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kpFDM.py
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import sys
import numpy as np
from scipy import rand
from scipy.linalg import toeplitz, eigvalsh
from scipy.sparse.linalg import eigsh, lobpcg, eigs
from scipy.sparse import lil_matrix, diags, block_diag, csr_matrix, bmat, kron
import matplotlib.pyplot as plt
import argparse
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
#from pyamg import smoothed_aggregation_solver
class UniversalConst(object):
def __init__(self):
"""
"""
self.RY = 13.6
self.A0 = 0.529167
self.eVAA2 = 3.67744
self.planck = 6.58211928e-16 # ev*s
self.m0 = 0.510998910e+6 #ev/c^2
self.c = 299792458e+10 # AA/s
self.hsqrO2m0 = (self.c**2)*(self.planck**2) / (2.*self.m0)
class DrawingFunctions(object):
def __init__(self):
"""
Parameters
----------
dimen : integer
system's dimensionality, i.e., quantum well, wire and dot
"""
def square(self, params, profile, value, idx):
"""
"""
if params['dimen'] == 1:
profile[params['startPos'][idx]:params['endPos'][idx]] = value
if params['dimen'] == 2:
profile[params['startPos'][idx]:params['endPos'][idx],params['startPos'][idx]:params['endPos'][idx]] = value
if params['dimen'] == 3:
print 'Not implemented yet'
return profile
class Potential(object):
def __init__(self, params):
"""
"""
# Set internal parameters
if params['dimen'] == 1:
if params['model'] == 'ZB2x2':
self.pot = np.zeros(params['N'])
if params['model'] == 'ZB6x6':
self.pot = np.zeros(3*params['N']).reshape((3,params['N']))
if params['model'] == 'ZB8x8':
self.pot = np.zeros(5*params['N']).reshape((5,params['N']))
if params['dimen'] == 2:
if params['model'] == 'ZB2x2':
self.pot = np.zeros(params['N']**2).reshape(params['N'],params['N'])
if params['model'] == 'ZB6x6':
self.pot = np.zeros(3*params['N']**2).reshape((3,params['N'],params['N']))
def buildPot(self, params, flag):
"""
"""
drawFunc = DrawingFunctions()
if params['potType'] == 'square':
if params['model'] == 'ZB2x2':
for i in range(params['nmat']):
#print 'constructing layer %d potential from %d(%f) to %d(%f)'%(i,params['startPos'][i],params['x'][params['startPos'][i]],
#params['endPos'][i],params['x'][params['endPos'][i]])
if flag == 'het':
value = params['gap'][0] + (params['gap'][i]-params['gap'][0])*(1.-params['bshift'])
if flag == 'kin':
value = params['elecmassParam'][i]
self.pot = drawFunc.square(params, self.pot, value, i)
if params['model'] == 'ZB6x6':
value = {}
for i in range(params['nmat']):
if flag == 'het':
value[0] = (params['gap'][0]-params['gap'][i])*params['bshift']
value[1] = value[0]
value[2] = value[0]-params['deltaSO'][i]
if flag == 'kin':
value[0] = params['gamma1'][i]
value[1] = params['gamma2'][i]
value[2] = params['gamma3'][i]
for j in range(3):
self.pot[j,:] = drawFunc.square(params, self.pot[j,:], value[j], i)
if params['model'] == 'ZB8x8':
value = {}
for i in range(params['nmat']):
if flag == 'het':
value[0] = params['gap'][0] + (params['gap'][i]-params['gap'][0])*(1.-params['bshift'])
value[1] = (params['gap'][0]-params['gap'][i])*params['bshift']
value[2] = -params['deltaSO'][i]
#value[3] = value[1]-params['deltaSO'][i]
aux = 3
if flag == 'kin':
value[0] = params['elecmassParam'][i]
value[1] = params['Ll'][i]
value[2] = params['Mm'][i]
value[3] = params['Nn'][i]
value[4] = params['P0'][i]
aux = 5
for j in range(aux):
self.pot[j,:] = drawFunc.square(params, self.pot[j,:], value[j], i)
else:
print 'Not implemented yet'
return self.pot
def plotPot(self, params):
"""
"""
UniConst = UniversalConst()
fig = plt.figure()
if params['model'] == 'ZB2x2':
if params['dimen'] == 1:
plt.plot(params['x']*UniConst.A0,self.pot)
plt.show()
if params['dimen'] == 2:
ax = fig.gca(projection='3d')
X, Y = np.meshgrid(params['x']*UniConst.A0, params['x']*UniConst.A0)
surf = ax.plot_surface(X, Y, self.pot, rstride=1, cstride=1, cmap=cm.coolwarm,
linewidth=0, antialiased=False)
ax.zaxis.set_major_locator(LinearLocator(10))
ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))
fig.colorbar(surf, shrink=0.5, aspect=5)
plt.show()
if params['model'] == 'ZB6x6':
plt.plot(params['x'],self.pot[0,:])
plt.plot(params['x'],self.pot[1,:])
plt.plot(params['x'],self.pot[2,:])
plt.show()
if params['model'] == 'ZB8x8':
plt.plot(params['x'],self.pot[0,:])
plt.plot(params['x'],self.pot[1,:])
plt.plot(params['x'],self.pot[1,:]+self.pot[2,:])
plt.show()
class IO(object):
def __init__(self):
"""
"""
self.const = UniversalConst()
self.parser = argparse.ArgumentParser(description='kp in real space by FDM')
self.parameters = {}
self.parse()
def parse(self):
"""
"""
self.parser.add_argument('-n','--NMAT',action='store', dest='nmat',
type=int, help='Type: integer. Number of material which composes the system.')
self.parser.add_argument('-d','--DIMEN',action='store', dest='dimen',
type=int,
help="""
Type: integer. Dimensionality of the system, i.e.,
1 -> quantum well,
2 -> quantum wire,
3 -> quantum dot.
