def calcTraces(options, GF1, GF2, basis, NCfile, ihw):
# Calculate various traces over the electronic structure
# Electron-phonon couplings
ihw = int(ihw)
M = N.array(NCfile.variables['He_ph'][ihw, options.iSpin, :, :], N.complex)
try:
M += 1.j * N.array(
NCfile.variables['ImHe_ph'][ihw, options.iSpin, :, :], N.complex)
except:
print 'Warning: Variable ImHe_ph not found'
# Calculation of intermediate quantity
MARGLGM = MM.mm(M, GF1.ARGLG, M)
MARGLGM2 = MM.mm(M, GF2.ARGLG, M)
# LOE expressions in compact form
t1 = MM.mm(MARGLGM, GF2.AR)
t2 = MM.mm(MARGLGM2, GF1.AL)
# Note that compared with Eq. (10) of PRB89, 081405 (2014) we here use
# the definition B_lambda = MM.trace(t1-dagger(t2)), which in turn gives
# ReB = MM.trace(t1).real-MM.trace(t2).real
# ImB = MM.trace(t1).imag+MM.trace(t2).imag
K23 = MM.trace(t1).imag + MM.trace(t2).imag
K4 = MM.trace(MM.mm(M, GF1.ALT, M, GF2.AR))
aK23 = 2 * (MM.trace(t1).real - MM.trace(t2).real) # asymmetric part
# Non-Hilbert term defined here with a minus sign
GF1.nHT[ihw] = NEGF.AssertReal(K23 + K4, 'nHT[%i]' % ihw)
GF1.HT[ihw] = NEGF.AssertReal(aK23, 'HT[%i]' % ihw)
# Power, damping and current rates
GF1.P1T[ihw] = NEGF.AssertReal(MM.trace(MM.mm(M, GF1.A, M, GF2.A)),
'P1T[%i]' % ihw)
GF1.P2T[ihw] = NEGF.AssertReal(MM.trace(MM.mm(M, GF1.AL, M, GF2.AR)),
'P2T[%i]' % ihw)
GF1.ehDampL[ihw] = NEGF.AssertReal(MM.trace(MM.mm(M, GF1.AL, M, GF2.AL)),
'ehDampL[%i]' % ihw)
GF1.ehDampR[ihw] = NEGF.AssertReal(MM.trace(MM.mm(M, GF1.AR, M, GF2.AR)),
'ehDampR[%i]' % ihw)
# Remains from older version (see before rev. 219):
#GF.dGnout.append(EC.calcCurrent(options,basis,GF.HNO,mm(Us,-0.5j*(tmp1-dagger(tmp1)),Us)))
#GF.dGnin.append(EC.calcCurrent(options,basis,GF.HNO,mm(Us,mm(G,MA1M,Gd)-0.5j*(tmp2-dagger(tmp2)),Us)))
# NB: TF Should one use GF.HNO (nonorthogonal) or GF.H (orthogonalized) above?
if options.LOEscale == 0.0:
# Check against original LOE-WBA formulation
isym1 = MM.mm(GF1.ALT, M, GF2.AR, M)
isym2 = MM.mm(MM.dagger(GF1.ARGLG), M, GF2.A, M)
isym3 = MM.mm(GF1.ARGLG, M, GF2.A, M)
isym = MM.trace(isym1) + 1j / 2. * (MM.trace(isym2) - MM.trace(isym3))
print 'LOE-WBA check: Isym diff', K23 + K4 - isym
iasym1 = MM.mm(MM.dagger(GF1.ARGLG), M, GF2.AR - GF2.AL, M)
iasym2 = MM.mm(GF1.ARGLG, M, GF2.AR - GF2.AL, M)
iasym = MM.trace(iasym1) + MM.trace(iasym2)
print 'LOE-WBA check: Iasym diff', aK23 - iasym
# Compute inelastic shot noise terms according to the papers
# Haupt, Novotny & Belzig, PRB 82, 165441 (2010) and
# Avriller & Frederiksen, PRB 86, 155411 (2012)
# Zero-temperature limit
TT = MM.mm(GF1.GammaL,
GF1.AR) # this matrix has the correct shape for MM
ReGr = (GF1.Gr + GF1.Ga) / 2.
