This is more of a physical question.
I am considering a system set up of a superconductor connected to a non-superconducting metal. As in: [Lead][Conductor][Superconductor] In Kwant I set the superconductor up with an electron lattice and a hole lattice.
I can simulate this is two ways; one is the superconductor as a lead, and the other is the superconductor as part of the scattering system.
So, [Lead][Conductor Region][Superconducting Lead] or [Lead][Conductor Region][Superconductor Region]
If I look at the conduction between the electron and the hole lead on the left leads, I simulate slightly different conduction values for the case of the SC in the scattering region and the SC as a lead on the right side.
Physically, as I understand it, there should be basically no difference at least at low enough energy values. Is the slight difference due to this "low enough energy" threshold, or am I missing something physical or numerical from kwant that would cause this difference to exist regardless?
Dear Henry, Attaching a superconducting lead to a system and attaching a finite superconducting part will usually lead to different results, especially for resonant systems. The only situation the two can lead to slightly similar results is when the Fermi energy lies in the gap of the superconductor. In that case, the lead will be equivalent to a slab of length equal to the penetration length. In the two cases, the conductance from left to right is zero.
I hope this helps, Adel
On Thu, Mar 18, 2021 at 5:01 PM Henry Axt henry.axt@gmail.com wrote:
This is more of a physical question.
I am considering a system set up of a superconductor connected to a non-superconducting metal. As in: [Lead][Conductor][Superconductor] In Kwant I set the superconductor up with an electron lattice and a hole lattice.
I can simulate this is two ways; one is the superconductor as a lead, and the other is the superconductor as part of the scattering system.
So, [Lead][Conductor Region][Superconducting Lead] or [Lead][Conductor Region][Superconductor Region]
If I look at the conduction between the electron and the hole lead on the left leads, I simulate slightly different conduction values for the case of the SC in the scattering region and the SC as a lead on the right side.
Physically, as I understand it, there should be basically no difference at least at low enough energy values. Is the slight difference due to this "low enough energy" threshold, or am I missing something physical or numerical from kwant that would cause this difference to exist regardless?
Dear Adel,
I am indeed looking at the case where the Fermi energy is in the gap of the superconductor. Do you mean to say that the simulation with the superconductor in the scattering region is that same as a simulation with a superconductor as a lead and the scattering region's length increased by the penetration length?
I'm not quite I understand why there would be a difference at these energies. At least not in the nature I see them, where if you consider the case where the superconductor is in the scattering and you increase the superconducting region's length, yet the differences between these two simulations don't change.
Regards, Henry
Dear Henry, I am talking about the lead. It doesn't matter what you have in the scattering region if you have a lead where the Fermi energy lies in the gap, the physics should be the same if you consider just a finite part from the lead, with a length typically, of the order of penetration length (few times this characteristic length if you want more precision.) This is valid for any lead, not just a superconducting one. The reason is that in all cases, in the deleted part, the wave function is exponentially small.
I hope this helps. Adel
On Sun, Mar 21, 2021 at 8:05 PM Henry Axt henry.axt@gmail.com wrote:
Dear Adel,
I am indeed looking at the case where the Fermi energy is in the gap of the superconductor. Do you mean to say that the simulation with the superconductor in the scattering region is that same as a simulation with a superconductor as a lead and the scattering region's length increased by the penetration length?
I'm not quite I understand why there would be a difference at these energies. At least not in the nature I see them, where if you consider the case where the superconductor is in the scattering and you increase the superconducting region's length, yet the differences between these two simulations don't change.
Regards, Henry
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Abbout Adel -
Henry Axt