class STM:
def __init__(self,
h1,
s1,
h2,
s2,
h10,
s10,
h20,
s20,
eta1,
eta2,
w=0.5,
pdos=[],
logfile=None):
"""XXX
1. Tip
2. Surface
h1: ndarray
Hamiltonian and overlap matrix for the isolated tip
calculation. Note, h1 should contain (at least) one
principal layer.
h2: ndarray
Same as h1 but for the surface.
h10: ndarray
periodic part of the tip. must include two and only
two principal layers.
h20: ndarray
same as h10, but for the surface
The s* are the corresponding overlap matrices. eta1, and eta
2 are (finite) infinitesimals. """
self.pl1 = len(h10) // 2 #principal layer size for the tip
self.pl2 = len(h20) // 2 #principal layer size for the surface
self.h1 = h1
self.s1 = s1
self.h2 = h2
self.s2 = s2
self.h10 = h10
self.s10 = s10
self.h20 = h20
self.s20 = s20
self.eta1 = eta1
self.eta2 = eta2
self.w = w #asymmetry of the applied bias (0.5=>symmetric)
self.pdos = []
self.log = logfile
def initialize(self, energies, bias=0):
"""
energies: list of energies
for which the transmission function should be evaluated.
bias.
Will precalculate the surface greenfunctions of the tip and
surface.
"""
self.bias = bias
self.energies = energies
nenergies = len(energies)
pl1, pl2 = self.pl1, self.pl2
nbf1, nbf2 = len(self.h1), len(self.h2)
#periodic part of the tip
hs1_dii = self.h10[:pl1, :pl1], self.s10[:pl1, :pl1]
hs1_dij = self.h10[:pl1, pl1:2 * pl1], self.s10[:pl1, pl1:2 * pl1]
#coupling betwen per. and non. per part of the tip
h1_im = np.zeros((pl1, nbf1), complex)
s1_im = np.zeros((pl1, nbf1), complex)
h1_im[:pl1, :pl1], s1_im[:pl1, :pl1] = hs1_dij
hs1_dim = [h1_im, s1_im]
#periodic part the surface
hs2_dii = self.h20[:pl2, :pl2], self.s20[:pl2, :pl2]
hs2_dij = self.h20[pl2:2 * pl2, :pl2], self.s20[pl2:2 * pl2, :pl2]
#coupling betwen per. and non. per part of the surface
h2_im = np.zeros((pl2, nbf2), complex)
s2_im = np.zeros((pl2, nbf2), complex)
h2_im[-pl2:, -pl2:], s2_im[-pl2:, -pl2:] = hs2_dij
hs2_dim = [h2_im, s2_im]
#tip and surface greenfunction
self.selfenergy1 = LeadSelfEnergy(hs1_dii, hs1_dij, hs1_dim, self.eta1)
self.selfenergy2 = LeadSelfEnergy(hs2_dii, hs2_dij, hs2_dim, self.eta2)
self.greenfunction1 = GreenFunction(
self.h1 - self.bias * self.w * self.s1, self.s1,
[self.selfenergy1], self.eta1)
self.greenfunction2 = GreenFunction(
self.h2 - self.bias * (self.w - 1) * self.s2, self.s2,
[self.selfenergy2], self.eta2)
#Shift the bands due to the bias.
bias_shift1 = -bias * self.w
bias_shift2 = -bias * (self.w - 1)
self.selfenergy1.set_bias(bias_shift1)
self.selfenergy2.set_bias(bias_shift2)
#tip and surface greenfunction matrices.
nbf1_small = nbf1 #XXX Change this for efficiency in the future
nbf2_small = nbf2 #XXX -||-
coupling_list1 = range(nbf1_small) # XXX -||-
coupling_list2 = range(nbf2_small) # XXX -||-
self.gft1_emm = np.zeros((nenergies, nbf1_small, nbf1_small), complex)
self.gft2_emm = np.zeros((nenergies, nbf2_small, nbf2_small), complex)
for e, energy in enumerate(self.energies):
if self.log != None: # and world.rank == 0:
T = time.localtime()
self.log.write(' %d:%02d:%02d, ' % (T[3], T[4], T[5]) +
'%d, %d, %02f\n' % (world.rank, e, energy))
gft1_mm = self.greenfunction1.retarded(energy)[coupling_list1]
gft1_mm = np.take(gft1_mm, coupling_list1, axis=1)
gft2_mm = self.greenfunction2.retarded(energy)[coupling_list2]
gft2_mm = np.take(gft2_mm, coupling_list2, axis=1)
self.gft1_emm[e] = gft1_mm
self.gft2_emm[e] = gft2_mm
if self.log != None and world.rank == 0:
self.log.flush()
def get_transmission(self, v_12, v_11_2=None, v_22_1=None):
"""XXX
v_12:
coupling between tip and surface
v_11_2:
correction to "on-site" tip elements due to the
surface (eq.16). Is only included to first order.
v_22_1:
corretion to "on-site" surface elements due to he
tip (eq.17). Is only included to first order.