""")
self.parser.add_argument('-m','--MODEL',action='store', dest='model',type=str,
choices=['ZB2x2', 'ZB6x6', 'ZB8x8'], help="""
Hamiltonian model: ZB2x2, ZB6x6, ZB8x8, WZ2x2, ....
""")
self.parser.add_argument('-p','--GAPS',action='store', dest='gap',
type=float, nargs='+', help="""
Material's gaps in the form: gap_material1, gap_material2, gap_material3, ... .
Units of eV.
""")
self.parser.add_argument('-t','--type',action='store',dest='potType',
type=str, help="""
Potential type, i.e.,
square, hexagon, circle, sphere, etc
""")
self.parser.add_argument('-s','--STARTPOS',action='store',dest='startPos',
type=float, nargs='+', help="""
Starting position of material: v1, v2, v3, ... .
Units of Angstroms
""")
self.parser.add_argument('-e','--ENDPOS',action='store',dest='endPos',
type=float, nargs='+', help="""
Ending position of the band mismatch in the form: v1, v2, v3, ... .
Units of Angstroms
""")
self.parser.add_argument('-st','--STEP',action='store',dest='step',type=float, help="""
Discretization step in Angstrom
""")
self.parser.add_argument('-dr','--DIRECTION',action='store',dest='direction',type=str, help="""
Direction to compute the band structure, ex: kx, ky ou kz
""")
self.parser.add_argument('-me','--ELECMASS',action='store',dest='elecmass',
type=float, nargs='+', help="""
Electron effective masses in the form: v1, v2, v3, ... .
Units of m0. If WZ input e1 and e2 for all materials.
""")
self.parser.add_argument('-g1', '--gamma1',action='store',dest='gamma1',
type=float, nargs='+', help="""
Holes mass parameters in the form: gamma1, gamma1, ...
""")
self.parser.add_argument('-g2', '--gamma2',action='store',dest='gamma2',
type=float, nargs='+', help="""
Holes mass parameters in the form: gamma2, gamma2, ...
""")
self.parser.add_argument('-g3', '--gamma3',action='store',dest='gamma3',
type=float, nargs='+', help="""
Holes mass parameters in the form: gamma3, gamma3, ...
""")
self.parser.add_argument('-dso', '--DELTASO', action='store', dest='deltaSO',
type=float, nargs='+', help="""
Delta SO in the form: deltaso1, deltaso2, ...
""")
self.parser.add_argument('-lp','--LATPAR', action='store',dest='latpar',
type=float, help="""
General lattice parameter. Units of Angstrom
""")
self.parser.add_argument('-np', '--NPOINTS', action='store', dest='npoints',
type=int, help="""
Number of k points to compute
""")
self.parser.add_argument('-pc', '--PERCENTAGE', action='store', dest='percent',
type=float, help="""
Percentage of the k-mesh to compute
""")
self.parser.add_argument('-bs', '--BSHIFT', action='store', dest='shift',
type=float, help="""
Band shift in percentage for valance band, ex: 0.4
""")
self.parser.add_argument('-ncb', '--NUMCB', action='store', dest='numcb',
type=int, help="""
Number of conduction bands to compute
""")
self.parser.add_argument('-nvb', '--NUMVB', action='store', dest='numvb',
type=int, help="""
Number of valance bands to compute
""")
self.parser.add_argument('-ep', '--INTERBAND', action='store', dest='ep',
type=float, nargs='+', help="""
Interband coupling parameter
""")
self.parser.add_argument('-p0', action='store', dest='p0',
type=float, nargs='+', help="""
Interband coupling parameter
""")
self.parser.add_argument('-lobpcg', '--LOBPCG', action='store', dest='lobpcg',
type=int, choices=[0, 1], default=0, help="""
1 uses lobpcg - not fully tested
0 uses default sparse solver - best choice
""")
self.parser.add_argument('-full', '--FULL', action='store', dest='full',
type=int, choices=[0, 1], default=0, help="""
1 compute all eigenvalues and eigenvectors
0 compute desired number according to numcb + numvb
""")
self.args = self.parser.parse_args()
self.verification()
self.buildParamDict()
def verification(self):
"""
"""
assert self.args.nmat > 1
