def Broaden(options,VV,II):
"""
Broadening corresponding to Lock in measurements for the
conductance and IETS spectra. Also resample II, Pow, and nPh
to match a common voltage list
"""
II=II.copy()
II=II.real
# First derivative dI and bias list dV
dI=(II[1:len(II)]-II[:-1])/(VV[1]-VV[0])
dV=(VV[1:len(VV)]+VV[:-1])/2
# Second derivative and bias ddV
ddI=(dI[1:len(dI)]-dI[:-1])/(VV[1]-VV[0])
ddV=(dV[1:len(dV)]+dV[:-1])/2
# Modulation amplitude
VA=N.sqrt(2.0)*options.Vrms
# New bias ranges for broadening
tmp=int(N.floor(VA/(dV[1]-dV[0]))+1)
BdV=dV[tmp:-tmp]
BddV=ddV[tmp:-tmp]
# Initiate derivatives
BdI=0*BdV
BddI=0*BddV
# Calculate first derivative with Vrms broadening
for iV, V in enumerate(BdV):
SIO.printDone(iV,len(BdV),'Inelastica.Broaden: First-derivative Vrms broadening')
wt=(N.array(range(200))/200.0-0.5)*N.pi
VL=V+VA*N.sin(wt)
dIL=MM.interpolate(VL,dV,dI)
BdI[iV]=2/N.pi*N.sum(dIL*(N.cos(wt)**2))*(wt[1]-wt[0])
# Calculate second derivative with Vrms broadening
for iV, V in enumerate(BddV):
SIO.printDone(iV,len(BddV),'Inelastica.Broaden: Second-derivative Vrms broadening')
wt=(N.array(range(200))/200.0-0.5)*N.pi
VL=V+VA*N.sin(wt)
ddIL=MM.interpolate(VL,ddV,ddI)
BddI[iV]=8.0/3.0/N.pi*N.sum(ddIL*(N.cos(wt)**4))*(wt[1]-wt[0])
# Reduce to one voltage grid
NN=options.biasPoints
V = N.linspace(options.minBias,options.maxBias,NN)
NI=MM.interpolate(V,VV,II)
NdI=MM.interpolate(V,dV,dI)
NddI=MM.interpolate(V,ddV,ddI)
NBdI=MM.interpolate(V,BdV,BdI)
NBddI=MM.interpolate(V,BddV,BddI)
return V, NI ,NdI, NddI, NBdI, NBddI
def calcIETS(options,GFp,GFm,basis,hw):
# Calculate product of electronic traces and voltage functions
print 'Inelastica.calcIETS: nHTp =',GFp.nHT*PC.unitConv # OK
print 'Inelastica.calcIETS: nHTm =',GFm.nHT*PC.unitConv # OK
print 'Inelastica.calcIETS: HTp =',GFp.HT # OK
print 'Inelastica.calcIETS: HTm =',GFm.HT # OK
# Set up grid and Hilbert term
kT = options.Temp/11604.0 # (eV)
# Generate grid for numerical integration of Hilbert term
max_hw=max(hw)
max_win=max(-options.minBias,max_hw)+20*kT+4*options.Vrms
min_win=min(-options.maxBias,-max_hw)-20*kT-4*options.Vrms
pts=int(N.floor((max_win-min_win)/kT*3))
Egrid=N.linspace(min_win,max_win,pts)
print "Inelastica.calcIETS: Hilbert integration grid : %i pts [%f,%f]" % (pts,min(Egrid),max(Egrid))
NN = options.biasPoints
print 'Inelastica.calcIETS: Biaspoints =',NN
# Add some points for the Lock in broadening
approxdV=(options.maxBias-options.minBias)/(NN-1)
NN+=int(((8*options.Vrms)/approxdV)+.5)
Vl=N.linspace(options.minBias-4*options.Vrms,options.maxBias+4*options.Vrms,NN)
# Vector implementation on Vgrid:
wp = (1+N.sign(Vl))/2. # weights for positive V
wm = (1-N.sign(Vl))/2. # weights for negative V
# Mode occupation and power dissipation
Pow = N.zeros((len(hw),NN),N.float) # (modes,Vgrid)
nPh = N.zeros((len(hw),NN),N.float)
t0 = N.clip(Vl/kT,-700,700)
cosh0 = N.cosh(t0) # Vgrid
