To to separate spins, electron and hole
Dear all, I am using Kwant to study a system with both spins and electron and hole, so the hopping matrix is 4X4. Now I want to know how to separate the spins, electron and hole. I study this through the "2.6. Superconductors: orbital degrees of freedom, conservation laws and symmetries" smatrix = kwant.smatrix(syst, energy) data.append(smatrix.submatrix((0, 0), (0, 0)).shape[0] -smatrix.transmission((0, 0), (0, 0)) +smatrix.transmission((0, 1), (0, 0))) I do not find more information about this for kwant. For my system, if I have 3 leads, and the hopping and onsite energy is set in this order: (e↑,0,0,0)- spin up electron,first row of the 4X4matrix (0,e↓,0,0)- spin down electron,second row of the 4X4matrix (0,0, h↑ ,0)- spin up hole,third row of the 4X4matrix (0,0, 0, h ↓ )- spin down hole,fourth row of the 4X4matrix I want to obtain the transmissions from 0 →2. smatrix = kwant.smatrix(syst, energy) The transmission from h↑ to e↑ is: smatrix.transmission((2, 1), (0, 2)) The transmission from h ↓ to e↑ is: smatrix.transmission((2, 1), (0, 3)) Is my understanding correct? Thanks very much in advance! Hosein Khani
Hi, I know this is a very old discussion, but I'm in a similar position and want to look at a superconducting system with spin. Have you been able to resolve this? Best Regards, Daniel
Hi Daniel, Khani, If you want to use multiple degrees of freedom in the leads, specify a conservation law with the matrix that has different eigenvalues for each combination of the quantities of interest. For example, if your sites have 4 orbitals, like Khani describes, you can specify syst = kwant.Builder(conservation_law=np.identity(np.arange(4)), ...). Hope this helps, Anton On Tue, 22 Jun 2021 at 15:45, Daniel Hauck <daniel.hauck@kit.edu> wrote:
Hi,
I know this is a very old discussion, but I'm in a similar position and want to look at a superconducting system with spin.
Have you been able to resolve this?
Best Regards, Daniel
Hi Anton, thank you for the fast answer, that sounds very helpful! Just a small question. The documentation tells me that the eigenvalues have to be integer and the order determines the order of blocks. Is the exact value of the eigenvalues of any importance? Best, Daniel Am 22.06.21 um 16:52 schrieb Anton Akhmerov:
Hi Daniel, Khani,
If you want to use multiple degrees of freedom in the leads, specify a conservation law with the matrix that has different eigenvalues for each combination of the quantities of interest. For example, if your sites have 4 orbitals, like Khani describes, you can specify syst = kwant.Builder(conservation_law=np.identity(np.arange(4)), ...).
Hope this helps, Anton
On Tue, 22 Jun 2021 at 15:45, Daniel Hauck <daniel.hauck@kit.edu> wrote:
Hi,
I know this is a very old discussion, but I'm in a similar position and want to look at a superconducting system with spin.
Have you been able to resolve this?
Best Regards, Daniel
integer and the order determines the order of blocks. Is the exact value of the eigenvalues of any importance?
The only meaning of each eigenvalue is the number of the block of the conserved quantity. If memory serves me right, we adopted a convention where they have to be consecutive integers. Cheers, Anton
Best, Daniel
Am 22.06.21 um 16:52 schrieb Anton Akhmerov:
Hi Daniel, Khani,
If you want to use multiple degrees of freedom in the leads, specify a conservation law with the matrix that has different eigenvalues for each combination of the quantities of interest. For example, if your sites have 4 orbitals, like Khani describes, you can specify syst = kwant.Builder(conservation_law=np.identity(np.arange(4)), ...).
Hope this helps, Anton
On Tue, 22 Jun 2021 at 15:45, Daniel Hauck <daniel.hauck@kit.edu> wrote:
Hi,
I know this is a very old discussion, but I'm in a similar position and want to look at a superconducting system with spin.
Have you been able to resolve this?
Best Regards, Daniel
Dear All, I want to work with the same system with a little bit different. (e↑,0,0,0)- spin up electron,first row of the 4X4matrix (0,e↓,0,0)- spin down electron,second row of the 4X4matrix (0,0, h ↓, 0 )- spin down hole,third row of the 4X4matrix (0,0, 0,h↑ )- spin up hole, fourth row of the 4X4matrix and I want to add spins in a superconductor system that is connected to two normal leads. In the superconductor is it right to separate the system into holes and electrons as mentioned in "https://kwant-project.org/doc/1.0/tutorial/tutorial5"? I did it and then added the normal leads as similar to tutorial5 (lat_h and lat_e) but when I ran to compute the smatrix.transmission((0, 1), (0, 0)) there is an error. IndexError: index 2 is out of bounds for axis 0 with size 2 If I want to use the other method mentioned in "https://kwant-project.org/doc/1/tutorial/superconductors" to build the system How can I build the main system and add the parameters of the Hamiltonian, my sites have 4 orbitals and I did not find any information on how to add parameters to build the system and leads. Thanks very much in advance! Zahra Aslani
participants (4)
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Anton Akhmerov -
Daniel Hauck -
Khani Hosein -
zahraslani＠gmail.com