Mailman 3 October 2021 - Kwant-discuss

Defining uniaxial strain in specified region of graphene
by shrushti.tapar07＠gmail.com 20 Jan '23

20 Jan '23

I want to create the graphene strained superlattice-like structure, having uniaxial strain defined at the specified region. Please, someone can suggest to me how to define the strained region and interface between unstrained and strained graphene regions. Thanks in Advance Shrushti

4 6

Gate-defined Nanowire Quantum Dot
by Jonathan Fields 15 Sep '22

15 Sep '22

Dear Reader, I am new to KWANT and trying to figure out if it is suitable for calculating transport properties of gate-defined quantum dots made out of nanowires, along the lines of the structure used in https://arxiv.org/abs/cond-mat/0609463. Now, I understand that the mailing list is not a place to ask people to do my work for me, and my question is also not for someone to do this. What I am looking for is some insights into if this is possible (and not all that difficult) with the package. At first sight (and going through the tutorials as well as the APS March Meeting material) this does not seem straightforward; what I struggle with is how to define this type of dot in KWANT. Now, one way would of course be to built the entire 3D geometry of the system, but this will be computationally expensive, and probably also rather tricky to do in terms of defining everything, from the hexagonal wire itself to all of the gates and oxide layers and such. Some abstraction would be preferred, perhaps even reducing the dimensionality and making a 2D system, such as often done in the tutorial. Is this a good idea? My problem is that if one does this, then I run into the problem of how to model the 'half wrap-around' type gates typically used in these devices. In the transport through barrier section of the APS March Meeting material there is a section on how to model realistic potentials, but this would not work all that well for these wrap around type gates. On the other hand, in a way they are perhaps not so different from the QPC in that section. One could model the three gates as something like https://i.imgur.com/WZC983c.png as they do essentially form channels in the wire. Apart from if this sacrifices too much of the nanowire nature in favor of a 2DEG system, I do suppose such a system should in principle be able to be treated as a quantum dot. I haven't been able to confirm this as I am not yet sure how one can apply a source-drain voltage in KWANT; I first thought that this would probably be related to the energy of the modes, but then again I have not been able to produce Coulomb diamonds in this way. The question is getting rather lenghty, and also a bit unclear at this point. Perhaps I should finish up by stating it in a concise form; would you think that it is possible to simulate the transport of such a gate defined nanowire quantum dot device with KWANT, and if so, is the approach I am suggesting above a viable one, or would you go about it very differently? Kind regards Jonathan <http://aka.ms/weboutlook>

4 4

current-voltage diagram
by loojoo026＠gmail.com 08 Apr '22

08 Apr '22

dear all I have done my project using Kwant and I have drawn a conductance-energy diagram for the system. The question I have is how can I get the current-voltage diagram? thanks Leo

4 4

How the spin is positioned in the Smatrix?
by Qingtian Zhang 06 Mar '22

06 Mar '22

Dear all, I am trying square lattice with spin-orbit coupling and Zeeman splititng just like the example of Tutorial 2.3.1. Now I want to get the spin-dependent conductance：Guu,Gud,Gdu,and Gdd, where "u" indicates up spin, d indicates down spin. We can have the scattering matrix through Smatrix=kwant.smatrix(sys, energy), but how the spin is positioned in the scattering matrix? I have checked some simple cases, it seems the Smatrix is organized like this: | r t | S= | t' r' | but how the spin is included? Thanks in advance. Qingtiian Zhang The code is: import kwant from matplotlib import pyplot from numpy import matrix import tinyarray sigma_0 = tinyarray.array([[1, 0], [0, 1]]) sigma_x = tinyarray.array([[0, 1], [1, 0]]) sigma_y = tinyarray.array([[0, -1j], [1j, 0]]) sigma_z = tinyarray.array([[1, 0], [0, -1]]) sys=kwant.Builder() lat=kwant.lattice.square() a=1 t=1.0 alpha=0.5 e_z=0.08 W=2 L=2 sys[(lat(x, y) for x in range(L) for y in range(W))] = \ 4 * t * sigma_0 + e_z * sigma_z # hoppings in x-direction sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ -t * sigma_0 - 1j * alpha * sigma_y # hoppings in y-directions sys[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ -t * sigma_0 + 1j * alpha * sigma_x #### Define the left lead. #### lead = kwant.Builder(kwant.TranslationalSymmetry((-a, 0))) lead[(lat(0, j) for j in xrange(W))] = 4 * t * sigma_0 + e_z * sigma_z # hoppings in x-direction lead[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ -t * sigma_0 - 1j * alpha * sigma_y # hoppings in y-directions lead[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ -t * sigma_0 + 1j * alpha * sigma_x #### Attach the leads and return the finalized system. #### sys.attach_lead(lead) sys.attach_lead(lead.reversed()) kwant.plot(sys) sys=sys.finalized() print "Hamiltonian=" print sys.hamiltonian_submatrix() Smatrix=kwant.smatrix(sys, energy=3.) print "The scattering matrix=" print matrix.round((Smatrix.data),2) print "T=",(Smatrix.transmission(1, 0))