sinh0 = N.sinh(t0)
for i in (hw>options.modeCutoff).nonzero()[0]:
P1T = wm*GFm.P1T[i]+wp*GFp.P1T[i]
P2T = wm*GFm.P2T[i]+wp*GFp.P2T[i]
# Bose distribution
nB = 1/(N.exp(N.clip(hw[i]/kT,-300,300))-1) # number
t1 = N.clip(hw[i]/(2*kT),-700,700) # number
coth1 = N.cosh(t1)/N.sinh(t1)
# Emission rate and e-h damping
damp = P1T*hw[i]/N.pi # Vgrid
emis = P2T*(hw[i]*(cosh0-1)*coth1-Vl*sinh0)/(N.cosh(2*t1)-cosh0)/N.pi
# Determine mode occupation
if options.PhHeating:
nPh[i,:] = emis/(hw[i]*P1T/N.pi+options.PhExtDamp)+nB
else:
nPh[i,:] = nB
# Mode-resolved power dissipation
Pow[i,:] = hw[i]*((nB-nPh[i])*damp+emis)
# Current: non-Hilbert part (InH)
InH = N.zeros((NN,),N.float) # Vgrid
IsymF = N.zeros((NN,),N.float)
for i in (hw>options.modeCutoff).nonzero()[0]:
nHT = wm*GFm.nHT[i]+wp*GFp.nHT[i] # Vgrid
t1 = hw[i]/(2*kT) # number
t1 = N.clip(t1,-700,700)
coth1 = N.cosh(t1)/N.sinh(t1)
t2 = (hw[i]+Vl)/(2*kT) # Vgrid
t2 = N.clip(t2,-700,700)
coth2 = N.cosh(t2)/N.sinh(t2)
t3 = (hw[i]-Vl)/(2*kT) # Vgrid
t3 = N.clip(t3,-700,700)
coth3 = N.cosh(t3)/N.sinh(t3) # Vgrid
# Isym function
Isym = 0.5*(hw[i]+Vl)*(coth1-coth2) # Vgrid
Isym -= 0.5*(hw[i]-Vl)*(coth1-coth3)
# non-Hilbert part
InH += (Isym+2*Vl*nPh[i])*nHT # Vgrid
IsymF += Isym
# Current: Add Landauer part, GFm.TeF = GFp.TeF
InH += GFp.TeF*Vl # Vgrid
# Current: Asymmetric/Hilbert part (IH)
try:
import scipy.special as SS
print "Inelastica: Computing asymmetric term using digamma function,"
print "... see G. Bevilacqua et al., Eur. Phys. J. B (2016) 89: 3"
IH = N.zeros((NN,),N.float)
IasymF = N.zeros((NN,),N.float)
for i in (hw>options.modeCutoff).nonzero()[0]:
v0 = hw[i]/(2*N.pi*kT)
vp = (hw[i]+Vl)/(2*N.pi*kT)
vm = (hw[i]-Vl)/(2*N.pi*kT)
Iasym = kT*(2*v0*SS.psi(1.j*v0)-vp*SS.psi(1.j*vp)-vm*SS.psi(1.j*vm)).real
IasymF += Iasym
IH += GFp.HT[i]*N.array(Vl>0.0,dtype=int)*Iasym
IH += GFm.HT[i]*N.array(Vl<0.0,dtype=int)*Iasym
except:
print "Computing using explit Hilbert transformation"
IH = N.zeros((NN,),N.float)
IasymF = N.zeros((NN,),N.float)
# Prepare box/window function on array
Vl2 = N.outer(Vl,N.ones(Egrid.shape))
Egrid2 = N.outer(N.ones(Vl.shape),Egrid)
# Box/window function nF(E-Vl2)-nF(E-0):
kasse = MM.box(0,-Vl2,Egrid2,kT) # (Vgrid,Egrid)
ker = None
for i in (hw>options.modeCutoff).nonzero()[0]:
# Box/window function nF(E-hw)-nF(E+hw)
tmp = MM.box(-hw[i],hw[i],Egrid,kT)
hilb, ker = MM.Hilbert(tmp,ker) # Egrid
# Calculate Iasym for each bias point
for j in range(len(Vl)):
Iasym = MM.trapez(Egrid,kasse[j]*hilb,equidistant=True).real/2
IasymF[j] += Iasym
if Vl[j]>0:
IH[j] += GFp.HT[i]*Iasym
else:
IH[j] += GFm.HT[i]*Iasym
# Compute inelastic shot noise terms here:
absVl = N.absolute(Vl)
Inew = N.zeros(len(Vl),N.float)
Snew = N.zeros(len(Vl),N.float)
print 'Noise factors:'
print GFp.dIel
print GFp.dIinel
print GFp.dSel
print GFp.dSinel
for i in (hw>options.modeCutoff).nonzero()[0]:
# Elastic part
Inew += GFp.dIel[i]*Vl
