def graphene():
dCC = param.GRAPHENE_CC_DISTANCE
res = xyz.sheet([[.75**.5*dCC,1.5*dCC,0],[-.75**.5*dCC,1.5*dCC,0]])
res.atoms.extend([
xyz.atom('C',(0.,.5*dCC,0.),eye(3)),
xyz.atom('C',(0.,-.5*dCC,0.),eye(3)),
])
return res
def graphene_supercell(M,N):
assert M >= 0 and N >= 0
d_CC = param.GRAPHENE_CC_DISTANCE
a = d_CC * 3**.5 # length of a graphene lattice vector
l_x = a * (M**2 + N**2 + M*N)**0.5 # circumference of the tube
# rho = l_circ / (2*pi) # radius of the tube
Q = gcd(M+2*N,2*M+N)
l_y = a * (3.0 * (M**2 + N**2 + M*N))**0.5 / Q # length of one unit cell
N_atoms = 4 * (M**2 + N**2 + M*N) / Q # number of atoms per unit cell
M_perp = (M+2*N) / Q # periodic vector in lattice coordinates
N_perp = - (2*M+N) / Q #
# graphene lattice vectors in real coordinates (x,y):
a_1 = array([l_x*N_perp , -l_y*N]) / (M*N_perp - M_perp*N)
a_2 = array([l_x*M_perp , -l_y*M]) / (N*M_perp - N_perp*M)
res = xyz.sheet([[l_x,0,0],[0,l_y,0]])
coords = []
for i in range(0,M+N):
# integer division always rounds to lower value (i.e.: (a/b)*b <= a )
# we need to round up, so we do -((-a)/b)
j_min = -((-(i*M))/(M+N))
assert (j_min-1) * (M+N) < i*M <= j_min * (M+N)
j_max = -((-(i*M + M_perp*N - M*N_perp))/(M+N))
assert (j_max-1) * (M+N) < (i*M + M_perp*N - M*N_perp) <= j_max * (M+N)
for j in range(j_min,j_max):
for offset in [(a_1 + a_2)/3,(a_1 + a_2)*2/3]:
x,y = j*a_1 + (i-j)*a_2 + offset
x %= l_x
y %= l_y
res.atoms.extend([
xyz.atom('C',(x,y,0),eye(3)),
])
assert len(res.atoms) == N_atoms
return res