Transmission in SN junction
Dear all, I am new to Kwant and try to play a little with some of the examples. I have a bit of experience in calculating the transmission in SN- or SNS-junction so I tried to play a little with the example in 2.6. "Superconductors: orbital degrees of freedom, conservation laws and symmetries". Something strange come up with it. If I try to calculate the transmission into the superconductor lead by exchanging the calculation of the conductance in line 74 of the example file by data.append(smatrix.transmission((1, 1), (0, 1))) I get an error message which tells me that there exists no second subblock. Nevertheless, it should be possible to calculate the transmission of holes from the normal lead into hole-like quasiparticles in the superconductor lead. (This is what I have intended to do there.) So the question rather is why is there a hole degree of freedom in the normal conductor but not in the superconductor lead?
Hi,
If I try to calculate the transmission into the superconductor lead by exchanging the calculation of the conductance in line 74 of the example file by
data.append(smatrix.transmission((1, 1), (0, 1)))
I get an error message which tells me that there exists no second subblock. Nevertheless, it should be possible to calculate the transmission of holes from the normal lead into hole-like quasiparticles in the superconductor lead. (This is what I have intended to do there.)
So the question rather is why is there a hole degree of freedom in the normal conductor but not in the superconductor lead?
The most likely explanation is that the scattering matrix is being solved for at an energy inside the superconducting gap, hence no propagating (quasiparticle) modes. What's the exact error message? Maybe it could be improved. Happy Kwanting, Joe
Hi, thank you for the quick answer. I had a similiar thought but then I am wondering why I do not get the error for an electron transmission "data.append(smatrix.transmission((1, 0), (0, 0)))" Nevertheless, here is the error message for the hole example: Traceback (most recent call last): File ".../TKwant/Superconductor.py", line 120, in <module> main() File ".../TKwant/Superconductor.py", line 114, in main plot_conductance(syst, energies=[0.002 * i for i in range(-10, 100)]) File ".../TKwant/Superconductor.py", line 74, in plot_conductance data.append(smatrix.transmission((1, 1), (0, 1))) File "...\TKwant\venv\lib\site-packages\kwant\solvers\common.py", line 871, in transmission return self._transmission(lead_out, lead_in) File "...\TKwant\venv\lib\site-packages\kwant\solvers\common.py", line 857, in _transmission return np.linalg.norm(self.submatrix(lead_out, lead_in)) ** 2 File "...\TKwant\venv\lib\site-packages\kwant\solvers\common.py", line 677, in submatrix return self.data[self.block_coords(lead_out, lead_in)] File "...\TKwant\venv\lib\site-packages\kwant\solvers\common.py", line 658, in block_coords return self.out_block_coords(lead_out), self.in_block_coords(lead_in) File "...\TKwant\venv\lib\site-packages\kwant\solvers\common.py", line 838, in out_block_coords self.out_block_offsets[lead_ind][block_ind + 1]) IndexError: index 2 is out of bounds for axis 0 with size 2
thank you for the quick answer. I had a similiar thought but then I am wondering why I do not get the error for an electron transmission
"data.append(smatrix.transmission((1, 0), (0, 0)))"
I would recommend plotting the bandstructure of the superconducting lead to figure out what is happening. Joe
Hi, I have found my mistake. From my background I expected to have a separate look on electron-like and hole-like quasiparticles in the superconductor. However, Kwant is not able to distinuish between those in the superconductor lead since no conservation law is defined for this lead. This is also mentioned in the documentation, but I have missed it until this morning. Thank you for your help anyway. Markus
participants (2)
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Joseph Weston -
markus.heckschen＠uni-due.de