"""
dim0 = v_12.shape[0]
dim1 = v_12.shape[1]
nenergies = len(self.energies)
T_e = np.empty(nenergies, float)
v_21 = dagger(v_12)
for e, energy in enumerate(self.energies):
gft1 = self.gft1_emm[e]
if v_11_2 != None:
gf1 = np.dot(v_11_2, np.dot(gft1, v_11_2))
gf1 += gft1 #eq. 16
else:
gf1 = gft1
gft2 = self.gft2_emm[e]
if v_22_1 != None:
gf2 = np.dot(v_22_1, np.dot(gft2, v_22_1))
gf2 += gft2 #eq. 17
else:
gf2 = gft2
a1 = (gf1 - dagger(gf1))
a2 = (gf2 - dagger(gf2))
self.v_12 = v_12
self.a2 = a2
self.v_21 = v_21
self.a1 = a1
v12_a2 = np.dot(v_12, a2[:dim1])
v21_a1 = np.dot(v_21, a1[-dim0:])
self.v12_a2 = v12_a2
self.v21_a1 = v21_a1
T = -np.trace(np.dot(v12_a2[:, :dim1], v21_a1[:, -dim0:])) #eq. 11
assert abs(T.imag).max() < 1e-14
T_e[e] = T.real
self.T_e = T_e
return T_e
def get_current(self, bias, v_12, v_11_2=None, v_22_1=None):
"""Very simple function to calculate the current.
Asummes zero temperature.
bias: type? XXX
bias voltage (V)
v_12: XXX
coupling between tip and surface.
v_11_2:
correction to onsite elements of the tip
due to the potential of the surface.
v_22_1:
correction to onsite elements of the surface
due to the potential of the tip.
"""
energies = self.energies
T_e = self.get_transmission(v_12, v_11_2, v_22_1)
bias_window = -np.array([bias * self.w, bias * (self.w - 1)])
bias_window.sort()
self.bias_window = bias_window
#print 'bias window', np.around(bias_window,3)
#print 'Shift of tip lead do to the bias:', self.selfenergy1.bias
#print 'Shift of surface lead do to the bias:', self.selfenergy2.bias
i1 = sum(energies < bias_window[0])
i2 = sum(energies < bias_window[1])
step = 1
if i2 < i1:
step = -1
return np.sign(bias) * np.trapz(x=energies[i1:i2:step],
y=T_e[i1:i2:step])
class STM:
def __init__(self, h1, s1, h2, s2, h10, s10, h20, s20, eta1, eta2, w=0.5):
"""XXX
1. Tip
2. Surface
h1: ndarray
Hamiltonian and overlap matrix for the isolated tip
calculation. Note, h1 should contain (at least) one
principal layer.
h2: ndarray
Same as h1 but for the surface.
h10: ndarray
periodic part of the tip. must include two and only
two principal layers.
h20: ndarray
same as h10, but for the surface
The s* are the corresponding overlap matrices. eta1, and eta
2 are (finite) infinitesimals. """
self.pl1 = len(h10) / 2 # principal layer size for the tip
self.pl2 = len(h20) / 2 # principal layer size for the surface
self.h1 = h1
self.s1 = s1
self.h2 = h2
self.s2 = s2
self.h10 = h10
self.s10 = s10
self.h20 = h20
self.s20 = s20
self.eta1 = eta1
self.eta2 = eta2
self.w = w # asymmetry of the applied bias (0.5=>symmetric)
def initialize(self, energies, bias=0):
"""
energies: list of energies
for which the transmission function should be evaluated.
bias.
Will precalculate the surface greenfunctions of the tip and
surface.
