Mailman 3 October 2023 - Kwant-discuss

Package announcement: Pymablock
by Anton Akhmerov 12 Nov '23

12 Nov '23

Hello fellow Kwanters, I am happy to announce Pymablock, a Python package useful to combine with Kwant. Its main purpose is constructing effective models using perturbation theory, which may help you in different ways. Pymablock allows you to analyse the behavior of a few levels of a large Hamiltonian, or to construct a symbolic k.p model. We originally wrote the code for one of our projects, but then saw that this tool is useful almost for the entire group, so we decided to turn it into a package. We spent countless hours generalizing, optimizing, and testing it so that it is efficient and reliable. Now it handles multiple perturbations to any order, and it is compatible with symbolic and numerical calculations. We hope that Pymablock will save you a lot of effort and computation time. To see where it can help, check out our its documentation (https://pymablock.rtfd.io/), and in particular the tutorials about the k.p model of bilayer graphene (https://pymablock.readthedocs.io/en/latest/tutorial/bilayer_graphene.html) or the induced superconducting gap (https://pymablock.readthedocs.io/en/latest/tutorial/induced_gap.html). Just like Kwant, Pymablock is open source (https://gitlab.kwant-project.org/qt/pymablock), and you are welcome to follow and contribute to its development. Let us know if you have any questions or comments! Also if there's interest we can organize an online introduction of the package Best, Anton Akhmerov and the Pymablock maintainers: Isidora Araya Day and Sebastian Miles

3 3

How to introduce buckling in monolayer buckled Xenes like silicene, germanene, stanene etc.
by Swastik Sahoo 03 Nov '23

03 Nov '23

Hello, I want to introduce buckling term to the lattice structure of buckled monolayer Xenes like silicene, germanene, stanene etc. to differentiate them from planar graphene. Will the lattice structure be able to show the buckling ? Thanks and Regards, Swastik Sahoo. Research Scholar, EE Dept. IIT Bombay. Ph. No- 9980387383 mail id:- swastik.sahoo79(a)gmail.com swastik(a)ee.iitb.ac.in

3 2

Question about adding smooth disorder
by Jaja Li 26 Oct '23

26 Oct '23

Dear Kwant developers and users, I'm trying to add disorder on graphene by method below. I randomly add on-site energy on lattice point. Now I want to make disorder smooth by using moving average. What I thought is first print the Hamiltonian matrix , then moving average the on-site energy elements , then replace the old matrix with the new one for calculating conductance , but I have no idea how to print the Hamiltonian matrix and re place the matrix or there are better ways to simulating smooth disorder. Could you please help me? Thanks a lot for reading my questions! ----------------------------------------------------------------------------------------------------------------------------------------------------------------------- def makeSystem(W, L): #L = 99.5 # the geomertry of scattering matrix def rectangle(pos): x, y = pos return x > 0 and x < W and y > 0 and y < L def disorder(site, params): (x, y) = site.pos if(y > L/2): y = L - y e = np.random.normal(0, 5 * params.U0 / 3 * np.exp(-y/L*20) + params.U0 / 3 / 2) #　params.sum += np.abs(e) return e def lead0_shape(pos): x, y = pos return (0 < y < L) # modeling bilayer graphene scattering region syst = kwant.Builder() syst[graphene.shape(rectangle, (0, 0))] = disorder syst[[kwant.builder.HoppingKind(*hopping) for hopping in hoppings]] = t ----------------------------------------------------------------------------------------------------------------------------------------------------------------------- Best, JC Lee

2 1

Realistic values of hopping parameters
by Yu Li 18 Oct '23

18 Oct '23

Dear all, Now I’m studying some transport property based on multilayered system, with nonmagnetic layer/ferromagnetic layer (NM/FM) stack. May I ask when creating a tight binding system, and setting hoppings by the following function: syst[(lat(1, 0), lat(1, 1))] = t, how to associate the hopping with a realistic system? Such as hoppings between FM and FM atoms, or between FM and NM atoms? I found in many literatures people just simply put t=1, but I assume the value should depend on the type of atoms. My another question is, is it possible to define more than one type of hopping between two sites? For the tight-binding approximation of p electrons, there are two types of hopping integrals: Vppσ, and Vppπ, so I’m wondering if it’s possible to simulate the effect of both hoppings? Thanks a lot for reading my questions! Cheers, Yu Li

4 3

About kwant.greens_function
by Gabriel Garcia 17 Oct '23

17 Oct '23

Hi devs, I have been studying Kwant, specifically, Green’s functions. I am trying to obtain the electron density from the definition of the correlation function. The code follows below, ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- data3 = [] energies2 = [] Es = np.linspace(0, 30, 100) for ie in Es: E = ie * 0.01 G = kwant.greens_function(fsyst, E) # Funcoes de Green retardada indo da lead0 para lead1 G_r = G.submatrix(1,0) # Funcao de Green avancada G_a = conj((G_r).T) # Self-energy da lead 0 SigmaL_r = lead_0.selfenergy(E) # Retardada SigmaL_a = conj((SigmaL_r).T) # Avancada # Self-energy da lead 1 SigmaR_r = lead_1.selfenergy(E) # Retardada SigmaR_a = conj((SigmaR_r).T) # Avancada # Matriz de Alargamento Gamma_L = 1j*(SigmaL_r-SigmaL_a) # referente a lead_0 Gamma_R = 1j*(SigmaR_r-SigmaR_a) # referente a lead_1 # Funcao de distribuicao de Fermi-Dirac em T=0 f_L = np.heaviside(mu_L - E, 1) f_R = np.heaviside(mu_R - E, 1) # Funcao inscattering Sigma_in = (f_L)*(Gamma_L) + (f_R)*(Gamma_R) # Funcao de correlacao G_n = np.dot(np.dot(G_r, Sigma_in), G_a) data3.append(imag(np.trace(G_n))) energies2.append(E) plt.figure() plt.plot(energies2, data3) plt.xlabel("energy [eV]") plt.ylabel("electron density") plt.show() ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- From this definition, is it possible to obtain this electron density as a function of the sites position? How can I do that? Best, Gabriel

2 5