def dos_heterostructure(hetero,energies=[0.0],num_rep=100,
mixing=0.7,eps=0.0001,green_guess=None,max_error=0.0001):
""" Calculates the density of states
of a heterostructure by a
green function approach, input is a heterostructure class"""
dos = [] # list with the density of states
iden = np.matrix(np.identity(len(intra),dtype=complex)) # create idntity
for energy in energies: # loop over energies
# right green function
intra = hetero.right_intra
inter = hetero.right_inter
gr = dyson(intra,inter,energy=energy,num_rep=num_rep,mixing=mixing,
eps=eps,green_guess=green_guess,max_error=max_error)
# left green function
intra = hetero.right_intra
inter = hetero.right_inter
gl = dyson(intra,inter,energy=energy,num_rep=num_rep,mixing=mixing,
eps=eps,green_guess=green_guess,max_error=max_error)
# central green function
selfl = inter.H*gl*inter # left selfenergy
selfr = inter*gr*inter.H # right selfenergy
gc = energy*iden -intra -selfl -selfr # dyson equation for the center
gc = gc.I # calculate inverse
dos.append(-gc.trace()[0,0].imag) # calculate the trace of the Green function
return dos
def dos_heterostructure(hetero,energies=[0.0],num_rep=100,
mixing=0.7,eps=0.0001,green_guess=None,max_error=0.0001):
""" Calculates the density of states
of a heterostructure by a
green function approach, input is a heterostructure class"""
dos = [] # list with the density of states
iden = np.matrix(np.identity(len(intra),dtype=complex)) # create idntity
for energy in energies: # loop over energies
# right green function
intra = hetero.right_intra
inter = hetero.right_inter
gr = dyson(intra,inter,energy=energy,num_rep=num_rep,mixing=mixing,
eps=eps,green_guess=green_guess,max_error=max_error)
# left green function
intra = hetero.right_intra
inter = hetero.right_inter
gl = dyson(intra,inter,energy=energy,num_rep=num_rep,mixing=mixing,
eps=eps,green_guess=green_guess,max_error=max_error)
# central green function
selfl = inter.H*gl*inter # left selfenergy
selfr = inter*gr*inter.H # right selfenergy
gc = energy*iden -intra -selfl -selfr # dyson equation for the center
gc = gc.I # calculate inverse
dos.append(-gc.trace()[0,0].imag) # calculate the trace of the Green function
return dos
def dos_semiinfinite(intra,inter,energies=[0.0],num_rep=100,
mixing=0.7,eps=0.0001,green_guess=None,max_error=0.0001):
""" Calculates the surface density of states by using a
green function approach"""
dos = [] # list with the density of states
for energy in energies: # loop over energies
gf = dyson(intra,inter,energy=energy,num_rep=num_rep,mixing=mixing,
eps=eps,green_guess=green_guess,max_error=max_error)
dos.append(-gf.trace()[0,0].imag) # calculate the trace of the Green function
return dos
def dos_semiinfinite(intra,inter,energies=[0.0],num_rep=100,
mixing=0.7,eps=0.0001,green_guess=None,max_error=0.0001):
""" Calculates the surface density of states by using a
green function approach"""
dos = [] # list with the density of states
for energy in energies: # loop over energies
gf = dyson(intra,inter,energy=energy,num_rep=num_rep,mixing=mixing,
eps=eps,green_guess=green_guess,max_error=max_error)
dos.append(-gf.trace()[0,0].imag) # calculate the trace of the Green function
return dos
def dyson(intra, inter, energy=0.0, gf=None, is_sparse=False, initial=None):
""" Solves the dyson equation for a one dimensional
system with intra matrix 'intra' and inter to the nerest cell
'inter'"""
# get parameters
if gf == None: gf = gf_convergence("lead")
mixing = gf.mixing
eps = gf.eps
max_error = gf.max_error
num_rep = gf.num_rep
optimal = gf.optimal
try:
intra = intra.todense()
inter = inter.todense()
except:
a = 1
if initial == None: # if green not provided. initialize at zero
from numpy import zeros
g_guess = intra * 0.0j
else:
g_guess = initial
# calculate using fortran
if optimal:
print "Fortran dyson calculation"
from green_fortran import dyson # import fortran subroutine
(g, num_redo) = dyson(intra,
inter,
energy,
num_rep,
mixing=mixing,
eps=eps,
green_guess=g_guess,
max_error=max_error)
print " Converged in ", num_redo, "iterations\n"
from numpy import matrix
g = matrix(g)
# calculate using python
if not optimal:
g_old = g_guess # first iteration
iden = np.matrix(np.identity(len(intra),
dtype=complex)) # create identity
e = iden * (energy + 1j * eps) # complex energy
while True: # loop over iterations
self = inter * g_old * inter.H # selfenergy
g = (e - intra - self).I # dyson equation
if np.max(np.abs(g - g_old)) < gf.max_error: break
# print np.max(np.abs(g-g_old))
g_old = mixing * g + (1. - mixing) * g_old # new green function
if is_sparse:
from scipy.sparse import csc_matrix
g = csc_matrix(g)
return g
def dyson(intra, inter, energy=0.0, gf=None, is_sparse=False, initial=None):
""" Solves the dyson equation for a one dimensional
system with intra matrix 'intra' and inter to the nerest cell
'inter'"""
# get parameters
if gf == None:
gf = gf_convergence("lead")
mixing = gf.mixing
eps = gf.eps
max_error = gf.max_error
num_rep = gf.num_rep
optimal = gf.optimal
try:
intra = intra.todense()
inter = inter.todense()
except:
a = 1
if initial == None: # if green not provided. initialize at zero
from numpy import zeros
g_guess = intra * 0.0j
else:
g_guess = initial
# calculate using fortran
if optimal:
print "Fortran dyson calculation"
from green_fortran import dyson # import fortran subroutine
(g, num_redo) = dyson(
intra, inter, energy, num_rep, mixing=mixing, eps=eps, green_guess=g_guess, max_error=max_error
)
print " Converged in ", num_redo, "iterations\n"
from numpy import matrix
g = matrix(g)
# calculate using python
if not optimal:
g_old = g_guess # first iteration
iden = np.matrix(np.identity(len(intra), dtype=complex)) # create identity
e = iden * (energy + 1j * eps) # complex energy
while True: # loop over iterations
self = inter * g_old * inter.H # selfenergy
g = (e - intra - self).I # dyson equation
if np.max(np.abs(g - g_old)) < gf.max_error:
break
# print np.max(np.abs(g-g_old))
g_old = mixing * g + (1.0 - mixing) * g_old # new green function
if is_sparse:
from scipy.sparse import csc_matrix
g = csc_matrix(g)
return g