3 3

Spin polarized transport calculation
by L.M J 06 Mar '22

06 Mar '22

Dear Kwant users and developers I have two questions related to the spin calculation using kwant. 1. I'm wondering if we can do spin-polarized transport in kwant? For example, can we can get the separate Conductance Vs Energy diagram for spin up and spin down terms. I'm thinking one way of doing this is to set up the Rashba Hamiltonian as a whole. And then manually extract the spin up and spin down hamiltonian and do the transport calculation separately. But this will eliminate some extra terms that I don't know whether this is correct anymore. Any suggestions? 2. How can we set up the spin polarization for a particular site? For example, in some of the topological insulator, can we set up spin polarization on the edge as up and the other side of the edge as down, and then do the transport? Or this question is completely wrong? Thanks for advance. Sincerely, Liming

3 3

Parallel Computation
by diegobruno244＠gmail.com 03 Mar '22

03 Mar '22

Kwant Community, I would like to know if it is possible to do parallel computing using kwant? To do parallel computing can be used numba, CUDA, multiprocessing, Parallel. This work for kwant? And if possible are there any examples?

2 2

Graphene Conductor-Superconductor Conductance above Gap
by Henry Axt 21 Feb '22

21 Feb '22

Hello, I set up a graphene lattice with periodic boundary conditions that is connected to a superconductor (simulated with an electron and hole lattice). When observing the transmission between the electron and hole lattice, I see a small amount conductance above the superconducting gap. I do not see this with something like a square lattice. What could explain this?

2 1

Creating virtual self-energy leads to extract Green's function between arbitrary sites:
by Sayandip Dhara 10 Nov '21