assert self.args.dimen >= 1
assert (self.args.potType == 'square')
assert self.args.model in ['ZB2x2', 'ZB6x6', 'ZB8x8']
if self.args.model in ['ZB2x2'] or self.args.model in ['ZB8x8']:
assert self.args.numcb > 0
else:
if self.args.model in ['ZB6x6', 'ZB8x8']:
assert self.args.numvb > 0
assert len(self.args.gamma1) == self.args.nmat
assert len(self.args.gamma2) == self.args.nmat
assert len(self.args.gamma3) == self.args.nmat
assert len(self.args.deltaSO) == self.args.nmat
#if self.args.model in ['ZB8x8']:
# assert len(self.args.ep) == self.args.nmat
if self.args.model in ['ZB2x2', 'ZB6x6', 'ZB8x8']:
assert len(self.args.gap) == self.args.nmat
if self.args.model in ['ZB2x2', 'ZB8x8']:
assert len(self.args.elecmass) == self.args.nmat
else:
assert len(self.args.gap)/2 == self.args.nmat
assert len(self.args.elecmass)/2 == self.args.nmat
if self.args.dimen == 1:
assert self.args.direction in ['kx', 'ky']
else:
assert self.args.direction in ['kz']
def buildParamDict(self):
"""
"""
# Primary parameters
self.parameters['nmat'] = self.args.nmat
self.parameters['dimen'] = self.args.dimen
self.parameters['model'] = self.args.model
self.parameters['potType'] = self.args.potType
self.parameters['startPos'] = self.args.startPos
self.parameters['endPos'] = self.args.endPos
self.parameters['step'] = self.args.step
self.parameters['direction'] = self.args.direction
self.parameters['gap'] = self.args.gap
self.parameters['elecmass'] = self.args.elecmass
self.parameters['gamma1'] = self.args.gamma1
self.parameters['gamma2'] = self.args.gamma2
self.parameters['gamma3'] = self.args.gamma3
self.parameters['deltaSO'] = self.args.deltaSO
self.parameters['Ep'] = self.args.ep
self.parameters['P0'] = self.args.p0
self.parameters['latpar'] = self.args.latpar
self.parameters['npoints'] = self.args.npoints
self.parameters['percentage'] = self.args.percent
self.parameters['bshift'] = self.args.shift
self.parameters['numcb'] = self.args.numcb
self.parameters['numvb'] = self.args.numvb
self.parameters['lobpcg'] = self.args.lobpcg
self.parameters['full'] = self.args.full
# Secondary parameters
#self.parameters['Len'] = self.parameters['endPos'][0] - self.parameters['startPos'][0]
#self.parameters['Enorm'] = self.const.hsqrO2m0/(self.const.A0**2)
if (self.parameters['endPos'][0]-self.parameters['startPos'][0])%self.parameters['step'] != 0:
sys.exit("Discretization interval isnt divisible by total size, try another")
else:
self.parameters['N'] = (self.parameters['endPos'][0]-self.parameters['startPos'][0])/self.parameters['step']
if self.parameters['dimen'] in [1, 2]:
self.parameters['x'] = np.linspace(self.parameters['startPos'][0],self.parameters['endPos'][0],self.parameters['N'])
self.parameters['x'] /= self.const.A0
else:
print 'Not implemented yet x'
# Converting startPos and endPos to vector index
startPos = np.zeros(self.parameters['nmat'])
endPos = np.zeros(self.parameters['nmat'])
if self.parameters['dimen'] in [1,2]:
for i in range(self.parameters['nmat']):
startPos[i] = abs(self.parameters['startPos'][0]-self.parameters['startPos'][i])/self.parameters['step']
endPos[i] = startPos[0] + (self.parameters['endPos'][0]+self.parameters['endPos'][i])/self.parameters['step']
else:
print 'Not implemented yet dimen'
self.parameters['startPos'] = [int(x) for x in startPos]
self.parameters['endPos'] = [int(x) for x in endPos]
# dimensionalization
#self.parameters['step'] /= self.const.A0
if self.args.model in ['ZB2x2']:
self.parameters['elecmassParam'] = [self.const.eVAA2/x for x in self.parameters['elecmass']]
if self.args.model in ['ZB6x6']:
self.parameters['gamma1'] = [self.const.eVAA2*x for x in self.parameters['gamma1']]
self.parameters['gamma2'] = [self.const.eVAA2*x for x in self.parameters['gamma2']]
