def get_geometry(name="square",
n=5,
nedges=None,
rot=0.,
clean=True,
geo=None,
shift=[0., 0., 0.]):
""" Create a 0d island"""
lattice_name = name
if lattice_name == "honeycomb":
geometry_builder = geometry.honeycomb_lattice
if nedges == None: nedges = 6
elif lattice_name == "square":
geometry_builder = geometry.square_lattice
if nedges == None: nedges = 4
elif lattice_name == "kagome":
geometry_builder = geometry.kagome_lattice
if nedges == None: nedges = 3
elif lattice_name == "lieb":
geometry_builder = geometry.lieb_lattice
if nedges == None: nedges = 4
elif lattice_name == "triangular":
geometry_builder = geometry.triangular_lattice
if nedges == None: nedges = 3
else: raise
# first create a raw unit cell
if geo is not None:
print("Geometry generator taken from input")
g = geo # builder is input geometry
else:
g = geometry_builder() # build a 2d unit cell
nf = float(n) # get the desired size, in float
g = g.supercell(int(7 * n)) # create supercell
g.set_finite() # set as finite system
g.center() # center the geometry
# now scuplt the geometry
g = sculpt.rotate(g, rot) # initial rotation
# now shift the lattice
g.x += shift[0]
g.y += shift[1]
g.z += shift[2]
g.xyz2r()
def f(x, y):
return x > -nf * (np.cos(np.pi / 3) + 1.) # function to use as cut
for i in range(nedges): # loop over rotations, 60 degrees
g = sculpt.intersec(g, f) # retain certain atoms
g = sculpt.rotate(g, 2. * np.pi / nedges) # rotate 60 degrees
if clean: # if it is cleaned
g = sculpt.remove_unibonded(g) # remove single bonded atoms
g = sculpt.remove_unibonded(g) # remove single bonded atoms
g.center() # center the geometry
return g
def get_geometry(name="square",n=5,nedges=None,rot=0.,clean=True):
""" Create a 0d island"""
lattice_name = name
if lattice_name=="honeycomb":
geometry_builder = geometry.honeycomb_lattice
if nedges==None: nedges = 6
elif lattice_name=="square":
geometry_builder = geometry.square_lattice
if nedges==None: nedges = 4
elif lattice_name=="kagome":
geometry_builder = geometry.kagome_lattice
if nedges==None: nedges = 3
elif lattice_name=="lieb":
geometry_builder = geometry.lieb_lattice
if nedges==None: nedges = 4
elif lattice_name=="triangular":
geometry_builder = geometry.triangular_lattice
if nedges==None: nedges = 3
else: raise
# first create a raw unit cell
g = geometry_builder() # build a 2d unit cell
nf = float(n) # get the desired size, in float
g = g.supercell(7*n) # create supercell
g.set_finite() # set as finite system
g.center() # center the geometry
# now scuplt the geometry
g = sculpt.rotate(g,rot) # initial rotation
def f(x,y): return x>-nf*(np.cos(np.pi/3)+1.) # function to use as cut
for i in range(nedges): # loop over rotations, 60 degrees
g = sculpt.intersec(g,f) # retain certain atoms
g = sculpt.rotate(g,2.*np.pi/nedges) # rotate 60 degrees
if clean: # if it is cleaned
g = sculpt.remove_unibonded(g) # remove single bonded atoms
g.center() # center the geometry
return g
def generate_mullen_surface(nx,ny):
"""Generate a Mullen surface, return bulk hamiltonian and surface cell"""
g = geometry.honeycomb_lattice_zigzag_cell()
g = g.supercell([2*nx+2+1,1]) # two dimensional
gb = g.copy() # copy geometry
g.dimensionality = 1 # reduce dimensionality
g = sculpt.remove_unibonded(g)
gb = sculpt.remove_unibonded(gb)
g.center()
gb.center()
# now add the hexagon
dy = max(g.y) + 1.9
dx = 0.
xx = np.array([dx,0.,0.])
g.r = [ri+xx for ri in g.r] # displace whole
r1 = np.array([-1.,0.+dy,0.])
r2 = np.array([1.,0.+dy,0.])
r3 = np.array([.5,np.sqrt(3.0)/2.+dy,0.])
r4 = np.array([-.5,np.sqrt(3.0)/2.+dy,0.])
r5 = np.array([.5,-np.sqrt(3.0)/2.+dy,0.])
r6 = np.array([-.5,-np.sqrt(3.0)/2.+dy,0.])
