def compute_group_velocities(self):
xarg = mp.cartesian_to_reciprocal(mp.Vector3(1), self.geometry_lattice)
vx = self.mode_solver.compute_group_velocity_component(xarg)
yarg = mp.cartesian_to_reciprocal(mp.Vector3(y=1), self.geometry_lattice)
vy = self.mode_solver.compute_group_velocity_component(yarg)
zarg = mp.cartesian_to_reciprocal(mp.Vector3(z=1), self.geometry_lattice)
vz = self.mode_solver.compute_group_velocity_component(zarg)
return [mp.Vector3(x, y, z) for x, y, z in zip(vx, vy, vz)]
def compute_group_velocities(self):
xarg = mp.cartesian_to_reciprocal(mp.Vector3(1), self.geometry_lattice)
vx = self.mode_solver.compute_group_velocity_component(xarg)
yarg = mp.cartesian_to_reciprocal(mp.Vector3(y=1), self.geometry_lattice)
vy = self.mode_solver.compute_group_velocity_component(yarg)
zarg = mp.cartesian_to_reciprocal(mp.Vector3(z=1), self.geometry_lattice)
vz = self.mode_solver.compute_group_velocity_component(zarg)
return [mp.Vector3(x, y, z) for x, y, z in zip(vx, vy, vz)]
def find_k(self, p, omega, band_min, band_max, korig_and_kdir, tol,
kmag_guess, kmag_min, kmag_max, *band_funcs):
num_bands_save = self.num_bands
kpoints_save = self.k_points
nb = band_max - band_min + 1
kdir = korig_and_kdir[1] if type(
korig_and_kdir) is list else korig_and_kdir
lat = self.geometry_lattice
kdir1 = mp.cartesian_to_reciprocal(
mp.reciprocal_to_cartesian(kdir, lat).unit(), lat)
if type(korig_and_kdir) is list:
korig = korig_and_kdir[0]
else:
korig = mp.Vector3()
# k0s is a list caching the best k value found for each band:
if type(kmag_guess) is list:
k0s = kmag_guess
else:
k0s = [kmag_guess] * (band_max - band_min + 1)
# dict to memoize all "band: k" results
bktab = {}
def rootfun(b):
def _rootfun(k):
# First, look in the cached table
tab_val = bktab.get((b, k), None)
if tab_val:
print("find-k {} at {}: {} (cached)".format(
b, k, tab_val[0]))
return tab_val
# Otherwise, compute bands and cache results
else:
self.num_bands = b
self.k_points = [korig + kdir1.scale(k)]
self.run_parity(p, False)
v = self.mode_solver.compute_group_velocity_component(
kdir1)
# Cache computed values
for _b, _f, _v in zip(range(band_min, b - band_min + 1,
1), self.freqs[band_min - 1:],
v[band_min - 1:]):
tabval = bktab.get((_b, k0s[_b - band_min]), None)
if not tabval or abs(_f - omega) < abs(tabval[0]):
k0s[_b - band_min + 1] = k
bktab[(_b, k)] = (_f - omega, _v)
fun = self.freqs[-1] - omega
print("find-k {} at {}: {}".format(b, k, fun))
return (fun, v[-1])
return _rootfun
# Don't let previous computations interfere
if self.mode_solver:
self.randomize_fields()
ks = []
for b in range(band_max, band_max - nb, -1):
ks.append(
mp.find_root_deriv(rootfun(b), tol, kmag_min, kmag_max,
k0s[b - band_min]))
if band_funcs:
for b, k in zip(range(1, band_max + 1), reversed(ks)):
self.num_bands = b
self.k_points = [korig + kdir1.scale(k)]
def bfunc(ms, b_prime):
if b_prime == b:
for f in band_funcs:
apply_band_func_thunk(ms, f, b, True)
self.run_parity(p, False, bfunc)
self.num_bands = num_bands_save
self.k_points = kpoints_save
ks = list(reversed(ks))
print("{}kvals:, {}, {}, {}".format(self.parity, omega, band_min,
band_max),
end='')
for k in korig:
print(", {}".format(k), end='')
for k in kdir1:
print(", {}".format(k), end='')
for k in ks:
print(", {}".format(k), end='')
print()
return ks
## Limites IBZ REPERE RECIPROQUE
k_point_gamma = mp.Vector3(0, 0)
k_point_M_rec = mp.Vector3(1 / 2, 1 / 2)
k_point_K_rec = mp.Vector3(1 / 2, 0)
k_point_K_cart = mp.Vector3(math.sqrt(2) / 2, 0)
k_point_M_cart = mp.Vector3(math.sqrt(2) / 4, math.sqrt(2) / 4)
dk_x = (math.sqrt(2) / 2) / (nbr_points_x + 1)
dk_y = (math.sqrt(2) / 4) / (nbr_points_y + 1)
seg = []
for j in range(0, nbr_points_y + 2):
k_point_gamma_dk_cart = k_point_gamma + mp.Vector3(0, j * dk_y)
k_point_K_dk_cart = k_point_K_cart + mp.Vector3(0, j * dk_y)
k_point_gamma_dk_rec = mp.cartesian_to_reciprocal(k_point_gamma_dk_cart,
geometry_lattice)
k_point_K_dk_rec = mp.cartesian_to_reciprocal(k_point_K_dk_cart,
geometry_lattice)
seg_temp = mp.interpolate(nbr_points_x,
[k_point_gamma_dk_rec, k_point_K_dk_rec])
seg = seg + seg_temp
def outputgv(ms):
global gv
gv.append(ms.compute_group_velocities())
gv = []
ms = mpb.ModeSolver()
def find_k(self, p, omega, band_min, band_max, korig_and_kdir, tol,
kmag_guess, kmag_min, kmag_max, *band_funcs):
num_bands_save = self.num_bands
kpoints_save = self.k_points
nb = band_max - band_min + 1
kdir = korig_and_kdir[1] if type(korig_and_kdir) is list else korig_and_kdir
lat = self.geometry_lattice
kdir1 = mp.cartesian_to_reciprocal(mp.reciprocal_to_cartesian(kdir, lat).unit(), lat)
if type(korig_and_kdir) is list:
korig = korig_and_kdir[0]
else:
korig = mp.Vector3()
# k0s is a list caching the best k value found for each band:
if type(kmag_guess) is list:
k0s = kmag_guess
else:
k0s = [kmag_guess] * (band_max - band_min + 1)
# dict to memoize all "band: k" results
bktab = {}
def rootfun(b):
def _rootfun(k):
# First, look in the cached table
tab_val = bktab.get((b, k), None)
if tab_val:
print("find-k {} at {}: {} (cached)".format(b, k, tab_val[0]))
return tab_val
# Otherwise, compute bands and cache results
else:
self.num_bands = b
self.k_points = [korig + kdir1.scale(k)]
self.run_parity(p, False)
v = self.mode_solver.compute_group_velocity_component(kdir1)
# Cache computed values
for _b, _f, _v in zip(range(band_min, b - band_min + 1, 1),
self.freqs[band_min - 1:],
v[band_min - 1:]):
tabval = bktab.get((_b, k0s[_b - band_min]), None)
if not tabval or abs(_f - omega) < abs(tabval[0]):
k0s[_b - band_min + 1] = k
bktab[(_b, k)] = (_f - omega, _v)
fun = self.freqs[-1] - omega
print("find-k {} at {}: {}".format(b, k, fun))
return (fun, v[-1])
return _rootfun
# Don't let previous computations interfere
if self.mode_solver:
self.randomize_fields()
ks = []
for b in range(band_max, band_max - nb, -1):
ks.append(mp.find_root_deriv(rootfun(b), tol, kmag_min, kmag_max, k0s[b - band_min]))
if band_funcs:
for b, k in zip(range(band_max, band_max - nb, -1), reversed(ks)):
self.num_bands = b
self.k_points = [korig + kdir1.scale(k)]
def bfunc(ms, b_prime):
if b_prime == b:
for f in band_funcs:
apply_band_func_thunk(ms, f, b, True)
self.run_parity(p, False, bfunc)
self.num_bands = num_bands_save
self.k_points = kpoints_save
ks = list(reversed(ks))
print("{}kvals:, {}, {}, {}".format(self.parity, omega, band_min, band_max), end='')
for k in korig:
print(", {}".format(k), end='')
for k in kdir1:
print(", {}".format(k), end='')
for k in ks:
print(", {}".format(k), end='')
print()
return ks