self.parameters['gamma3'] = [self.const.eVAA2*x for x in self.parameters['gamma3']]
if self.parameters['model'] == 'ZB8x8':
if self.parameters['Ep'] != 0:
self.parameters['P0'] = [np.sqrt(self.const.eVAA2*x) for x in self.parameters['Ep']]
EpOEg = [x/y for (x,y) in zip(self.parameters['Ep'],self.parameters['gap'])]
self.parameters['gamma1'] = [self.const.eVAA2*x - (1./3.)*y for (x,y) in zip(self.parameters['gamma1'],EpOEg)]
self.parameters['gamma2'] = [self.const.eVAA2*x - (1./6.)*y for (x,y) in zip(self.parameters['gamma2'],EpOEg)]
self.parameters['gamma3'] = [self.const.eVAA2*x - (1./6.)*y for (x,y) in zip(self.parameters['gamma3'],EpOEg)]
self.parameters['elecmassParam'] = [1./w - ((y+(2./3.)*z)/(y+z))*x for (x,y,z,w) in zip(EpOEg,self.parameters['gap'],self.parameters['deltaSO'],self.parameters['elecmass'])]
self.parameters['elecmassParam'] = [self.const.eVAA2*x for x in self.parameters['elecmassParam']]
else:
#self.parameters['P0'] = [0 for x in self.parameters['gamma1']]
self.parameters['gamma1'] = [self.const.eVAA2*x for x in self.parameters['gamma1']]
self.parameters['gamma2'] = [self.const.eVAA2*x for x in self.parameters['gamma2']]
self.parameters['gamma3'] = [self.const.eVAA2*x for x in self.parameters['gamma3']]
self.parameters['elecmassParam'] = [self.const.eVAA2*x for x in self.parameters['elecmass']]
self.parameters['P0'] = [x for x in self.const.p0]
self.parameters['Ll'] = [-(x+4.*y) for (x,y) in zip(self.parameters['gamma1'],self.parameters['gamma2'])]
self.parameters['Mm'] = [-(x-2.*y) for (x,y) in zip(self.parameters['gamma1'],self.parameters['gamma2'])]
self.parameters['Nn'] = [-3.*x for x in self.parameters['gamma3']]
return self.parameters
class ZincBlend(object):
def __init__(self, params):
"""
"""
self.const = UniversalConst()
self.symmetry = 'cubic'
self.N = int(params['N'])
if params['dimen'] == 1:
#self.directbasis = np.array([params['latpar']/self.const.A0, params['latpar']/self.const.A0, 1. ])
self.directbasis = np.array([params['latpar'], params['latpar'], 1. ])
else:
if params['dimen'] == 2:
self.directbasis = np.array([ 1., 1., params['latpar']/self.const.A0])
else:
print 'Not implemented yet basis'
# set Bravais basis in reciprocal space
#self.reciprocalbasis = 2.*np.pi/self.directbasis
self.reciprocalbasis = np.pi/self.directbasis
if params['dimen'] == 1:
if params['direction'] == 'kx':
kxlim = self.reciprocalbasis[0]*params['percentage']/100
self.kmesh = np.linspace(-kxlim,kxlim,2*params['npoints']+1)
if params['direction'] == 'ky':
kylim = self.reciprocalbasis[1]*params['percentage']/100
self.kmesh = np.linspace(0,kylim,params['npoints'])
else:
if params['dimen'] == 2:
if params['direction'] == 'kz':
kxlim = self.reciprocalbasis[2]*params['percentage']/100
self.kmesh = np.linspace(0,kxlim,params['npoints'])
else:
print 'Not implemented yet mesh'
class ZBHamilton(ZincBlend):
def __init__(self, params, potHet, Kin):
"""
"""
ZincBlend.__init__(self,params)
self.potHet = potHet
self.Kin = Kin
self.step = params['step']
self.der = derivateCoefs(params['N']-2)
def buildHam2x2(self, params, kpoints):
"""
"""
kx = kpoints[0]
ky = kpoints[1]
kz = kpoints[2]
if params['dimen'] == 1:
HT = lil_matrix((2*(self.N-2),2*(self.N-2)), dtype=np.float64)
cond = lil_matrix(((self.N-2),(self.N-2)), dtype=np.float64)
ksquare = kx**2 + ky**2
aux = self.Kin[1:self.N-1]
auxfw = np.dot(self.der.forward(),aux)
auxbw = np.dot(self.der.backward(),aux)
auxct = np.dot(self.der.central(),aux)
cond.setdiag(auxct,0)
cond.setdiag(-auxfw[0:self.N-3],1)
cond.setdiag(-auxfw[self.N-4],self.N-3)
cond.setdiag(-auxbw[1:self.N-2],-1)
cond.setdiag(-auxbw[0],-self.N+3)
cond *= (1./(2.*self.step**2))
cond += diags(self.Kin[1:self.N-1],0)*ksquare + diags(self.potHet[1:self.N-1],0)
