Re: [Kwant] Defining orbitals in a 3D structure with 3 basis atoms.

Hi all, Sergio, if you want to create a Polyatomic lattice you have to pass all the basis vectors and orbital numbers in a single call to 'kwant.lattice.general', otherwise there's no way Kwant can know that you want the 3 sublattices to be considered as a single Polyatomic lattice!     prim_vecs = [...]  # Bravais lattice vectors     basis [ [...], [...], [...]]  # position vectors of the 3 basis atoms     norbs = [3, 6, 3]     lat = general(prim_vecs, basis=basis, norbs=norbs)     a, b, c = lat.sublattices     ...     syst[a(0, 0, 0), b(0, 0, 0)] =  [...] # a-b hopping in same unit cell     syst[a(0, 0, 0), c(1, 0, 0)] =  [...] # a-c hopping in between unit cells This is covered briefly in the tutorial [1]; do you think we can improved that section of the tutorial in some way? Happy Kwanting, Joe [1]: https://kwant-project.org/doc/1/tutorial/graphene On 06/07/2018 12:05 PM, alexandre.bernard1@u-psud.fr wrote:

Hello,

First of all, I am new to kwant, so I hope I will give you relevant insights.

It seems to me that:

1) There are some mistakes in the syntax you are using, so you should check again the examples available in the doc : https://kwant-project.org/doc/1/

2) Since you consider different numbers of orbitals for your atoms, I think you should use only one "superatom" with 12 orbitals per unit cell. Then Kwant allows to define 12x12 matrices both for the on-site terms (your matrix elements within the superatom) and for the hopping terms (your matrix elements between superatoms).

I hope this is a bit helpfull.

Best regards,

Alexandre BERNARD

------------------------------------------------------------------------ *De: *"Sergio Castillo Robles" *À: *kwant-discuss@kwant-project.org *Envoyé: *Mercredi 6 Juin 2018 03:54:21 *Objet: *[Kwant] Defining orbitals in a 3D structure with 3 basis atoms.

Hello everyone, i would appreciate any suggestion you could give me to solve this.

Well, im trying to create a structure with 3 basis atoms in the unit cell, each atom has a different number of orbitals a=3, b=6 and c=3. I have tried with polyatomic module and creating one lattice for each atom with no success

The thing is that i cant figure it out how to create a lattice with different orbitals in each site. I have the on-site and hopping energies matrix so i need to be able to introduce this values.

Im pretty new using kwant so any advice is appreciated.

Here is the code i've working on (ignore the matrix elements for the moment):

import kwant import tinyarray import numpy from matplotlib import pyplot

VecPrim = [(3.176, 0, 0), (1.588, 2.7504, 0), (0, 0, 17.49)] base =  [(0, 0, 0), (1.588, 0.9168, 0.8745), (0, 0, 1.749)]

           ### This is the part that i cant get it right, i have tried kwant.lattice.polyatomic            ### and defining 3 lattices one for each atom, but no success     a = kwant.lattice.general(prim_vecs = VecPrim, basis = (0, 0, 0)) Cpx, Cpy, Cpz, = a.sublattices b = kwant.lattice.general(prim_vecs = VecPrim, basis = (1.588, 0.9168, 0.8745)) xy, xz, yz, x2y2, z2, s = b.sublattices c = kwant.lattice.general(prim_vecs = VecPrim, basis = (0, 0, 1.749)) Npx, Npy, Npz = c.sublattices

            ### Ignore from here ###

def make_cuboid(t=1.0, a=15, b=10, c=5):     def cuboid_shape(pos):         x, y, z = pos         return 0 <= x < a and 0 <= y < b and 0 <= z < c      syst = kwant.Builder()     syst[lat.shape(cuboid_shape, (0, 0, 0))] = 4 * t         syst[lat(0, 0, 0)] = numpy.array([[-1.888842, -0.014064-0.000409j, 0.026908+0.003422j, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                      [-0.014064+0.000409j, -1.784936, -0.031384+0.021565j, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                      [0.026908-0.003422j, -0.031384-0.021565j, 0.710443, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                      [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                      [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                      [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                      [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                      [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                      [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                      [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                      [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])         syst[lat(0, 1, 0)] = numpy.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 7.168134, -0.005189-0.047376j, 0.001352+0.000103j, -0.001189-0.00095j, -0.048166-0.007663j, 0.429882+0.00052j, 0, 0, 0],                                          [0, 0, 0, -0.005189+0.047376j, 0.245358, 0.113162-0.072937j, 0.660849-0.06348j, -0.017571+0.035587j, 0.020961-0.017679j, 0, 0, 0],                                          [0, 0, 0, 0.001352-0.000103j, 0.113162+0.072937j, 1.338059, -0.003126-0.016285j, -0.624702-0.065652j, 0.002353+0.001639j, 0, 0, 0],                                          [0, 0, 0, -0.001189+0.00095j, 0.660849+0.06348j, -0.003126+0.016285j, 1.325337, 0.110694+0.01548j, 0.009041+0.004483j, 0, 0, 0],                                          [0, 0, 0, -0.048166+0.007663j, -0.017571-0.035587j, -0.624702+0.065652j, 0.110694-0.01548j, 0.362102, -0.030934+0.002401j, 0, 0, 0],                                          [0, 0, 0, 0.429882-0.00052j, 0.020961+0.017679j, 0.002353-0.001639j, 0.009041-0.004483j, -0.030934-0.002401j, -0.650839, 0, 0, 0]                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])

