy r (float): Radius of the quantum dot Returns: syst (kwant.Builder): The system lat (kwant.lattice): The lattice """ lat = kwant.lattice.square(a, norbs=1) syst = kwant.Builder() # Define the quantum dot def circle(pos): (x, y) = pos rsq = x ** 2 + y ** 2 return rsq <= r ** 2 def hopx(tosite, fromsite, peierls): phi = peierls(tosite, fromsite) return -hop * t * phi def hopy(tosite, fromsite, peierls): phi = peierls(tosite, fromsite) return -hop * t * phi syst[lat.shape(circle, (0, 0))] = eps0 * t # hoppings in x-direction syst[kwant.builder.HoppingKind((1, 0), lat, lat)] = hopx # hoppings in y-directions syst[kwant.builder.HoppingKind((0, 1), lat, lat)] = hopy # Closed system, no leads return syst, lat And then I diagonalize the resulting Hamiltonian for different values of the magnetic field (in units of the flux quantum hc/e in cgs units): def sorted_eigs(ev): evals, evecs = ev # Sort eigenvalues in ascending order and get the corresponding indices sorted_indices = np.argsort(evals) # Use the sorted indices to sort evals sorted_evals = evals[sorted_indices] # Use the sorted indices to sort eigenvectors accordingly sorted_eigenvectors = evecs[:, sorted_indices] return sorted_evals, sorted_eigenvectors for iB in np.linspace(0, 0.03, 30): B = iB def B_syst(pos): return B peierls_syst = gauge(B_syst) params = dict(peierls=peierls_syst) ham_mat = syst.hamiltonian_submatrix(params=params, sparse=True) # Diaglonalize the Hamiltonian evals, evecs = sorted_eigs(sla.eigsh(ham_mat.tocsc(), k=10, sigma=0.05)) If I compare the results to Fig. 2 (a) of [Graf, M., & Vogl, P. Electromagnetic fields and dielectric response in empirical tight-binding theory. Physical Review B, 51(8), 4940 (1995)], I get results that are those for a magnetic field B that is ~2 times as small. Looking at the source code, specifically line 791 of https://gitlab.kwant-project.org/kwant/kwant/blob/v1.5.0/kwant/physics/gaug… I find that the phases are written with a factor of pi in the exponent. However, looking at [Graf, M., & Vogl, P. Electromagnetic fields and dielectric response in empirical tight-binding theory. Physical Review B, 51(8), 4940 (1995)], if I express the magnetic field in units of the flux quantum / l^2 (as is suggested in the docstring at line 1005) I expect to get a factor of h / hbar = 2*pi in the exponent, consistent with the discrepancy. Is my reasoning correct? Is the KWANT definition for the flux quantum perhaps hc/(2e) (ie the superconducting flux quantum)? Any help would be greatly appreciated. Thanks.

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F(ferromagnet) - S(superconductor) Junction Conductance in Kwant – Need Help with Spin-Resolved Conductance.
by Jabed Umar April 14, 2025