HT += kron(cond ,[[1,0],[0,0]], format='lil')
HT += kron(cond ,[[0,0],[0,1]], format='lil')
del aux
del auxfw
del auxbw
del auxct
if params['dimen'] == 2:
HT = lil_matrix(((self.N-2)**2,(self.N-2)**2), dtype=np.float64)
diag = np.zeros((self.N-2)**2)
offdiag1 = np.zeros((self.N-2)**2)
diag2 = np.zeros((self.N-2)**2-self.N+2)
ksquare = kz**2
for i in range(1,self.N-1):
diag[(i-1)*(self.N-2):i*(self.N-2)] = (1./(2.*self.step**2))*4.*self.Kin[1:self.N-1,i-1] +\
(1./(2.*self.step**2))*np.convolve(self.Kin[:,i-1],[1,0,1],'valid') +\
(1./(2.*self.step**2))*np.convolve(self.Kin[i-1,:],[1,0,1],'valid') +\
self.Kin[1:self.N-1,i-1]*ksquare +\
self.potHet[1:self.N-1,i-1]
offdiag1[(i-1)*(self.N-2):i*(self.N-2)] = (1./(2.*self.step**2))*np.convolve(self.Kin[:,i-1],[1,1],'same')[1:self.N-1]
if i < self.N-2:
diag2[(i-1)*(self.N-2):i*(self.N-2)] = (1./(2.*self.step**2))*np.convolve(self.Kin[i-1,:],[1,1],'same')[1:self.N-1]
HT.setdiag(diag,0)
HT.setdiag(-offdiag1,1)
HT.setdiag(-offdiag1,-1)
HT.setdiag(-diag2,self.N)
HT.setdiag(-diag2,-self.N)
del diag
del offdiag1
del diag2
#print 'HT is hermitian? ',np.allclose(HT.conjugate(), HT)
#np.savetxt('HT.dat',HT.todense())
return HT.tocsr()
def buildHam6x6(self, params, kpoints):
"""
"""
kx = kpoints[0]
ky = kpoints[1]
kz = kpoints[2]
#kx = 0.03704796
if params['dimen'] == 1:
HT = lil_matrix((6*(self.N-2),6*(self.N-2)), dtype=np.complex128)
Q = lil_matrix((self.N-2,self.N-2), dtype=np.float64)
T = lil_matrix((self.N-2,self.N-2), dtype=np.float64)
S = lil_matrix((self.N-2,self.N-2), dtype=np.complex128)
SC = lil_matrix((self.N-2,self.N-2), dtype=np.complex128)
Saux = lil_matrix((self.N-2,self.N-2), dtype=np.complex128)
R = lil_matrix((self.N-2,self.N-2), dtype=np.complex128)
RC = lil_matrix((self.N-2,self.N-2), dtype=np.complex128)
ZERO = lil_matrix((self.N-2,self.N-2), dtype=np.float64)
gamma1 = lil_matrix((self.N-2,self.N-2), dtype=np.float64)
gamma2 = lil_matrix((self.N-2,self.N-2), dtype=np.float64)
gamma3 = lil_matrix((self.N-2,self.N-2), dtype=np.float64)
gamma1.setdiag(self.Kin[0,1:self.N-1],0)
gamma2.setdiag(self.Kin[1,1:self.N-1],0)
gamma3.setdiag(self.Kin[2,1:self.N-1],0)
# Q
aux = self.Kin[0,1:self.N-1] - 2.*self.Kin[1,1:self.N-1]
auxfw = np.dot(self.der.forward(),aux)
auxbw = np.dot(self.der.backward(),aux)
auxct = np.dot(self.der.central(),aux)
Q.setdiag(auxct,0)
Q.setdiag(-auxfw[0:self.N-3],1)
Q.setdiag(-auxfw[self.N-4],self.N-3)
Q.setdiag(-auxbw[1:self.N-2],-1)
Q.setdiag(-auxbw[0],-self.N+3)
Q *= (1./(2.*self.step**2))
Q += ( (gamma1+gamma2)*(kx**2 + ky**2) )
Q *= -1
#np.savetxt('Q.dat',Q.todense())
# T
aux = self.Kin[0,1:self.N-1] + 2.*self.Kin[1,1:self.N-1]
auxfw = np.dot(self.der.forward(),aux)
auxbw = np.dot(self.der.backward(),aux)
auxct = np.dot(self.der.central(),aux)
T.setdiag(auxct,0)
T.setdiag(-auxfw[0:self.N-3],1)
T.setdiag(-auxfw[self.N-4],self.N-3)
T.setdiag(-auxbw[1:self.N-2],-1)
T.setdiag(-auxbw[0],-self.N+3)
T *= (1./(2.*self.step**2))
T += ( (gamma1-gamma2)*(kx**2 + ky**2) )
T *= -1
#np.savetxt('T.dat',T.todense())
# S
aux = np.dot(self.der.backward(),self.Kin[2,1:self.N-1])
aux1 = np.dot(self.der.forward(),self.Kin[2,1:self.N-1])
S.setdiag(-aux,0)
S.setdiag(aux[0], -self.N+3)
S.setdiag(aux,1)
S*=(1./(4.*self.step))
S -= S.transpose()
SC.setdiag(-aux1,0)
SC.setdiag(aux1[self.N-4], self.N-3)
SC.setdiag(aux1,-1)
SC*=(1./(4.*self.step))
SC -= SC.transpose()
S*=2.*np.sqrt(3.)*complex(kx,ky)
SC*=2.*np.sqrt(3.)*complex(kx,-ky)
#np.savetxt('S.dat',S.todense())
#np.savetxt('SC.dat',SC.todense())
# R
R = -np.sqrt(3.)*(gamma2*(kx**2 - ky**2)-2.*complex(0,1.)*gamma3*kx*ky)
RC = -np.sqrt(3.)*(gamma2*(kx**2 - ky**2)+2.*complex(0,1.)*gamma3*kx*ky)
#np.savetxt('R.dat',R.todense())
IU = complex(0,1.)
sqr2 = np.sqrt(2.)
rqs2 = 1./np.sqrt(2.)
sqr3 = np.sqrt(3.)