    syst[lat(0, 0, 1)] = numpy.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, -3.398186, 0.001839+0.001631j, -0.117366+0.00498j],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0.001839-0.001631j, -3.401815, 0.023339+0.009067j],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, -0.117366-0.00498j, 0.023339-0.009067j, -0.637207]])         syst[lat(0, 0, 1), lat (0, 0, 0)] = ([[0, 0, 0, 0, 0, 0, 0, 0, 0, -1.852931+0.147524j, 0.274586-0.034451j, -0.015051-0.001677j],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, -0.274338-0.015064j, -1.796449-0.055331j, -0.034396+0.019407j],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, -0.103127+0.001438j, 0.004816-0.00237j, 3.410475+0.001248j],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [-1.852931-0.147524j, -0.274338+0.015064j, -0.103127-0.001438j, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0.274586+0.034451j, -1.796449+0.055331j, 0.004816+0.00237j, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [-0.015051+0.001677j, -0.034396-0.019407j, 3.410475-0.001248j, 0, 0, 0, 0, 0, 0, 0, 0, 0]])         syst[lat(0, 1, 0), lat(0, 0, 0)] = ([[0, 0, 0, 0.003644+0.00088j, -0.305706-0.050514j, 0.638425-0.083597j, -1.105645+0.086829j, 1.463462-0.012994j, -0.01338-0.00264j, 0, 0, 0],                                          [0, 0, 0, -0.046131+0.04229j, -1.963829-0.280977j, -1.171301-0.088146j, -1.112788-0.056971j, 0.174769+0.106872j, -0.058159-0.007987j, 0, 0, 0],                                          [0, 0, 0, 0.23188+0.001924j, -0.597505-0.078772j, -0.146976-0.012943j, -0.210584+0.002248j, 0.177022+0.031485j, 0.953363-0.001855j, 0, 0, 0],                                          [0.003644-0.00088j, -0.046131-0.04229j, 0.23188-0.001924j, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [-0.305706+0.050514j, -1.963829+0.280977j, -0.597505+0.078772j, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0.638425+0.083597j, -1.171301+0.088146j, -0.146976+0.012943j, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [-1.105645-0.086829j, -1.112788+0.056971j, -0.210584-0.002248j, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [1.463462+0.012994j, 0.174769-0.106872j, 0.177022-0.031485j, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [-0.01338+0.00264j, -0.058159+0.007987j, 0.953363+0.001855j, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])         syst[lat(0, 0, 1), lat(0, 1, 0)] = ([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0.184152+0.002778j, 0.321743-0.010571j, 0.183538-0.00067j],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0.275145+0.007691j, -0.54144+0.012815j, 0.045847+0.015379j],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0.47922+0.015775j, 1.256012+0.007326j, -0.523174+0.00585j],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 1.255561-0.002255j, 1.903063+0.010647j, -0.876392+0.010246j],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 1.282837-0.091022j, -0.54898+0.001161j, 0.057341-0.004095j],                                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0.02765-0.001793j, -0.002902-0.001866j, -0.746426-0.000748j],                                          [0, 0, 0, 0.184152-0.002778j, 0.275145-0.007691j, 0.47922-0.015775j, 1.255561+0.002255j, 1.282837+0.091022j, 0.02765+0.001793j, 0, 0, 0],                                          [0, 0, 0, 0.321743+0.010571j, -0.54144-0.012815j, 1.256012-0.007326j, 1.903063-0.010647j, -0.54898-0.001161j,-0.002902+0.001866j, 0, 0, 0],                                          [0, 0, 0, 0.183538+0.00067j, 0.045847-0.015379j, -0.523174-0.00585j, -0.876392-0.010246j, 0.057341+0.004095j,-0.746426+0.000748j, 0, 0, 0]])                                                          ### 'Till here #####         syst[[kwant.builder.HoppingKind(*hopping) for hopping in hoppings]] = -6     lead = kwant.Builder(kwant.TranslationalSymmetry((-3.176, 0, 0)))     def lead_shape(pos):         return 0 <= pos[1] < b and 0 <= pos[2] < c     lead[lat.shape(lead_shape, (0, 0, 0))] = 4 * t     lead[[kwant.builder.HoppingKind(*hopping) for hopping in hoppings]] = -6     syst.attach_lead(lead)     syst.attach_lead(lead.reversed())     return syst

def plot_conductance(syst, energies):     data = []     for energy in energies:         smatrix = kwant.smatrix(syst, energy)         data.append(smatrix.transmission(1, 0))     pyplot.figure()     pyplot.plot(energies, data)     pyplot.xlabel("energy [t]")     pyplot.ylabel("conductance [e^2/h]")     pyplot.show()     def main():        syst = make_cuboid()     kwant.plot(syst)     syst = make_cuboid(a=100, b=28, c=4)        def family_colors(site):          if site.family == d:             return 'yellow'         elif site.family == e:             return 'gray'         else:             return 'blue'     kwant.plot(syst, site_size=0.25, site_lw=0.025, hop_lw=0.05,                site_color=family_colors)     syst = syst.finalized()     plot_conductance(syst, energies=[0.01 * i - 0.3 for i in range(100)])

if __name__ == '__main__':     main()