Graphene Sparse vs Dense - Energy calculation values dependent on graphene length
This is related to my other post, but as I see them as different (maybe not?) problems, I will post a second thread. The situation is, again, a graphene strip with periodic boundary conditions in one direction and open boundaries in the other. Using the sparse solver from linalg, I have solved for energies and gotten reasonable results for the energies, except for the case when the length (along the axis of the open boundary condition) is metallic. Attached is a code that shows it for length = 17, which is a metallic length for graphene (has energies at zero), but it does not produce messy energy calculation for when it is not a metallic length, i.e. something like length = 16. """ Graphene wire with periodic boundary conditions in the vertical direction. """ import kwant from math import pi, sqrt, tanh, cos, ceil, floor, atan, acos, asin from cmath import exp import numpy as np import scipy import scipy.linalg as lina sin_30, cos_30, tan_30 = (1 / 2, sqrt(3) / 2, 1 / sqrt(3)) def create_closed_system(length, width, lattice_spacing, onsite_potential, hopping_parameter, boundary_hopping): padding = 0.5*lattice_spacing*tan_30 def calc_total_length(length): total_length = length N = total_length//lattice_spacing # Number of times a graphene hexagon fits in horizontially fully new_length = N*lattice_spacing + lattice_spacing*0.5 diff = total_length - new_length if diff != 0: length = length - diff total_length = new_length return total_length def calc_width(width,lattice_spacing, padding): stacking_width = lattice_spacing*((tan_30/2)+(1/(2*cos_30))) N = width//stacking_width if N % 2 == 0.0: # Making sure that N is odd. N = N-1 new_width = N*stacking_width + padding width = new_width return width, int(N) def rectangle(pos): x,y = pos if (0 < x <= total_length) and (-padding <= y <= width -padding): return True return False def lead_shape(pos): x, y = pos return 0 - padding <= y <= width def tag_site_calc(x): return int(-1*(x*0.5+0.5)) #Initation of geometrical limits of the lattice of the system total_length = calc_total_length(length) width, N = calc_width(width, lattice_spacing, padding) # The definition of the potential over the entire system def potential_e(site,pot): return pot ### Definig the lattices ### graphene_e = kwant.lattice.honeycomb(a=lattice_spacing,name='e') a, b = graphene_e.sublattices sys = kwant.Builder() # The following functions are required for input in the def onsite_shift_e(site, pot): return potential_e(site,pot) sys[graphene_e.shape(rectangle, (0.5*lattice_spacing, 0))] = onsite_shift_e sys[graphene_e.neighbors()] = -hopping_parameter ### Boundary conditions for scattering region ### for site in sys.sites(): (x,y) = site.tag if float(site.pos[1]) < 0: if str(site.family) == "<Monatomic lattice e1>": sys[b(x,y),a(int(x+tag_site_calc(N)),N)] = -boundary_hopping kwant.plot(sys) return sys def eigen_vectors_and_values(sys,sparse_dense,k): #sparse = 0, dense = 1 if sparse_dense == 0: ham_mat = sys.hamiltonian_submatrix(params=dict(pot=0.0), sparse=True) eigen_val, eigen_vec = scipy.sparse.linalg.eigsh(ham_mat.tocsc(), k=k, sigma=0, return_eigenvectors=True) if sparse_dense == 1: ham_mat = sys.hamiltonian_submatrix(params=dict(pot=0.0), sparse=False) eigen_val, eigen_vec = lina.eigh(ham_mat) #sort the ee and ev in ascending order idx = eigen_val.argsort() eigen_val= eigen_val[idx] eigen_vec = eigen_vec[:,idx] if sparse_dense == 1: eigen_val = eigen_val[int(len(eigen_val)*0.5-k*0.5):] # Remove first part eigen_val = eigen_val[:k] # Take first k-values eigen_vec = eigen_vec[:,int(len(eigen_val)*0.5-k*0.5):] eigen_vec = eigen_vec[:,:k] return eigen_vec, eigen_val def main(): sys = create_closed_system(length = 17.0, width = 20.0, lattice_spacing = 1.0, onsite_potential = 0.0, hopping_parameter = 1.0, boundary_hopping = 1.0) sys = sys.finalized() #sparse = 0, dense = 1 eigen_vec, eigen_val = eigen_vectors_and_values(sys,sparse_dense=0,k=50) eigen_vec2, eigen_val2 = eigen_vectors_and_values(sys,sparse_dense=1,k=50) print("Eigenenergy difference (between sparse and dense): ") for i_ in range(len(eigen_val)): print(eigen_val[i_] - eigen_val2[i_] ) return if __name__ == "__main__": main()
participants (2)
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Abbout Adel
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Henry Axt