"""
# I dont know why this doesnt work!!!
HT = bmat([[Q , S , R , ZERO , IU*rqs2*S ,-IU*sqr2*R ],
[ SC , T , ZERO , R ,-IU*rqs2*(Q-T) , IU*sqr3*rqs2*S],
[ RC , ZERO , T ,-S ,-IU*sqr3*rqs2*SC,-IU*rqs2*(Q-T) ],
[ ZERO , RC ,-SC , Q ,-IU*sqr2*RC ,-IU*rqs2*SC ],
[-IU*rqs2*SC, IU*rqs2*(Q-T) , IU*sqr3*rqs2*S, IU*sqr2*R, .5*(Q+T) , ZERO ],
[ IU*sqr2*RC,-IU*sqr3*rqs2*SC, IU*rqs2*(Q-T) , IU*rqs2*S, ZERO , .5*(Q+T) ]
])
"""
HT += kron(Q ,[[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]], format='lil')
HT += kron(S ,[[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]], format='lil')
HT += kron(R ,[[0,0,1,0,0,0],[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]], format='lil')
HT += kron(ZERO ,[[0,0,0,1,0,0],[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]], format='lil')
HT += kron(IU*rqs2*S ,[[0,0,0,0,1,0],[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]], format='lil')
HT += kron(-IU*sqr2*R ,[[0,0,0,0,0,1],[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]], format='lil')
HT += kron(SC ,[[0,0,0,0,0,0],[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]], format='lil')
HT += kron(T ,[[0,0,0,0,0,0],[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]], format='lil')
HT += kron(ZERO ,[[0,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(R ,[[0,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(-IU*rqs2*(Q-T) ,[[0,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(IU*sqr3*rqs2*S ,[[0,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(RC ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(ZERO ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(T ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(-S ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(-IU*sqr3*rqs2*SC ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(-IU*rqs2*(Q-T) ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(ZERO ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(RC ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(-SC ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(Q ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(-IU*sqr2*RC ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(-IU*rqs2*SC ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(-IU*rqs2*SC ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(IU*rqs2*(Q-T) ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(IU*sqr3*rqs2*S ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(IU*sqr2*R ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(.5*(Q+T) ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,0]], format='lil')
HT += kron(ZERO ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,0,0]], format='lil')
HT += kron(IU*sqr2*RC ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[1,0,0,0,0,0]], format='lil')
HT += kron(-IU*sqr3*rqs2*SC ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,1,0,0,0,0]], format='lil')
HT += kron(IU*rqs2*(Q-T) ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,1,0,0,0]], format='lil')
HT += kron(IU*rqs2*S ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,1,0,0]], format='lil')
HT += kron(ZERO ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,1,0]], format='lil')
HT += kron(.5*(Q+T) ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,1]], format='lil')
HT += kron(diags(self.potHet[0,1:self.N-1],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]], format='lil')
HT += kron(diags(self.potHet[1,1:self.N-1],0) ,[[0,0,0,0,0,0],[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]], format='lil')
HT += kron(diags(self.potHet[1,1:self.N-1],0) ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(diags(self.potHet[0,1:self.N-1],0) ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(diags(self.potHet[2,1:self.N-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],[0,0,0,0,1,0],[0,0,0,0,0,0]], format='lil')
HT += kron(diags(self.potHet[2,1:self.N-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],[0,0,0,0,0,1]], format='lil')
del Q
del T
del S
del SC
del R
del RC
del ZERO
del gamma1
del gamma2
del gamma3
del aux
del aux1
del auxfw
del auxbw
del auxct
if params['dimen'] == 2:
#kz = 0.05557194
HT = lil_matrix((6*(self.N-2)**2,6*(self.N-2)**2), dtype=np.complex128)
Q = lil_matrix(((self.N-2)**2,(self.N-2)**2), dtype=np.float64)
diagQ = np.zeros((self.N-2)**2)