10 Nov '21

Hello, I am trying to extract Green's function between two arbitrary sites in a system. I have noticed from one of the previous threads that one way to do it is to attach virtual leads with zero self-energy on those specific sites. However, I am having trouble with the suggested function. It is telling me that whichever site I want to attach is not in the scattering region. The following is the code: import kwant from types import SimpleNamespace from copy import copy import tinyarray import numpy as np import csv import ipywidgets #import holoviews as hv #hv.extension('bokeh') from scipy import sparse from matplotlib import pyplot from scipy.optimize import minimize sigma_x = tinyarray.array([[0, 1], [1, 0]]) sigma_y = tinyarray.array([[0, -1j], [1j, 0]]) sigma_z = tinyarray.array([[1, 0], [0, -1]]) sigma_0 = tinyarray.array([[1, 0], [0, 1]]) tau_x = tinyarray.array([[0, 1], [1, 0]]) tau_y = tinyarray.array([[0, -1j], [1j, 0]]) tau_z = tinyarray.array([[1, 0], [0, -1]]) tau_0 = tinyarray.array([[1, 0], [0, 1]]) # mu=0.5, # t=-1.,delta=0.5,V_N=1.25, phi=0, L=3 def make_system_ex3(L=10): lat = kwant.lattice.chain(norbs=2) syst = kwant.Builder() #### Define the scattering region. #### def onsite_sc(site,t,mu,delta): return (2.*t-mu )*tau_z + delta*tau_x def onsite_N(site,t,mu,V_N): return (2.*t-mu + V_N)*tau_z syst[(lat(x) for x in range(1, L))] = onsite_sc #superconducting onsite hamiltonian syst[lat(L)] = onsite_N #normal onsite hamiltonian syst[(lat(x) for x in range(L+1,2*L+1))] = onsite_sc #superconducting onsite hamiltonian def hop(site1,site2,t,phi): return -t*np.matmul(np.exp(1j*phi*tau_z),tau_z) syst[(lat(L-1), lat(L))] = hop for i in range(1,L-1): syst[(lat(i), lat(i+1))] = -t*tau_z for i in range(L,2*L): syst[(lat(i), lat(i+1))] = -t*tau_z #### Define the leads. #### sym_left = kwant.TranslationalSymmetry([-1]) lead0 = kwant.Builder(sym_left) lead0[(lat(0))] = (2.*t-mu)*tau_z + delta*tau_x lead0[lat.neighbors()] = -t*tau_z sym_right = kwant.TranslationalSymmetry([1]) lead1 = kwant.Builder(sym_right) lead1[(lat(2*L+1))] = (2.*t-mu)*tau_z + delta*tau_x lead1[lat.neighbors()] = -t*tau_z # #### Attach the leads and return the system. #### syst.attach_lead(lead0) syst.attach_lead(lead1) return syst,lat ---------------------------------------------------------------------------------------------------------------------------- mu=1 t=1.0 delta=0.5 V_N=1 phi=0 L=10 par = dict(t=t,mu=mu,delta=delta,phi=phi,V_N=V_N) # syst,lat = make_system_ex3(L=10) def mount_vlead(sys, vlead_interface, norb): dim = norb zero_array = np.zeros((dim, dim), dtype=float) def selfenergy_func(energy, args=()): return zero_array vlead = kwant.builder.SelfEnergyLead(selfenergy_func, vlead_interface,()) sys.leads.append(vlead) mount_vlead(syst,[L-1], 2) # number of orbitals =4. Here we mount lead number 2 mount_vlead(syst,[L], 2) # number of orbitals =4. Here we mount lead number 3 syst =syst.finalized() G12=kwant.greens_function(syst, energy=-1.8*1j, in_leads=[L-1],out_leads=[L],\ check_hermiticity=False,params=par).data G21=kwant.greens_function(syst, energy=-1.8*1j, in_leads=[L],out_leads=[L-1],\ check_hermiticity=False,params=par).data ---------------------------------------------------------------------------------------------------------------------------------- The error message I am getting is " ValueError: Lead 2 is attached to a site that does not belong to the scattering region: 9" It would be great if you can suggest to me where I am going wrong. Thanks, Sayandip

2 3

Interpolation is slow
by Mani Chandra 30 Oct '21

30 Oct '21

Hello, We're dealing with a 5000 x 5000 site system, and the time to interpolate the densities and currents using kwant.plotter.interpolate_density and kwant.plotter.interpolate_current are by far the rate limiting steps in the calculation: System assembly : 15 mins Computing scattering states: 3 hrs Interpolating density and current (for use in plotting): 6 hrs! Is there any way to speed up the interpolation routines? I see that the present implementation in plotter.py involves a for loop (in python) over each site/hopping. Perhaps a vectorized implementation may help? Thanks, Mani

2 8

Conductivity calculation using the kpm method for a spinful system
by mondal18＠iitg.ac.in 29 Oct '21

