Re: [Kwant] SN junction with repulsive interaction in the normal layer

Dear Abhishek, Repulsive interactions do not correspond to a mean field superconducting pairing with negative sign. I'm not exactly sure what you want to make and why you would expect for example a zero bias peak, but it seems that your problem relies somehow on interactions beyond mean field, which is not a part of Kwant right now. Best regards, Anton On Tue, Jul 14, 2015, 01:27 abhishek kumar wrote:

Hello,

I have been trying to understand the conductance for Normal metal-superconductor proximity system with repulsive interaction in the normal layer numerically. The system I intend to solve is a semi-infinite superconductor, located at x<0, in contact with a semi-infinite normal metal with induced superconducting order parameter up to 0

import kwant

from matplotlib import pyplot

def make_system(a=1, t=1.0, W=10, L=30, barrier=1.5, barrierpos=(14, 15),

mu=0.4, Delta_N=0.04, Delta_S=0.1, Deltapos_N=9, Deltapos_S=15):

lat_e = kwant.lattice.square(a, name='e')

lat_h = kwant.lattice.square(a, name='h')

sys = kwant.Builder()

#### Define the scattering region. ####

sys[(lat_e(x, y) for x in range(L) for y in range(W))] = 4 * t - mu

sys[(lat_h(x, y) for x in range(L) for y in range(W))] = mu - 4 * t

# hoppings for both electrons and holes

sys[lat_e.neighbors()] = -t

sys[lat_h.neighbors()] = t

for i in range(Deltapos_N, L):

for j in xrange(W):

if i < barrierpos[0]:

sys[lat_e(i, j), lat_h(i, j)] = -Delta_N

elif i in range(barrierpos[0], barrierpos[1]):

sys[lat_e(i,j)] = 4*t + barrier - mu

sys[lat_h(i,j)] = mu - 4*t - barrier

else:

sys[lat_e(i, j), lat_h(i, j)] = Delta_S

#### Define the leads. ####

# Symmetry for the left leads.

sym_left = kwant.TranslationalSymmetry((-a, 0))

# left electron lead

lead0 = kwant.Builder(sym_left)

lead0[(lat_e(0, j) for j in xrange(W))] = 4 * t - mu

lead0[lat_e.neighbors()] = -t

# left hole lead

lead1 = kwant.Builder(sym_left)

lead1[(lat_h(0, j) for j in xrange(W))] = mu - 4 * t

lead1[lat_h.neighbors()] = t

# Then the lead to the right

# this one is superconducting and thus is comprised of electrons

# AND holes

sym_right = kwant.TranslationalSymmetry((a, 0))

lead2 = kwant.Builder(sym_right)

lead2 += lead0

lead2 += lead1

lead2[((lat_e(0, j), lat_h(0, j)) for j in xrange(W))] = Delta_S

#### Attach the leads and return the system. ####

sys.attach_lead(lead0)

sys.attach_lead(lead1)

sys.attach_lead(lead2)

return sys

def plot_conductance(sys, energies):

# Compute conductance

data = []

for energy in energies:

smatrix = kwant.smatrix(sys, energy)

# Conductance is N - R_ee + R_he

data.append(smatrix.submatrix(0, 0).shape[0] -

smatrix.transmission(0, 0) +

smatrix.transmission(1, 0))

pyplot.figure()

pyplot.plot(energies, data)

pyplot.xlabel("energy [t]")

pyplot.ylabel("conductance [e^2/h]")

pyplot.show()

kwant.plotter.bands(sys.leads[0])

def main():

sys = make_system()

# Check that the system looks as intended.

kwant.plot(sys)

# Finalize the system.

sys = sys.finalized()

plot_conductance(sys, energies=[0.002 * i +0.00001 for i in xrange(100)])

if __name__ == '__main__':

main()

I expect a peak in the conductance at zero energy. Now the question I am having here is that I am able to observe the peak when chemical potential (\mu) is of the order of bulk superconducting order parameter (Delta_S) which is unphysical. Also, I must have induced order parameter in the normal layer (Delta_N) much smaller than bulk superconducting order parameter. Can you suggest me something on that? I have analytical results for this type of system and I just want agreement of the same from numerics.

Thanks Abhishek -- -- Abhishek Kumar Department of Physical Sciences University of Florida, Gainesville FL 32608 Alternate e-mail ID - kumarabhi@ufl.edu

Mobile - +1-3522831740

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