Snew += GFp.dSel[i]*absVl
# Inelastic part
indx = (absVl-hw[i]<0).nonzero()[0]
fct = absVl-hw[i]
fct[indx] = 0.0 # set elements to zero
Inew += GFp.dIinel[i]*fct*N.sign(Vl)
Snew += GFp.dSinel[i]*fct
# Get the right units for gamma_eh, gamma_heat
gamma_eh_p=N.zeros((len(hw),),N.float)
gamma_eh_m=N.zeros((len(hw),),N.float)
gamma_heat_p=N.zeros((len(hw),),N.float)
gamma_heat_m=N.zeros((len(hw),),N.float)
for i in (hw>options.modeCutoff).nonzero()[0]:
# Units [Phonons per Second per dN where dN is number extra phonons]
gamma_eh_p[i]=GFp.P1T[i]*hw[i]*PC.unitConv
gamma_eh_m[i]=GFm.P1T[i]*hw[i]*PC.unitConv
# Units [Phonons per second per eV [eV-ihw]
gamma_heat_p[i]=GFp.P2T[i]*PC.unitConv
gamma_heat_m[i]=GFm.P2T[i]*PC.unitConv
print 'Inelastica.calcIETS: gamma_eh_p =',gamma_eh_p # OK
print 'Inelastica.calcIETS: gamma_eh_m =',gamma_eh_m # OK
print 'Inelastica.calcIETS: gamma_heat_p =',gamma_heat_p # OK
print 'Inelastica.calcIETS: gamma_heat_m =',gamma_heat_m # OK
V, I, dI, ddI, BdI, BddI = Broaden(options,Vl,InH+IH)
V, Is, dIs, ddIs, BdIs, BddIs = Broaden(options,Vl,IsymF)
V, Ia, dIa, ddIa, BdIa, BddIa = Broaden(options,Vl,IasymF)
# Interpolate quantities to new V-grid
NPow=N.zeros((len(Pow),len(V)),N.float)
NnPh=N.zeros((len(Pow),len(V)),N.float)
for ii in range(len(Pow)):
NPow[ii]=MM.interpolate(V,Vl,Pow[ii])
NnPh[ii]=MM.interpolate(V,Vl,nPh[ii])
# Interpolate inelastic noise
NV,NI,NdI,NddI,NBdI,NBddI = Broaden(options,Vl,GFp.TeF*Vl+Inew)
NV,NS,NdS,NddS,NBdS,NBddS = Broaden(options,Vl,Snew)
print 'Inelastica.calcIETS: V[:5] =',V[:5] # OK
print 'Inelastica.calcIETS: V[-5:][::-1] =',V[-5:][::-1] # OK
print 'Inelastica.calcIETS: I[:5] =',I[:5] # OK
print 'Inelastica.calcIETS: I[-5:][::-1] =',I[-5:][::-1] # OK
print 'Inelastica.calcIETS: BdI[:5] =',BdI[:5] # OK
print 'Inelastica.calcIETS: BdI[-5:][::-1] =',BdI[-5:][::-1] # OK
print 'Inelastica.calcIETS: BddI[:5] =',BddI[:5] # OK
print 'Inelastica.calcIETS: BddI[-5:][::-1] =',BddI[-5:][::-1] # OK
datafile = '%s/%s.IN'%(options.DestDir,options.systemlabel)
# ascii format
writeLOEData2Datafile(datafile+'p',hw,GFp.TeF,GFp.nHT,GFp.HT)
writeLOEData2Datafile(datafile+'m',hw,GFm.TeF,GFm.nHT,GFm.HT)
# netcdf format
outNC = initNCfile(datafile,hw,V)
write2NCfile(outNC,BddI/BdI,'IETS','Broadened BddI/BdI [1/V]')
write2NCfile(outNC,ddI/dI,'IETS_0','Intrinsic ddI/dI [1/V]')
write2NCfile(outNC,BdI,'BdI','Broadened BdI, G0')
write2NCfile(outNC,BddI,'BddI','Broadened BddI, G0')
write2NCfile(outNC,I,'I','Intrinsic I, G0 V')
write2NCfile(outNC,dI,'dI','Intrinsic dI, G0')
write2NCfile(outNC,ddI,'ddI','Intrinsic ddI, G0/V')
if options.LOEscale==0.0:
write2NCfile(outNC,GFp.nHT,'ISymTr','Trace giving Symmetric current contribution (prefactor to universal function)')
write2NCfile(outNC,GFp.HT,'IAsymTr','Trace giving Asymmetric current contribution (prefactor to universal function)')