tmp = MM.mm(GF1.Gr, M, ReGr, M, GF1.AR)
tmp = tmp + MM.dagger(tmp)
Tlambda0 = MM.mm(GF1.GammaL, tmp)
tmp1 = MM.mm(M, GF1.AR, M)
tmp2 = MM.mm(M, GF1.A, M, GF1.Gr, GF1.GammaR)
tmp = tmp1 + 1j / 2. * (MM.dagger(tmp2) - tmp2)
Tlambda1 = MM.mm(GF1.GammaL, GF1.Gr, tmp, GF1.Ga)
MARGL = MM.mm(M, GF1.AR, GF1.GammaL)
tmp1 = MM.mm(MARGL, GF1.AR, M)
tmp2 = MM.mm(MARGL, GF1.Gr, M, GF1.Gr, GF1.GammaR)
tmp = tmp1 + tmp2
tmp = tmp + MM.dagger(tmp)
Qlambda = MM.mm(-GF1.Ga, GF1.GammaL, GF1.Gr, tmp)
tmp = -2 * TT
OneMinusTwoT = tmp + N.identity(len(GF1.GammaL))
# Store relevant traces
GF1.dIel[ihw] = NEGF.AssertReal(MM.trace(Tlambda0), 'dIel[%i]' % ihw)
GF1.dIinel[ihw] = NEGF.AssertReal(MM.trace(Tlambda1),
'dIinel[%i]' % ihw)
GF1.dSel[ihw] = NEGF.AssertReal(
MM.trace(MM.mm(OneMinusTwoT, Tlambda0)), 'dSel[%i]' % ihw)
GF1.dSinel[ihw] = NEGF.AssertReal(
MM.trace(Qlambda + MM.mm(OneMinusTwoT, Tlambda1)),
'dSinel[%i]' % ihw)
def main(options):
"""
Main routine to compute inelastic transport characteristics (dI/dV, d2I/dV2, IETS etc)
Parameters
----------
options : an ``options`` instance
"""
CF.CreatePipeOutput(options.DestDir + '/' + options.Logfile)
VC.OptionsCheck(options, 'Inelastica')
CF.PrintMainHeader('Inelastica', options)
options.XV = '%s/%s.XV' % (options.head, options.systemlabel)
options.geom = MG.Geom(options.XV, BufferAtoms=options.buffer)
# Voltage fraction over left-center interface
VfracL = options.VfracL # default is 0.5
print 'Inelastica: Voltage fraction over left-center interface: VfracL =', VfracL
# Set up electrodes and device Greens function
elecL = NEGF.ElectrodeSelfEnergy(options.fnL, options.NA1L, options.NA2L,
options.voltage * VfracL)
elecL.scaling = options.scaleSigL
elecL.semiinf = options.semiinfL
elecR = NEGF.ElectrodeSelfEnergy(options.fnR, options.NA1R, options.NA2R,
options.voltage * (VfracL - 1.))
elecR.scaling = options.scaleSigR
elecR.semiinf = options.semiinfR
# Read phonons
NCfile = NC4.Dataset(options.PhononNetCDF, 'r')
print 'Inelastica: Reading ', options.PhononNetCDF
hw = NCfile.variables['hw'][:]
# Work with GFs etc for positive (V>0: \mu_L>\mu_R) and negative (V<0: \mu_L<\mu_R) bias voltages
GFp = NEGF.GF(options.TSHS,
elecL,
elecR,
Bulk=options.UseBulk,
DeviceAtoms=options.DeviceAtoms,
BufferAtoms=options.buffer)
# Prepare lists for various trace factors
#GF.dGnout = []
#GF.dGnin = []
GFp.P1T = N.zeros(len(hw), N.float) # M.A.M.A (total e-h damping)
GFp.P2T = N.zeros(len(hw), N.float) # M.AL.M.AR (emission)
GFp.ehDampL = N.zeros(len(hw), N.float) # M.AL.M.AL (L e-h damping)
GFp.ehDampR = N.zeros(len(hw), N.float) # M.AR.M.AR (R e-h damping)
GFp.nHT = N.zeros(len(hw), N.float) # non-Hilbert/Isym factor
GFp.HT = N.zeros(len(hw), N.float) # Hilbert/Iasym factor
GFp.dIel = N.zeros(len(hw), N.float)
GFp.dIinel = N.zeros(len(hw), N.float)
GFp.dSel = N.zeros(len(hw), N.float)
GFp.dSinel = N.zeros(len(hw), N.float)
#
GFm = NEGF.GF(options.TSHS,
elecL,
elecR,
Bulk=options.UseBulk,
DeviceAtoms=options.DeviceAtoms,
BufferAtoms=options.buffer)
GFm.P1T = N.zeros(len(hw), N.float) # M.A.M.A (total e-h damping)
GFm.P2T = N.zeros(len(hw), N.float) # M.AL.M.AR (emission)
GFm.ehDampL = N.zeros(len(hw), N.float) # M.AL.M.AL (L e-h damping)
GFm.ehDampR = N.zeros(len(hw), N.float) # M.AR.M.AR (R e-h damping)
GFm.nHT = N.zeros(len(hw), N.float) # non-Hilbert/Isym factor
GFm.HT = N.zeros(len(hw), N.float) # Hilbert/Iasym factor
GFm.dIel = N.zeros(len(hw), N.float)
GFm.dIinel = N.zeros(len(hw), N.float)
GFm.dSel = N.zeros(len(hw), N.float)
GFm.dSinel = N.zeros(len(hw), N.float)
# Calculate transmission at Fermi level
GFp.calcGF(options.energy + options.eta * 1.0j,
options.kpoint[0:2],
ispin=options.iSpin,
etaLead=options.etaLead,
useSigNCfiles=options.signc,
SpectralCutoff=options.SpectralCutoff)
