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()
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 ----- Mail original ----- De: "Sergio Castillo Robles" <sergio.castillo@uabc.edu.mx> 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()
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" <sergio.castillo@uabc.edu.mx> *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()
Hi everyone, thank you for your answers and suggestions, First of all i would like to say that im not experienced using Kwant, i read the examples provided in the web site and i think i understand a little more about the syntax used in kwant (Thank you Alexandre an Joseph). But im still confused about some definitions 1) Alexandre, thank you for you suggestions, but honestly Im not pretty sure how to define a "superatom" that reproduces the structure im working on. How should i define the sites for each atom in the lattice? 2) Joseph, thank you for the detailed explanation, i rewrote that part of the code following your instructions and i think is better now, but i cant figure a way to describe the interactions that occur "inside" the same atom, for example, Re has 6 orbitals, how can i express the hoppings that have place in the same site? Thank you for your time P.D. The code so far is giving me an error in the leads apparently /home/sergio/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:197: RuntimeWarning: When finalizing lead 0: Infinite system with disconnected cells. /home/sergio/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:197: RuntimeWarning: When finalizing lead 1: Infinite system with disconnected cells. ---------------------------------------------------------------------------ValueError Traceback (most recent call last)<ipython-input-3-882bfab14ea6> in <module>() 200 201 if __name__ == '__main__':--> 202 main() <ipython-input-3-882bfab14ea6> in main() 196 site_color=family_colors) 197 syst = syst.finalized()--> 198 plot_conductance(syst, energies=[0.01 * i - 0.3 for i in range(100)]) 199 200 <ipython-input-3-882bfab14ea6> in plot_conductance(syst, energies) 174 data = [] 175 for energy in energies:--> 176 smatrix = kwant.smatrix(syst, energy) 177 data.append(smatrix.transmission(1, 0)) 178 pyplot.figure() ~/anaconda3/lib/python3.6/site-packages/kwant/solvers/common.py in smatrix(self, sys, energy, args, out_leads, in_leads, check_hermiticity, params) 373 374 kept_vars = np.concatenate([coords for i, coords in--> 375 enumerate(linsys.indices) if i in 376 out_leads]) 377 ValueError: need at least one array to concatenate Here is the code so far: 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)] lat = kwant.lattice.general(prim_vecs = VecPrim, basis = base, name = ['C', 'Re', 'N'], norbs = [3, 6, 3]) C, Re, N = lat.sublattices C_C_ons = numpy.array ([[-1.888842, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1.784936, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 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]]) C_C_hop = numpy.array ([[0, -0.014064-0.000409j, 0.026908+0.003422j, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-0.014064+0.000409j, 0, -0.031384+0.021565j, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0.026908-0.003422j, -0.031384-0.021565j, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) Re_Re_ons = 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, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0.245358, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1.338059, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1.325337, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0.362102, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -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]]) Re_Re_hop = 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, -0.005189-0.047376j, 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, 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, 0, -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, 0, 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, -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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) N_N_ons = 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, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3.401815, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.637207]]) N_N_hop = 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, 0, 0.001839+0.001631j, -0.117366+0.00498j], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0.001839-0.001631j, 0, 0.023339+0.009067j], [0, 0, 0, 0, 0, 0, 0, 0, 0, -0.117366-0.00498j, 0.023339-0.009067j, 0]]) C_Re_hop = numpy.array([[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]]) C_N_hop = numpy.array ([[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]]) Re_N_hop = 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, 0.184152+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]]) 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[C(0, 0, 0)]= C_C_ons syst[Re(0, 0, 0)]= Re_Re_ons syst[N(0, 0, 0)]= N_N_ons syst[C(0, 0, 0), Re(0, 0, 0)] = C_Re_hop syst[C(0, 0, 0), N(0, 0, 0)] = C_N_hop syst[Re(0, 0, 0), N(0, 0, 0)] = Re_N_hop ##### syst[C(0, 0, 0), C(0, 0, 0)] = C_C_hop ##### syst[Re(0, 0, 0), Re(0, 0, 0)] = Re_Re_hop ##### syst[N(0, 0, 0), N(0, 0, 0)] = N_N_hop ##### 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 syst[C(0, 0, 0)]= C_C_ons syst[Re(0, 0, 0)]= Re_Re_ons syst[N(0, 0, 0)]= N_N_ons syst[C(0, 0, 0), Re(0, 0, 0)] = C_Re_hop syst[C(0, 0, 0), N(0, 0, 0)] = C_N_hop syst[Re(0, 0, 0), N(0, 0, 0)] = Re_N_hop #### 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 == C: return 'yellow' elif site.family == Re: 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() 2018-06-08 1:21 GMT-07:00 Joseph Weston <joseph.weston08@gmail.com>:
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" <sergio.castillo@uabc.edu.mx> <sergio.castillo@uabc.edu.mx> *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()
Hi again,
But im still confused about some definitions
1) Alexandre, thank you for you suggestions, but honestly Im not pretty sure how to define a "superatom" that reproduces the structure im working on. How should i define the sites for each atom in the lattice?
He means that instead of defining a lattice with 3 sites per unit cell with 3, 6, and 3 orbitals respectively, you should define a lattice with a *single* site per unit cell, which has 3 + 6 + 3 = 12 orbitals. Of course, plotting this thing is not so useful, and because you essentially lose the information about where the "real" atoms are in space (because you only have a single site representing 3 physical atoms) it becomes more complicated to do things like define the action of a position-dependent potential. I would recommend keeping the physical atoms as separate sites (as you are doing now).
2) Joseph, thank you for the detailed explanation, i rewrote that part of the code following your instructions and i think is better now, but i cant figure a way to describe the interactions that occur "inside" the same atom, for example, Re has 6 orbitals, how can i express the hoppings that have place in the same site?
If a site on one of your lattices represents a Re atom with 6 orbitals, then what Kwant calls the "onsite" Hamiltonian terms must be 6x6 matrices: the diagonal contains the actual onsite values, and the off-diagonal terms are hoppings between orbitals of the *same* Re atom (this is why Kwant still calls this an "onsite"). Similarly, hoppings between *different* Re atoms must be 6x6 matrices, and hoppings between Re and C (or N) atoms must be 6x3 matrices, to match the number of orbitals on each end of the hopping. In your code example there is a section where you set the onsite and hoppings for the 3 atoms inside the unit cell. This is nearly correct, except that you have 12x12 matrices for each of the onsite/hopping values, when you really need matrices with shapes that match the number of orbitals on the sites. On the other hand, you then use 'lat.shape' to assign an onsite value of '4' to all sites, so I think that you are confused about what exactly you are doing. You will have to use 'C.shape', 'Re.shape', and 'N.shape' (C, Re and N being your sublattices) to assign the onsite matrices of the appropriate shape to sites from each of the sublattices in turn, because sites from each sublattice have different numbers of orbitals.
P.D. The code so far is giving me an error in the leads apparently
/home/sergio/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:197: RuntimeWarning: When finalizing lead 0: Infinite system with disconnected cells. /home/sergio/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:197: RuntimeWarning: When finalizing lead 1: Infinite system with disconnected cells.
As the warning illustrates, the unit cells of your leads are not connected by hoppings, so all elements of the scattering matrix will be 0. Looking at your code I see that you indeed don't add any hoppings to your leads; you only populate a bunch of sites using 'lat.shape'. Happy Kwanting, Joe
participants (3)
-
alexandre.bernard1＠u-psud.fr -
Joseph Weston -
Sergio Castillo Robles