29 Oct '21

Dear developer, I was trying to calculate the conductivity of honeycomb lattice, where I have included the Haldane term along with the spin-orbit Rashba term (Kane-Mele model). I was following the tutorial provided in chapter 2.9 (https://kwant-project.org/doc/1/tutorial/kpm). The code shows an error when I include the spin in the system. My code is attached below, from matplotlib import pyplot as plt import tinyarray as tn import kwant import numpy as np t = 1 t2 = 0.3 sgm_0=tn.array([[1,0],[0,1]]) sgm_x=tn.array([[0,1],[1,0]]) sgm_y=tn.array([[0,-1j],[1j,0]]) sgm_z=tn.array([[1,0],[0,-1]]) def make_syst_topo(l=20, a=1, m=0): alpha = 0.01 syst = kwant.Builder() lat = kwant.lattice.honeycomb(a, norbs=1, name=['a', 'b']) a = lat.a b = lat.b def rectangle(pos): x, y = pos return - l<= x <= +l and - l<= y <= +l def rashba(site_i,site_j): d_ij = site_i.pos - site_j.pos return -1j*alpha*(sgm_x*d_ij[1]-sgm_y*d_ij[0]) def nn_hop(site_i, site_j): return rashba(site_i, site_j) - t * sgm_0 syst[lat.shape(rectangle, (0, 0))] = 0.0*sgm_0 syst[kwant.builder.HoppingKind((0, 0), a, b)] = nn_hop syst[kwant.builder.HoppingKind((0, 1), a, b)] = nn_hop syst[kwant.builder.HoppingKind((-1, 1), a, b)] = nn_hop syst[lat.a.neighbors()] = 1j * t2 * sgm_z syst[lat.b.neighbors()] = -1j * t2*sgm_z syst.eradicate_dangling() return lat, syst.finalized() def plot_system(syst): kwant.plot(syst,site_size=0.1, hop_lw=0.01) # Plot fill density of states plus curves on the same axes. def plot_dos_and_curves(dos, labels_to_data): plt.figure(figsize=(10,8)) plt.fill_between(dos[0], dos[1], label="DoS [a.u.]", alpha=0.5, color='gray') for label, (x, y) in labels_to_data: plt.plot(x, y, label=label, linewidth=2) plt.legend(loc='upper center', framealpha=0.5, fontsize=12) plt.xlabel(r'$E/t$'); # plt.ylabel('ylabel') plt.show() plt.clf() def conductivity_example(): # construct the Haldane model lat, fsyst = make_syst_topo() # find 'A' and 'B' sites in the unit cell at the center of the disk where = lambda s: np.linalg.norm(s.pos) < 1 # component 'xx' s_factory = kwant.kpm.LocalVectors(fsyst, where) cond_xx = kwant.kpm.conductivity(fsyst, alpha='x', beta='x', mean=True, num_vectors=None, vector_factory=s_factory) # component 'xx' s_factory = kwant.kpm.LocalVectors(fsyst, where) cond_yy = kwant.kpm.conductivity(fsyst, alpha='y', beta='y', mean=True, num_vectors=None, vector_factory=s_factory) # component 'xy' s_factory = kwant.kpm.LocalVectors(fsyst, where) cond_xy = kwant.kpm.conductivity(fsyst, alpha='x', beta='y', mean=True, num_vectors=None, vector_factory=s_factory) energies_x = cond_xx.energies energies_y = cond_yy.energies cond_array_xx = np.array([cond_xx(e, temperature=0.00) for e in energies_x]) cond_array_xy = np.array([cond_xy(e, temperature=0.00) for e in energies_x]) cond_array_yy = np.array([cond_yy(e, temperature=0.00) for e in energies_y]) # area of the unit cell per site area_per_site = np.abs(np.cross(*lat.prim_vecs)) / len(lat.sublattices) cond_array_xx /= area_per_site cond_array_xy /= area_per_site cond_array_yy /= area_per_site # ldos s_factory = kwant.kpm.LocalVectors(fsyst, where) spectrum = kwant.kpm.SpectralDensity(fsyst, num_vectors=None, vector_factory=s_factory) plot_dos_and_curves( (spectrum.energies, spectrum.densities * 8), [ (r'$\sigma_{xx} / 4$', (energies_x, cond_array_xx / 4)), (r'$\sigma_{xy}$', (energies_x, cond_array_xy)), (r'$\sigma_{yy} / 4$', (energies_y, cond_array_yy / 4))] ) def main(): fsyst = make_syst_topo()[1] plot_system(fsyst) conductivity_example() if __name__ == '__main__': main() I shall look forward to your kind reply.

1 0

Kwant-discuss October 2021