offdiagQ = np.zeros((self.N-2)**2)
diag2Q = np.zeros((self.N-2)**2-self.N+2)
T = lil_matrix(((self.N-2)**2,(self.N-2)**2), dtype=np.float64)
diagT = np.zeros((self.N-2)**2)
offdiagT = np.zeros((self.N-2)**2)
diag2T = np.zeros((self.N-2)**2-self.N+2)
S = lil_matrix(((self.N-2)**2,(self.N-2)**2), dtype=np.complex128)
offdiagS = np.zeros((self.N-2)**2)
offdiag2S = np.zeros((self.N-2)**2-self.N+2)
SC = lil_matrix(((self.N-2)**2,(self.N-2)**2), dtype=np.complex128)
R = lil_matrix(((self.N-2)**2,(self.N-2)**2), dtype=np.complex128)
R1 = np.zeros((self.N-3)*(self.N-2))
R2 = np.zeros((self.N-3)*(self.N-2))
R3 = np.zeros((self.N-3)*(self.N-2))
R4 = np.zeros((self.N-3)*(self.N-2))
diagR = np.zeros((self.N-2)**2)
offdiagR = np.zeros((self.N-2)**2)
offdiag2R = np.zeros((self.N-2)**2-self.N+2)
RC = lil_matrix(((self.N-2)**2,(self.N-2)**2), dtype=np.complex128)
ZERO = lil_matrix(((self.N-2)**2,(self.N-2)**2), dtype=np.float64)
QpT = lil_matrix(((self.N-2)**2,(self.N-2)**2), dtype=np.float64)
diagQpT = np.zeros((self.N-2)**2)
gamma1 = self.Kin[0,:]
gamma2 = self.Kin[1,:]
gamma3 = self.Kin[2,:]
ksquare = kz**2
for i in range(1,self.N-1):
auxQ = gamma1 - 2.*gamma2
auxT = gamma1 + 2.*gamma2
diagQ[(i-1)*(self.N-2):i*(self.N-2)] = -(1./(2.*self.step**2))*4.*(auxQ[1:self.N-1,i-1])-\
(1./(2.*self.step**2))*np.convolve(auxQ[:,i-1],[1,0,1],'valid') -\
(1./(2.*self.step**2))*np.convolve(auxQ[i-1,:],[1,0,1],'valid') -\
(gamma1[1:self.N-1,i-1]-2.*gamma2[1:self.N-1,i-1])*ksquare
diagT[(i-1)*(self.N-2):i*(self.N-2)] = -(1./(2.*self.step**2))*4.*(auxT[1:self.N-1,i-1])-\
(1./(2.*self.step**2))*np.convolve(auxT[:,i-1],[1,0,1],'valid') -\
(1./(2.*self.step**2))*np.convolve(auxT[i-1,:],[1,0,1],'valid') -\
(gamma1[1:self.N-1,i-1]+2.*gamma2[1:self.N-1,i-1])*ksquare
diagQpT = 0.5*(diagQ[(i-1)*(self.N-2):i*(self.N-2)] + diagT[(i-1)*(self.N-2):i*(self.N-2)]) +\
self.potHet[2,1:self.N-1,i-1]
diagQ[(i-1)*(self.N-2):i*(self.N-2)] += self.potHet[0,1:self.N-1,i-1]
diagT[(i-1)*(self.N-2):i*(self.N-2)] += self.potHet[1,1:self.N-1,i-1]
offdiagQ[(i-1)*(self.N-2):i*(self.N-2)] = (1./(2.*self.step**2))*np.convolve(auxQ[:,i-1],[1,1],'same')[1:self.N-1]
offdiagT[(i-1)*(self.N-2):i*(self.N-2)] = (1./(2.*self.step**2))*np.convolve(auxT[:,i-1],[1,1],'same')[1:self.N-1]
offdiagS[(i-1)*(self.N-2):i*(self.N-2)] = (1./(4.*self.step))*np.convolve(gamma3[:,i-1],[1,1],'same')[1:self.N-1]
R1[(i-1)*(self.N-3):i*(self.N-3)] = (1./(16.*self.step**2))*2.*gamma3[1:self.N-2,i] +\
(1./(16.*self.step**2))*gamma3[2:self.N-1,i] +\
(1./(16.*self.step**2))*gamma3[i,2:self.N-1]
R2[(i-1)*(self.N-3):i*(self.N-3)] = (1./(16.*self.step**2))*2.*gamma3[1:self.N-2,i] +\
(1./(16.*self.step**2))*gamma3[0:self.N-3,i] +\
(1./(16.*self.step**2))*gamma3[i,0:self.N-3]
R3[(i-1)*(self.N-3):i*(self.N-3)] = (1./(16.*self.step**2))*2.*gamma3[1:self.N-2,i] +\
(1./(16.*self.step**2))*gamma3[0:self.N-3,i] +\
(1./(16.*self.step**2))*gamma3[i,2:self.N-1]
R4[(i-1)*(self.N-3):i*(self.N-3)] = (1./(16.*self.step**2))*2.*gamma3[1:self.N-2,i] +\
(1./(16.*self.step**2))*gamma3[2:self.N-1,i] +\
(1./(16.*self.step**2))*gamma3[i,0:self.N-3]
diagR[(i-1)*(self.N-2):i*(self.N-2)] = -(1./(2.*self.step**2))*np.convolve(gamma2[:,i-1],[1,0,1],'valid') +\
(1./(2.*self.step**2))*np.convolve(gamma2[i-1,:],[1,0,1],'valid')
offdiagR[(i-1)*(self.N-2):i*(self.N-2)] = (1./(2.*self.step**2))*np.convolve(gamma2[:,i-1],[1,1],'same')[1:self.N-1]
if i < self.N-2:
diag2Q[(i-1)*(self.N-2):i*(self.N-2)] = (1./(2.*self.step**2))*np.convolve(auxQ[i-1,:],[1,1],'same')[1:self.N-1]
diag2T[(i-1)*(self.N-2):i*(self.N-2)] = (1./(2.*self.step**2))*np.convolve(auxT[i-1,:],[1,1],'same')[1:self.N-1]
offdiag2S[(i-1)*(self.N-2):i*(self.N-2)] = (1./(4.*self.step))*np.convolve(gamma3[i-1,:],[1,1],'same')[1:self.N-1]
offdiag2R[(i-1)*(self.N-2):i*(self.N-2)] = -(1./(2.*self.step**2))*np.convolve(gamma2[i-1,:],[1,1],'same')[1:self.N-1]
Q.setdiag(diagQ,0)
Q.setdiag(offdiagQ,1)
Q.setdiag(offdiagQ,-1)
Q.setdiag(diag2Q,self.N)
Q.setdiag(diag2Q,-self.N)
#np.savetxt('Q.dat',Q.todense())
T.setdiag(diagT,0)
T.setdiag(offdiagT,1)
T.setdiag(offdiagT,-1)
T.setdiag(diag2T,self.N)
T.setdiag(diag2T,-self.N)
#np.savetxt('T.dat',T.todense())
QpT.setdiag(diagQpT,0)
QpT.setdiag(0.5*(offdiagQ+offdiagT),1)
QpT.setdiag(0.5*(offdiagQ+offdiagT),-1)
QpT.setdiag(0.5*(diag2Q+diag2T),self.N)
QpT.setdiag(0.5*(diag2Q+diag2T),-self.N)