April 14, 2025

Hi all, --------- I'm simulating an FS (Ferromagnet–Superconductor) junction in Kwant (code attached below) to study conductance as a function of energy, and I'm observing the following: 1. Sub-gap conductance, which depends on Andreev reflection, reduces with increasing exchange field. 2. Supra-gap conductance remains the same as in an NS junction since the exchange field doesn't affect transport above the gap. 3. A divergence peak in conductance at E = Δ comes from the divergence in the density of states of the s-wave superconductor. These results are consistent and expected. ---------However, I would like to extract spin-resolved conductance, especially in the sub-gap regime, where spin-up and spin-down conductance should differ. This is because minority spins can always find a partner for Andreev's reflection, but majority spins may not. This leads to asymmetry in the Andreev reflection probabilities for different spin channels. ------------I'm using the S-matrix from Kwant to compute conductance. From what I understand: - Normal reflection corresponds to r_ee^{σσ'} - Andreev reflection corresponds to r_he^{σσ'} As I understand it, the issue is that Kwant does not explicitly label spin in the mode indices, which makes it difficult to separate the spin components in the conductance calculation. Has anyone worked on spin-resolved conductance in FS or NS junctions using Kwant? Any advice, tips, or example code would be really helpful. Thank you! ---------------------------------------------------------------------Code for FS junction import kwant import numpy as np from matplotlib import pyplot # Pauli matrices sigma_0 = np.identity(2) sigma_x = np.array([[0, 1], [1, 0]]) sigma_y = np.array([[0, -1j], [1j, 0]]) sigma_z = np.array([[1, 0], [0, -1]]) tau_0 = np.identity(2) tau_x = np.array([[0, 1], [1, 0]]) tau_y = np.array([[0, -1j], [1j, 0]]) tau_z = np.array([[1, 0], [0, -1]]) # Lattice and system parameters a = 1 # lattice constant W, L = 1, 100 # width and length barrier = 0 # barrier height barrierpos = (19, 20) # barrier x-position range mu = 0.5 Delta = 0.01 Deltapos = 20 # ferromagnetic region t = 0.25 h = 0.2 # exchange field strength (ferromagnetism) # Kronecker products for combined spin ⊗ particle-hole basis Delta_term = Delta * np.kron(sigma_x, tau_0) t_hop = -t * np.kron(sigma_z, tau_0) sz_tz = np.kron(sigma_z, tau_z) k = np.kron(sigma_z, tau_0) # Define lattice lat = kwant.lattice.square(norbs=4) # for particle-hole basis syst = kwant.Builder() # Ferromagnetic region for x in range(Deltapos): for y in range(W): syst[lat(x, y)] = (2 * t - mu) * k + h * sz_tz # Barrier region (still ferromagnetic) for x in range(barrierpos[0], barrierpos[1]): for y in range(W): syst[lat(x, y)] = (2 * t + barrier - mu) * k + h * sz_tz # Superconducting region for x in range(Deltapos, L): for y in range(W): syst[lat(x, y)] = (2 * t - mu) * k + Delta_term # Hoppings syst[lat.neighbors()] = t_hop # === Leads === # Ferromagnetic lead (left) sym_left = kwant.TranslationalSymmetry((-a, 0)) lead0 = kwant.Builder(sym_left, conservation_law=-np.kron(sigma_z, tau_0)) for y in range(W): lead0[lat(0, y)] = (2 * t - mu) * k + h * sz_tz lead0[lat.neighbors()] = t_hop # Superconducting lead (right) sym_right = kwant.TranslationalSymmetry((a, 0)) lead1 = kwant.Builder(sym_right) for y in range(W): lead1[lat(0, y)] = (2 * t - mu) * k + Delta_term lead1[lat.neighbors()] = t_hop # Attach leads and finalize syst.attach_lead(lead0) syst.attach_lead(lead1) syst = syst.finalized() # === Conductance plotting === def plot_conductance(syst, energies): data = [] for energy in energies: smatrix = kwant.smatrix(syst, energy) # G = N - R_ee + R_he data.append(smatrix.submatrix((0, 0), (0, 0)).shape[0] - smatrix.transmission((0, 0), (0, 0)) + smatrix.transmission((0, 1), (0, 0))) pyplot.figure() #pyplot.plot(energies, normalized_data) pyplot.plot(energies, data) pyplot.xlabel("Energy [t]") pyplot.ylabel("Normalized Conductance") pyplot.title("FS Junction Conductance") pyplot.grid(True) pyplot.show() energies = np.linspace(0, 0.1, 100) plot_conductance(syst, energies)

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Quantum transport
by 西科大刘燕 April 2, 2025

April 2, 2025

Dear all, How to calculate the local current in a graphene nanoribbon at a specific energy, where the device region contains Rashba spin-orbit coupling (RSOC), using the Kwant package?Can you provide a simple example? Any help and guidance would be appreciated! Best regards, Rease

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