write2NCfile(outNC,gamma_eh_p,'gamma_eh','e-h damping [*deltaN=1/Second]')
write2NCfile(outNC,gamma_heat_p,'gamma_heat','Phonon heating [*(bias-hw) (eV) = 1/Second]')
# New stuff related to the noise implementation
write2NCfile(outNC,NI,'Inew','Intrinsic Inew (new implementation incl. elastic renormalization, T=0)')
write2NCfile(outNC,NdI,'dInew','Intrinsic dInew (new implementation incl. elastic renormalization, T=0)')
write2NCfile(outNC,NddI,'ddInew','Intrinsic ddInew (new implementation incl. elastic renormalization, T=0)')
write2NCfile(outNC,NddI/NdI,'IETSnew_0','Intrinsic ddInew/dInew (new implementation incl. elastic renormalization, T=0) [1/V]')
write2NCfile(outNC,NBdI,'BdInew','Broadened BdInew (new implementation incl. elastic renormalization, T=0)')
write2NCfile(outNC,NBddI,'BddInew','Broadened BddInew (new implementation incl. elastic renormalization, T=0)')
write2NCfile(outNC,NBddI/NBdI,'IETSnew','Broadened BddInew/BdInew (new implementation incl. elastic renormalization, T=0) [1/V]')
write2NCfile(outNC,NdS,'dSnew','Inelastic first-derivative of the shot noise dSnew (T=0)')
else:
write2NCfile(outNC,GFp.nHT,'ISymTr_p','Trace giving Symmetric current contribution (prefactor to universal function)')
write2NCfile(outNC,GFp.HT,'IAsymTr_p','Trace giving Asymmetric current contribution (prefactor to universal function)')
write2NCfile(outNC,GFm.nHT,'ISymTr_m','Trace giving Symmetric current contribution (prefactor to universal function)')
write2NCfile(outNC,GFm.HT,'IAsymTr_m','Trace giving Asymmetric current contribution (prefactor to universal function)')
write2NCfile(outNC,gamma_eh_p,'gamma_eh_p','e-h damping [*deltaN=1/Second]')
write2NCfile(outNC,gamma_heat_p,'gamma_heat_p','Phonon heating [*(bias-hw) (eV) = 1/Second]')
write2NCfile(outNC,gamma_eh_m,'gamma_eh_m','e-h damping [*deltaN=1/Second]')
write2NCfile(outNC,gamma_heat_m,'gamma_heat_m','Phonon heating [*(bias-hw) (eV) = 1/Second]')
# Phonon occupations and power balance
write2NCfile(outNC,NnPh,'nPh','Number of phonons')
write2NCfile(outNC,N.sum(NnPh,axis=0),'nPh_tot','Total number of phonons')
write2NCfile(outNC,NPow,'Pow','Mode-resolved power balance')
write2NCfile(outNC,N.sum(NPow,axis=0),'Pow_tot','Total power balance')
# Write "universal functions"
write2NCfile(outNC,dIs,'dIs','dIsym function')
write2NCfile(outNC,dIa,'dIa','dIasym function')
write2NCfile(outNC,ddIs,'ddIs','ddIasym function')
write2NCfile(outNC,ddIa,'ddIa','ddIasym function')
# Write energy reference where Greens functions are evaluated
outNC.createDimension('number',1)
tmp=outNC.createVariable('EnergyRef','d',('number',))
tmp[:]=N.array(options.energy)
# Write LOEscale
tmp=outNC.createVariable('LOEscale','d',('number',))
tmp[:]=N.array(options.LOEscale)
# Write k-point
outNC.createDimension('vector',3)
tmp=outNC.createVariable('kpoint','d',('vector',))
tmp[:]=N.array(options.kpoint)
outNC.close()
return V, I, dI, ddI, BdI, BddI