S.setdiag(offdiagS,1)
S.setdiag(-offdiagS,-1)
S.setdiag(complex(0.,-1.)*offdiag2S,self.N)
S.setdiag(-complex(0.,-1.)*offdiag2S,-self.N)
S*=2.*np.sqrt(3.)*kz
#np.savetxt('S.dat',S.todense())
SC.setdiag(offdiagS,1)
SC.setdiag(-offdiagS,-1)
SC.setdiag(complex(0.,1.)*offdiag2S,self.N)
SC.setdiag(-complex(0.,1.)*offdiag2S,-self.N)
SC*=2.*np.sqrt(3.)*kz
R.setdiag(diagR,0)
R.setdiag(offdiagR,1)
R.setdiag(offdiagR,-1)
R.setdiag(offdiag2R,self.N)
R.setdiag(offdiag2R,-self.N)
R.setdiag(complex(0.,-1.)*R1,self.N+1)
R.setdiag(complex(0.,-1.)*R2,-self.N-1)
R.setdiag(complex(0.,1.)*R3,self.N-1)
R.setdiag(complex(0.,1.)*R4,-self.N+1)
R*=2.*np.sqrt(3.)
RC.setdiag(diagR,0)
RC.setdiag(offdiagR,1)
RC.setdiag(offdiagR,-1)
RC.setdiag(offdiag2R,self.N)
RC.setdiag(offdiag2R,-self.N)
RC.setdiag(complex(0.,1.)*R1,self.N+1)
RC.setdiag(complex(0.,1.)*R2,-self.N-1)
RC.setdiag(complex(0.,-1.)*R3,self.N-1)
RC.setdiag(complex(0.,-1.)*R4,-self.N+1)
RC*=2.*np.sqrt(3.)
#np.savetxt('R.dat',R.todense())
IU = complex(0,1.)
sqr2 = np.sqrt(2.)
rqs2 = 1./np.sqrt(2.)
sqr3 = np.sqrt(3.)
HT += kron(Q ,[[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]], format='lil')
HT += kron(S ,[[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]], format='lil')
HT += kron(R ,[[0,0,1,0,0,0],[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]], format='lil')
HT += kron(ZERO ,[[0,0,0,1,0,0],[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]], format='lil')
HT += kron(IU*rqs2*S ,[[0,0,0,0,1,0],[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]], format='lil')
HT += kron(-IU*sqr2*R ,[[0,0,0,0,0,1],[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]], format='lil')
HT += kron(SC ,[[0,0,0,0,0,0],[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]], format='lil')
HT += kron(T ,[[0,0,0,0,0,0],[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]], format='lil')
HT += kron(ZERO ,[[0,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(R ,[[0,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(-IU*rqs2*(Q-T) ,[[0,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(IU*sqr3*rqs2*S ,[[0,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(RC ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(ZERO ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(T ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(-S ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(-IU*sqr3*rqs2*SC ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(-IU*rqs2*(Q-T) ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(ZERO ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(RC ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(-SC ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(Q ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(-IU*sqr2*RC ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(-IU*rqs2*SC ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(-IU*rqs2*SC ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(IU*rqs2*(Q-T) ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(IU*sqr3*rqs2*S ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(IU*sqr2*R ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,0]], format='lil')
HT += kron(QpT ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,0]], format='lil')
HT += kron(ZERO ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,0,0]], format='lil')
HT += kron(IU*sqr2*RC ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[1,0,0,0,0,0]], format='lil')
HT += kron(-IU*sqr3*rqs2*SC ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,1,0,0,0,0]], format='lil')
HT += kron(IU*rqs2*(Q-T) ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,1,0,0,0]], format='lil')
HT += kron(IU*rqs2*S ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,1,0,0]], format='lil')
HT += kron(ZERO ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,1,0]], format='lil')
HT += kron(QpT ,[[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,1]], format='lil')
return HT.tocsr()
def buildHam8x8(self, params, kpoints):
"""
"""
kx = kpoints[0]
ky = kpoints[1]
kz = kpoints[2]
if params['dimen'] == 1:
ksquare = kx**2 + ky**2
IU = complex(0.,1.)
H0 = np.zeros(8*(self.N-2), dtype=np.float64)
Hso = lil_matrix((8*(self.N-2),8*(self.N-2)), dtype=np.complex128)
Hkp = lil_matrix((4*(self.N-2),4*(self.N-2)), dtype=np.complex128)