L = options.bufferL
# Pad lasto with zeroes to enable basis generation...
lasto = N.zeros((GFp.HS.nua + L + 1, ), N.int)
lasto[L:] = GFp.HS.lasto
basis = SIO.BuildBasis(options.fn, options.DeviceAtoms[0] + L,
options.DeviceAtoms[1] + L, lasto)
basis.ii -= L
TeF = MM.trace(GFp.TT).real
GFp.TeF = TeF
GFm.TeF = TeF
# Check consistency of PHrun vs TSrun inputs
IntegrityCheck(options, GFp, basis, NCfile)
# Calculate trace factors one mode at a time
print 'Inelastica: LOEscale =', options.LOEscale
if options.LOEscale == 0.0:
# LOEscale=0.0 => Original LOE-WBA method, PRB 72, 201101(R) (2005) [cond-mat/0505473].
GFp.calcGF(options.energy + options.eta * 1.0j,
options.kpoint[0:2],
ispin=options.iSpin,
etaLead=options.etaLead,
useSigNCfiles=options.signc,
SpectralCutoff=options.SpectralCutoff)
GFm.calcGF(options.energy + options.eta * 1.0j,
options.kpoint[0:2],
ispin=options.iSpin,
etaLead=options.etaLead,
useSigNCfiles=options.signc,
SpectralCutoff=options.SpectralCutoff)
for ihw in (hw > options.modeCutoff).nonzero()[0]:
calcTraces(options, GFp, GFm, basis, NCfile, ihw)
calcTraces(options, GFm, GFp, basis, NCfile, ihw)
writeFGRrates(options, GFp, hw, NCfile)
else:
# LOEscale=1.0 => Generalized LOE, PRB 89, 081405(R) (2014) [arXiv:1312.7625]
for ihw in (hw > options.modeCutoff).nonzero()[0]:
GFp.calcGF(options.energy + hw[ihw] * options.LOEscale * VfracL +
options.eta * 1.0j,
options.kpoint[0:2],
ispin=options.iSpin,
etaLead=options.etaLead,
useSigNCfiles=options.signc,
SpectralCutoff=options.SpectralCutoff)
GFm.calcGF(options.energy + hw[ihw] * options.LOEscale *
(VfracL - 1.) + options.eta * 1.0j,
options.kpoint[0:2],
ispin=options.iSpin,
etaLead=options.etaLead,
useSigNCfiles=options.signc,
SpectralCutoff=options.SpectralCutoff)
calcTraces(options, GFp, GFm, basis, NCfile, ihw)
if VfracL != 0.5:
GFp.calcGF(options.energy - hw[ihw] * options.LOEscale *
(VfracL - 1.) + options.eta * 1.0j,
options.kpoint[0:2],
ispin=options.iSpin,
etaLead=options.etaLead,
useSigNCfiles=options.signc,
SpectralCutoff=options.SpectralCutoff)
GFm.calcGF(options.energy -
hw[ihw] * options.LOEscale * VfracL +
options.eta * 1.0j,
options.kpoint[0:2],
ispin=options.iSpin,
etaLead=options.etaLead,
useSigNCfiles=options.signc,
SpectralCutoff=options.SpectralCutoff)
calcTraces(options, GFm, GFp, basis, NCfile, ihw)
# Multiply traces with voltage-dependent functions
data = calcIETS(options, GFp, GFm, basis, hw)
NCfile.close()
NEGF.SavedSig.close()
CF.PrintMainFooter('Inelastica')
return data