g.r = [ri for ri in g.r] + [r1,r2,r3,r4,r5,r6] # upper
g.r = np.array(g.r)
g.r2xyz()
g.write()
h = g.get_hamiltonian() # initialize hamiltonian
def funh(ri,rj):
dr = ri-rj
if .1<dr.dot(dr)<1.3: return 1.0
else: return 0.0
h = hamiltonians.generate_parametric_hopping(h,funh)
h.remove_spin() # remove spin degree of freedom
hb = gb.get_hamiltonian() # bulk hamiltonian
hb.remove_spin() # remove spin
return (h,hb)
def generate_mullen_surface(nx, ny):
"""Generate a Mullen surface, return bulk hamiltonian and surface cell"""
g = geometry.honeycomb_lattice_zigzag_cell()
g = g.supercell([2 * nx + 2 + 1, 1]) # two dimensional
gb = g.copy() # copy geometry
g.dimensionality = 1 # reduce dimensionality
g = sculpt.remove_unibonded(g)
gb = sculpt.remove_unibonded(gb)
g.center()
gb.center()
# now add the hexagon
dy = max(g.y) + 1.9
dx = 0.
xx = np.array([dx, 0., 0.])
g.r = [ri + xx for ri in g.r] # displace whole
r1 = np.array([-1., 0. + dy, 0.])
r2 = np.array([1., 0. + dy, 0.])
r3 = np.array([.5, np.sqrt(3.0) / 2. + dy, 0.])
r4 = np.array([-.5, np.sqrt(3.0) / 2. + dy, 0.])
r5 = np.array([.5, -np.sqrt(3.0) / 2. + dy, 0.])
r6 = np.array([-.5, -np.sqrt(3.0) / 2. + dy, 0.])
g.r = [ri for ri in g.r] + [r1, r2, r3, r4, r5, r6] # upper
g.r = np.array(g.r)
g.r2xyz()
g.write()
h = g.get_hamiltonian() # initialize hamiltonian
def funh(ri, rj):
dr = ri - rj
if .1 < dr.dot(dr) < 1.3: return 1.0
else: return 0.0
h = hamiltonians.generate_parametric_hopping(h, funh)
h.remove_spin() # remove spin degree of freedom
hb = gb.get_hamiltonian() # bulk hamiltonian
hb.remove_spin() # remove spin
return (h, hb)
def generate_pentagon_island(nx,ny,pentagons=[0]):
"""Generate a Mullen island"""
g = geometry.honeycomb_zigzag_ribbon(ny)
g = g.supercell(2*nx+1)
g.dimensionality = 0
minx = np.min(g.x)
def finite(x,y):
if x<minx+.1: return False
return True
g = sculpt.intersec(g,finite)
g = sculpt.remove_unibonded(g)
g.center()
# now add the hexagon
dy = max(g.y) + 1.9
ym = max(g.y) # position of zigzag atoms
xz = [] # list of zigzag atoms
for ir in g.r: # loop over atoms
if (ir[1]-ym)<0.1: xz.append(ir[0]) # store upper zigzag atom
for ip in pentagons: # loop over pentagons
# generate positions
r1 = np.array([-1.+dx,0.+dy,0.])
r2 = np.array([1.+dx,0.+dy,0.])
r3 = np.array([.5+dx,np.sqrt(3.0)/2.+dy,0.])
r4 = np.array([-.5+dx,np.sqrt(3.0)/2.+dy,0.])
r5 = np.array([.5+dx,-np.sqrt(3.0)/2.+dy,0.])
r6 = np.array([-.5+dx,-np.sqrt(3.0)/2.+dy,0.])
# add the extra hexagons
g.r = [ri for ri in g.r] + [r1,r2,r3,r4,r5,r6]
g.r = [ri for ri in g.r] + [-r1,-r2,-r3,-r4,-r5,-r6]
#g.r = [r1,r2,r3,r4,r5,r6]
g.r = np.array(g.r)
g.r2xyz()
g.write()
h = g.get_hamiltonian() # initialize hamiltonian
def funh(ri,rj):
dr = ri-rj
if .1<dr.dot(dr)<1.3: return 1.0
else: return 0.0
h = hamiltonians.generate_parametric_hopping(h,funh)
return h
def generate_pentagon_island(nx, ny, pentagons=[0]):
"""Generate a Mullen island"""
g = geometry.honeycomb_zigzag_ribbon(ny)
g = g.supercell(2 * nx + 1)
g.dimensionality = 0
minx = np.min(g.x)
def finite(x, y):
if x < minx + .1: return False
return True
g = sculpt.intersec(g, finite)
g = sculpt.remove_unibonded(g)
g.center()
# now add the hexagon
dy = max(g.y) + 1.9
ym = max(g.y) # position of zigzag atoms
xz = [] # list of zigzag atoms
for ir in g.r: # loop over atoms
if (ir[1] - ym) < 0.1: xz.append(ir[0]) # store upper zigzag atom
for ip in pentagons: # loop over pentagons
# generate positions
r1 = np.array([-1. + dx, 0. + dy, 0.])
r2 = np.array([1. + dx, 0. + dy, 0.])
r3 = np.array([.5 + dx, np.sqrt(3.0) / 2. + dy, 0.])
r4 = np.array([-.5 + dx, np.sqrt(3.0) / 2. + dy, 0.])
r5 = np.array([.5 + dx, -np.sqrt(3.0) / 2. + dy, 0.])
r6 = np.array([-.5 + dx, -np.sqrt(3.0) / 2. + dy, 0.])
