def geometry_film(g, nz=1):
"""Create the geometry of a film"""
go = g.supercell([1, 1, nz]) # create the supercell
go.dimensionality = 2 # reduce dimensionality
go = sculpt.set_xy_plane(go) # put in the xy plane
go.real2fractional()
go.fractional2real()
return go
def interface(h1,
h2,
energies=np.linspace(-1., 1., 100),
operator=None,
delta=0.01,
kpath=None):
"""Get the surface DOS of an interface"""
from scipy.sparse import csc_matrix, bmat
if kpath is None:
if h1.dimensionality == 3:
g2d = h1.geometry.copy() # copy Hamiltonian
import sculpt
g2d = sculpt.set_xy_plane(g2d)
kpath = klist.default(g2d, nk=100)
elif h1.dimensionality == 2:
kpath = [[k, 0., 0.] for k in np.linspace(0., 1., 40)]
else:
raise
fo = open("KDOS_INTERFACE.OUT", "w")
fo.write("# k, E, Bulk1, Surf1, Bulk2, Surf2, interface\n")
tr = timing.Testimator("KDOS") # generate object
ik = 0
h1 = h1.get_multicell() # multicell Hamiltonian
h2 = h2.get_multicell() # multicell Hamiltonian
for k in kpath:
tr.remaining(ik, len(kpath)) # generate object
ik += 1
# for energy in energies:
# (b1,s1,b2,s2,b12) = green.interface(h1,h2,k=k,energy=energy,delta=delta)
# out = green.interface(h1,h2,k=k,energy=energy,delta=delta)
outs = green.interface_multienergy(h1,
h2,
k=k,
energies=energies,
delta=delta)
for (energy, out) in zip(energies, outs):
if operator is None:
op = np.identity(h1.intra.shape[0] * 2) # normal cell
ops = np.identity(h1.intra.shape[0]) # supercell
# elif callable(operator): op = callable(op)
else:
op = operator # normal cell
ops = bmat([[csc_matrix(operator), None],
[None, csc_matrix(operator)]])
# write everything
fo.write(str(ik) + " " + str(energy) + " ")
for g in out: # loop
if g.shape[0] == op.shape[0]:
d = -(g * op).trace()[0, 0].imag # bulk
else:
d = -(g * ops).trace()[0, 0].imag # interface
fo.write(str(d) + " ")
fo.write("\n")
fo.flush() # flush
fo.close()
def build(h, nz=1):
"""Create Hamiltonian of a film from a 3d geometry"""
# if not h.dimensionality==3: raise
ho = multicell.supercell(h, nsuper=[1, 1, nz], sparse=False, ncut=3)
ho.dimensionality = 2 # reduce dimensionality
ho.geometry.dimensionality = 2 # reduce dimensionality
ho.geometry = sculpt.set_xy_plane(ho.geometry) # put in the xy plane
hoppings = [] # empty list
for t in ho.hopping: # loop over hoppings
if t.dir[2] == 0: hoppings.append(t) # remove in the z direction
ho.hopping = hoppings # overwrite hoppings
return ho
def hamiltonian_film(hin, nz=10):
"""Return the Hamiltonian of a film"""
h = hin.copy() # copy Hamiltonian
import multicell
h = multicell.supercell_hamiltonian(h, nsuper=[1, 1, nz])
hopout = [] # list
for i in range(len(h.hopping)): # loop over hoppings
if abs(h.hopping[i].dir[2]) < 0.1:
hopout.append(h.hopping[i])
h.hopping = hopout
h.dimensionality = 2
h.geometry.dimensionality = 2
import sculpt
h.geometry = sculpt.set_xy_plane(h.geometry)
return h
def surface(h1,
energies=np.linspace(-1., 1., 100),
operator=None,
delta=0.01,
kpath=None,
hs=None):
"""Get the surface DOS of an interface"""
from scipy.sparse import csc_matrix, bmat
if kpath is None:
if h1.dimensionality == 3:
g2d = h1.geometry.copy() # copy Hamiltonian
import sculpt
g2d = sculpt.set_xy_plane(g2d)
kpath = klist.default(g2d, nk=100)
elif h1.dimensionality == 2:
kpath = [[k, 0., 0.] for k in np.linspace(0., 1., 40)]
else:
raise
fo = open("KDOS.OUT", "w")
fo.write("# k, E, Surface, Bulk\n")
tr = timing.Testimator("KDOS") # generate object
ik = 0
h1 = h1.get_multicell() # multicell Hamiltonian
for k in kpath:
tr.remaining(ik, len(kpath)) # generate object
ik += 1
outs = green.surface_multienergy(h1,
k=k,
energies=energies,
delta=delta,
hs=hs)
for (energy, out) in zip(energies, outs):
# write everything
fo.write(str(ik) + " " + str(energy) + " ")
for g in out: # loop
if operator is None:
d = -g.trace()[0, 0].imag # only the trace
elif callable(operator):
d = operator(g, k=k) # call the operator
else:
d = -(g *
operator).trace()[0, 0].imag # assume it is a matrix
fo.write(str(d) + " ") # write in a file
fo.write("\n") # next line
fo.flush() # flush
fo.close()