Hello,
I am trying to how understand how to compute the wavefunctions of a system with superconducting leads as a function of the phase difference, just as in the case of normal leads, using fsys.wave_function() where I would do it as a function of the energy. However, the result is always an empty array. Is there a way to make it work ?
Thanks in advance,
Anil
Hi Anil,
Indeed, the wave_function method computes scattering wave functions, and since superconductors have no scattering modes inside the gap, there are also no scattering wave functions. I am assuming you want to find Andreev bound states. The most straightforward strategy for that is to have a finite size piece of the superconductor as a part of your system (as opposed to having an infinite superconducting lead), and to search for eigenstates in the closed system, similar to this Kwant tutorial: http://kwantproject.org/doc/1/tutorial/tutorial3#closedsystems
Best, Anton
On Mon, Jan 25, 2016 at 12:34 PM, anil anil.murani@upsud.fr wrote:
Hello,
I am trying to how understand how to compute the wavefunctions of a system with superconducting leads as a function of the phase difference, just as in the case of normal leads, using fsys.wave_function() where I would do it as a function of the energy. However, the result is always an empty array. Is there a way to make it work ?
Thanks in advance,
Anil
Dear Anton,
I know that I can do this with a finite system doing exact diagonalization, but I was wondering why it is not possible to use the same mode matching procedure as in the normal case but with evanescent waves in the superconducting leads.
Anil
On 25/01/2016 13:38, Anton Akhmerov wrote:
Hi Anil,
Indeed, the wave_function method computes scattering wave functions, and since superconductors have no scattering modes inside the gap, there are also no scattering wave functions. I am assuming you want to find Andreev bound states. The most straightforward strategy for that is to have a finite size piece of the superconductor as a part of your system (as opposed to having an infinite superconducting lead), and to search for eigenstates in the closed system, similar to this Kwant tutorial: http://kwantproject.org/doc/1/tutorial/tutorial3#closedsystems
Best, Anton
On Mon, Jan 25, 2016 at 12:34 PM, anil anil.murani@upsud.fr wrote:
Hello,
I am trying to how understand how to compute the wavefunctions of a system with superconducting leads as a function of the phase difference, just as in the case of normal leads, using fsys.wave_function() where I would do it as a function of the energy. However, the result is always an empty array. Is there a way to make it work ?
Thanks in advance,
Anil
Dear Anil,
Solving for Andreev bound states is an eigenproblem, so the information about them cannot be contained in the scattering matrix of the system at only a single energy. Of course in a short junction regime you can express all the states through the scattering amplitudes, but this requires an extra calculation step. In http://arxiv.org/abs/1408.1563 my collaborators and I have calculated Andreev level energies in the short junction limit starting from the scattering matrix using Kwant (see also the ancillary files with the source code). There would be an extra step required to get the wave functions of Andreev bound states, however in the short junction limit, most of the bound state wave functions are outside of the scattering region.
Best, Anton
On Mon, Jan 25, 2016 at 1:49 PM, anil anil.murani@upsud.fr wrote:
Dear Anton,
I know that I can do this with a finite system doing exact diagonalization, but I was wondering why it is not possible to use the same mode matching procedure as in the normal case but with evanescent waves in the superconducting leads.
Anil
On 25/01/2016 13:38, Anton Akhmerov wrote:
Hi Anil,
Indeed, the wave_function method computes scattering wave functions, and since superconductors have no scattering modes inside the gap, there are also no scattering wave functions. I am assuming you want to find Andreev bound states. The most straightforward strategy for that is to have a finite size piece of the superconductor as a part of your system (as opposed to having an infinite superconducting lead), and to search for eigenstates in the closed system, similar to this Kwant tutorial: http://kwantproject.org/doc/1/tutorial/tutorial3#closedsystems
Best, Anton
On Mon, Jan 25, 2016 at 12:34 PM, anil anil.murani@upsud.fr wrote:
Hello,
I am trying to how understand how to compute the wavefunctions of a system with superconducting leads as a function of the phase difference, just as in the case of normal leads, using fsys.wave_function() where I would do it as a function of the energy. However, the result is always an empty array. Is there a way to make it work ?
Thanks in advance,
Anil
Dear Anton,
thank you very much for your explanations, now I understand more the problem (which is indeed an eigenproblem).
Anil
On 26/01/2016 21:55, Anton Akhmerov wrote:
Dear Anil,
Solving for Andreev bound states is an eigenproblem, so the information about them cannot be contained in the scattering matrix of the system at only a single energy. Of course in a short junction regime you can express all the states through the scattering amplitudes, but this requires an extra calculation step. In http://arxiv.org/abs/1408.1563 my collaborators and I have calculated Andreev level energies in the short junction limit starting from the scattering matrix using Kwant (see also the ancillary files with the source code). There would be an extra step required to get the wave functions of Andreev bound states, however in the short junction limit, most of the bound state wave functions are outside of the scattering region.
Best, Anton
On Mon, Jan 25, 2016 at 1:49 PM, anil anil.murani@upsud.fr wrote:
Dear Anton,
I know that I can do this with a finite system doing exact diagonalization, but I was wondering why it is not possible to use the same mode matching procedure as in the normal case but with evanescent waves in the superconducting leads.
Anil
On 25/01/2016 13:38, Anton Akhmerov wrote:
Hi Anil,
Indeed, the wave_function method computes scattering wave functions, and since superconductors have no scattering modes inside the gap, there are also no scattering wave functions. I am assuming you want to find Andreev bound states. The most straightforward strategy for that is to have a finite size piece of the superconductor as a part of your system (as opposed to having an infinite superconducting lead), and to search for eigenstates in the closed system, similar to this Kwant tutorial: http://kwantproject.org/doc/1/tutorial/tutorial3#closedsystems
Best, Anton
On Mon, Jan 25, 2016 at 12:34 PM, anil anil.murani@upsud.fr wrote:
Hello,
I am trying to how understand how to compute the wavefunctions of a system with superconducting leads as a function of the phase difference, just as in the case of normal leads, using fsys.wave_function() where I would do it as a function of the energy. However, the result is always an empty array. Is there a way to make it work ?
Thanks in advance,
Anil
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anil

Anton Akhmerov