Hello Chung,
> 1-The lead's self energy is in principle a complex number. In kwant,
> If I want to add the self energy of a lead by hand, I can add the real
> part of it to the on-site energy of the site that lead is connected
> to. Where should I add the imaginary part of the self energy?
Kwant allows to to specify a lead by its self energy if you want. You
need only construct a "SelfEnergyLead" and manually attach it to your
Builder:
lat = kwant.lattice.chain(norbs=1)
syst = kwant.Builder()
syst[(lat(i) for i in range(4))] = 4
syst[lat.neighbors()] = -1
# not sure what this corresponds to, but whatever
def self_energy(energy, args=(), *, params=None):
return -1j
# 'interface' is where we wish to "attach" the lead to the system
left_lead = kwant.builder.SelfEnergyLead(self_energy,
interface=[lat(0)])
right_lead = kwant.builder.SelfEnergyLead(self_energy,
interface=[lat(3)])
syst.leads.append(left_lead) # tell the system about the lead
syst.leads.append(right_lead)
syst = syst.finalized()
In the above I made the assumption that you have a 1D system. In the
more general case 'self_energy' would need to return a matrix. Also the
self energy chosen above does not really correspond to anything in
particular (the self energy is energy dependent in general), it is just
meant to be illustrative.
You could also just put complex onsites on the interface sites in your
system directly, but then you would not be able to calculate transport
properties using Kwant (because you would not have told Kwant that there
were any leads!)
> 2- If I know the value of the level width function (\Gamma = 2πρt^2 =
> 1), and the lead is a 1D chain, can I calculate the value of the
> coupling parameter, t? Is there a way to obtain the DOS of the lead
> and then get t?
Sure, the DOS is just the reciprocal of dE/dk, the derivative of the
dispersion relation in the lead (up to a bunch or prefactors etc.)
Happy Kwanting,
Joe
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