# add the extra hexagons
g.r = [ri for ri in g.r] + [r1, r2, r3, r4, r5, r6]
g.r = [ri for ri in g.r] + [-r1, -r2, -r3, -r4, -r5, -r6]
#g.r = [r1,r2,r3,r4,r5,r6]
g.r = np.array(g.r)
g.r2xyz()
g.write()
h = g.get_hamiltonian() # initialize hamiltonian
def funh(ri, rj):
dr = ri - rj
if .1 < dr.dot(dr) < 1.3: return 1.0
else: return 0.0
h = hamiltonians.generate_parametric_hopping(h, funh)
return h
def generate_mullen_island(nx,ny,pristine=False):
"""Generate a Mullen island"""
g = geometry.honeycomb_zigzag_ribbon(ny)
g = g.supercell(2*nx+1+2)
g.dimensionality = 0
minx = np.min(g.x)
def finite(x,y):
if x<minx+.1: return False
return True
g = sculpt.intersec(g,finite)
g = sculpt.remove_unibonded(g)
g.center()
# now add the hexagon
dy = max(g.y) + 1.9
r1 = np.array([-1.,0.+dy,0.])
r2 = np.array([1.,0.+dy,0.])
r3 = np.array([.5,np.sqrt(3.0)/2.+dy,0.])
r4 = np.array([-.5,np.sqrt(3.0)/2.+dy,0.])
r5 = np.array([.5,-np.sqrt(3.0)/2.+dy,0.])
r6 = np.array([-.5,-np.sqrt(3.0)/2.+dy,0.])
if not pristine:
g.r = [ri for ri in g.r] + [r1,r2,r3,r4,r5,r6]
g.r = [ri for ri in g.r] + [-r1,-r2,-r3,-r4,-r5,-r6]
#g.r = [r1,r2,r3,r4,r5,r6]
g.r = np.array(g.r)
g.r2xyz()
g.write()
h = g.get_hamiltonian() # initialize hamiltonian
def funh(ri,rj):
dr = ri-rj
if .1<dr.dot(dr)<1.3: return 1.0
else: return 0.0
h = hamiltonians.generate_parametric_hopping(h,funh)
return h
def generate_mullen_island(nx, ny, pristine=False):
"""Generate a Mullen island"""
g = geometry.honeycomb_zigzag_ribbon(ny)
g = g.supercell(2 * nx + 1 + 2)
g.dimensionality = 0
minx = np.min(g.x)
def finite(x, y):
if x < minx + .1: return False
return True
g = sculpt.intersec(g, finite)
g = sculpt.remove_unibonded(g)
g.center()
# now add the hexagon
dy = max(g.y) + 1.9
r1 = np.array([-1., 0. + dy, 0.])
r2 = np.array([1., 0. + dy, 0.])
r3 = np.array([.5, np.sqrt(3.0) / 2. + dy, 0.])
r4 = np.array([-.5, np.sqrt(3.0) / 2. + dy, 0.])
r5 = np.array([.5, -np.sqrt(3.0) / 2. + dy, 0.])
r6 = np.array([-.5, -np.sqrt(3.0) / 2. + dy, 0.])
if not pristine:
g.r = [ri for ri in g.r] + [r1, r2, r3, r4, r5, r6]
g.r = [ri for ri in g.r] + [-r1, -r2, -r3, -r4, -r5, -r6]
#g.r = [r1,r2,r3,r4,r5,r6]
g.r = np.array(g.r)
g.r2xyz()
g.write()
h = g.get_hamiltonian() # initialize hamiltonian
def funh(ri, rj):
dr = ri - rj
if .1 < dr.dot(dr) < 1.3: return 1.0
else: return 0.0
h = hamiltonians.generate_parametric_hopping(h, funh)
return h
def clean(self, iterative=False):
return sculpt.remove_unibonded(self, iterative=iterative)
#g = geometry.square_lattice() # create a honeycomb lattice
#g = geometry.kagome_lattice() # create a honeycomb lattice
g = g.supercell(50) # create supercell
g.set_finite()
# create a hexagonal island
def f(x,y):
""" Retain a plane"""
return x>-3*(np.cos(np.pi/3)+1.)
#g = sculpt.rotate(g,np.pi/3.)
nedges = 3
for j in range(1):
for i in range(nedges): # loop over rotations
g = sculpt.intersec(g,f) # retain certain atoms
g = sculpt.rotate(g,2.*np.pi/nedges)
g.center()
g = sculpt.remove_unibonded(g)
h = g.get_hamiltonian()
hamiltonians.ldos(h,e=0.0)
g.write()
def clean(self): return sculpt.remove_unibonded(self)