"""
self.bias = bias
self.energies = energies
nenergies = len(energies)
pl1, pl2 = self.pl1, self.pl2
nbf1, nbf2 = len(self.h1), len(self.h2)
# periodic part of the tip
hs1_dii = self.h10[:pl1, :pl1], self.s10[:pl1, :pl1]
hs1_dij = self.h10[:pl1, pl1 : 2 * pl1], self.s10[:pl1, pl1 : 2 * pl1]
# coupling betwen per. and non. per part of the tip
h1_im = np.zeros((pl1, nbf1), complex)
s1_im = np.zeros((pl1, nbf1), complex)
h1_im[:pl1, :pl1], s1_im[:pl1, :pl1] = hs1_dij
hs1_dim = [h1_im, s1_im]
# periodic part the surface
hs2_dii = self.h20[:pl2, :pl2], self.s20[:pl2, :pl2]
hs2_dij = self.h20[pl2 : 2 * pl2, :pl2], self.s20[pl2 : 2 * pl2, :pl2]
# coupling betwen per. and non. per part of the surface
h2_im = np.zeros((pl2, nbf2), complex)
s2_im = np.zeros((pl2, nbf2), complex)
h2_im[-pl2:, -pl2:], s2_im[-pl2:, -pl2:] = hs2_dij
hs2_dim = [h2_im, s2_im]
# tip and surface greenfunction
self.selfenergy1 = LeadSelfEnergy(hs1_dii, hs1_dij, hs1_dim, self.eta1)
self.selfenergy2 = LeadSelfEnergy(hs2_dii, hs2_dij, hs2_dim, self.eta2)
self.greenfunction1 = GreenFunction(
self.h1 - self.bias * self.w * self.s1, self.s1, [self.selfenergy1], self.eta1
)
self.greenfunction2 = GreenFunction(
self.h2 - self.bias * (self.w - 1) * self.s2, self.s2, [self.selfenergy2], self.eta2
)
# Shift the bands due to the bias.
bias_shift1 = -bias * self.w
bias_shift2 = -bias * (self.w - 1)
self.selfenergy1.set_bias(bias_shift1)
self.selfenergy2.set_bias(bias_shift2)
# tip and surface greenfunction matrices.
nbf1_small = nbf1 # XXX Change this for efficiency in the future
nbf2_small = nbf2 # XXX -||-
coupling_list1 = range(nbf1_small) # XXX -||-
coupling_list2 = range(nbf2_small) # XXX -||-
self.gft1_emm = np.zeros((nenergies, nbf1_small, nbf1_small), complex)
self.gft2_emm = np.zeros((nenergies, nbf2_small, nbf2_small), complex)
for e, energy in enumerate(self.energies):
gft1_mm = self.greenfunction1.retarded(energy)[coupling_list1]
gft1_mm = np.take(gft1_mm, coupling_list1, axis=1)
gft2_mm = self.greenfunction2.retarded(energy)[coupling_list2]
gft2_mm = np.take(gft2_mm, coupling_list2, axis=1)
self.gft1_emm[e] = gft1_mm
self.gft2_emm[e] = gft2_mm
def get_transmission(self, v_12, v_11_2=None, v_22_1=None):
"""XXX
v_12:
coupling between tip and surface
v_11_2:
correction to "on-site" tip elements due to the
surface (eq.16). Is only included to first order.
v_22_1:
corretion to "on-site" surface elements due to he
tip (eq.17). Is only included to first order.
"""
dim0 = v_12.shape[0]
dim1 = v_12.shape[1]
nenergies = len(self.energies)
T_e = np.empty(nenergies, float)
v_21 = dagger(v_12)
for e, energy in enumerate(self.energies):
gft1 = self.gft1_emm[e]
if v_11_2 != None:
gf1 = np.dot(v_11_2, np.dot(gft1, v_11_2))
gf1 += gft1 # eq. 16
else:
gf1 = gft1
gft2 = self.gft2_emm[e]
if v_22_1 != None:
gf2 = np.dot(v_22_1, np.dot(gft2, v_22_1))
gf2 += gft2 # eq. 17
else:
gf2 = gft2
a1 = gf1 - dagger(gf1)
a2 = gf2 - dagger(gf2)
self.v_12 = v_12
self.a2 = a2
self.v_21 = v_21
self.a1 = a1
v12_a2 = np.dot(v_12, a2[:dim1])
v21_a1 = np.dot(v_21, a1[-dim0:])
self.v12_a2 = v12_a2
self.v21_a1 = v21_a1
T = -np.trace(np.dot(v12_a2[:, :dim1], v21_a1[:, -dim0:])) # eq. 11
T_e[e] = T
self.T_e = T_e
return T_e
def get_current(self, bias, v_12, v_11_2=None, v_22_1=None):
"""Very simple function to calculate the current.
Asummes zero temperature.
bias: type? XXX
bias voltage (V)
v_12: XXX
coupling between tip and surface.
v_11_2:
correction to onsite elements of the tip
due to the potential of the surface.
v_22_1:
correction to onsite elements of the surface
due to the potential of the tip.
"""
energies = self.energies
T_e = self.get_transmission(v_12, v_11_2, v_22_1)
bias_window = -np.array([bias * self.w, bias * (self.w - 1)])
bias_window.sort()
self.bias_window = bias_window
# print 'bias window', np.around(bias_window,3)
# print 'Shift of tip lead do to the bias:', self.selfenergy1.bias
# print 'Shift of surface lead do to the bias:', self.selfenergy2.bias
i1 = sum(energies < bias_window[0])
i2 = sum(energies < bias_window[1])
step = 1
if i2 < i1:
step = -1
return np.sign(bias) * np.trapz(x=energies[i1:i2:step], y=T_e[i1:i2:step])
