I have a question concerning the leads.
Suppose that I am considering a n-p-n or p-n-p junction,
where the scattering region (assumed with a cubic geometry)
is attached to two leads
(say along the direction y) having the same Hamiltonian but different
onsite energy.
In the scattering region, a nearest-neighbor hopping occurs along \hat{y}
c_{i + \hat{y}}^{\dagger} M c_{i} + H.c.,
with a matrix M not Hermitian in general.
Going to attach the leads, I have a doubt
if M is not Hermitian.
Indeed, I think I can still write for the right lead:
sym_right_lead = kwant.TranslationalSymmetry((0, a, 0))
right_lead = kwant.Builder(sym_right_lead)
for i in range(W):
for k in range(W):
right_lead[lat(i, 1, k), lat(i, 0, k)] = M
syst.attach_lead(right_lead)
However, for the left lead I have the doubt between
sym_left_lead = kwant.TranslationalSymmetry((0, -a, 0))
left_lead = kwant.Builder(sym_left_lead)
for i in range(W):
for k in range(W):
left_lead[lat(i, 1, k), lat(i, 0, k)] = M
syst.attach_lead(left_lead)
and the same code with M^{dagger}:
left_lead[lat(i, 1, k), lat(i, 0, k)] = M^{\dagger}
(or, I guess, equivalently the form in terms of the interchanged hopping:
left_lead[lat(i, 0, k), lat(i, 1, k)] = M).
Between the two options, nothing changes in the spectrum of the leads (fine !),
but I does for the conductance of the junction.
Can you help me ?
Thank you very much
L. L.
