While constructing series of hopping automatically using the hopping_generator modifier I noted that the model created in this way has troubles in dealing with periodic boundary conditions.
I attach a simple example for a basic graphene system
from math import pi, sqrt
import numpy as np
from scipy.spatial import cKDTree
import matplotlib.pyplot as plt
import pybinding as pb
from pybinding.repository.graphene import a, a_cc, t
def monolayer_graphene():
lat = pb.Lattice([a/2, a*np.sqrt(3)/2], [-a/2, a*np.sqrt(3)/2])
lat.add_sublattices(("A", [0, 0]),
("B", [0, a_cc]))
return lat
@pb.hopping_generator("intralayer", energy=t)
def intralayer_generator(x, y, z):
positions = np.stack([x, y, z], axis=1)
layer = (z == 0)
d_min = a_cc * 0.98
d_max = a_cc * 1.1
kdtree1 = cKDTree(positions[layer])
kdtree2 = cKDTree(positions[layer])
coo = kdtree1.sparse_distance_matrix(kdtree2, d_max, output_type='coo_matrix')
idx = coo.data > d_min
abs_idx = np.flatnonzero(layer)
row, col = abs_idx[coo.row[idx]], abs_idx[coo.col[idx]]
return row, col
lattice = monolayer_graphene()
model = pb.Model(lattice, intralayer_generator, pb.translational_symmetry())
solver = pb.solver.lapack(model)
Gamma = [0, 0]
K1 = [-4*pi / (3*sqrt(3)*a_cc), 0]
M = [0, 2*pi / (3*a_cc)]
K2 = [2*pi / (3*sqrt(3)*a_cc), 2*pi / (3*a_cc)]
bands = solver.calc_bands(K1, Gamma, M, K2)
bands.plot(point_labels=['K', r'$\Gamma$', 'M', 'K'])The bands are computed incorrectly (they're simply confused with the starting Hamiltonian eigenvalues).
Is there a way to enforce translation symmetry for a lattice with hoppings created by a generator?
While constructing series of hopping automatically using the
hopping_generatormodifier I noted that the model created in this way has troubles in dealing with periodic boundary conditions.I attach a simple example for a basic graphene system
The bands are computed incorrectly (they're simply confused with the starting Hamiltonian eigenvalues).
Is there a way to enforce translation symmetry for a lattice with hoppings created by a generator?