Re: [Kwant] smatrix for up and down spin channels in graphene with KM Hamiltonian
Dear sir, I've implemented the same on square lattice, and the conductance is coming out as expected. But when I did the same on graphene, the expected result is not coming. With Regards, Sudin
Dear Sir, Now I found the solution, I should have named the different kinds of lattices, like ================================================ lat_u = kwant.lattice.honeycomb(1, name='up') a,b = lat_u.sublattices lat_d = kwant.lattice.honeycomb(1, name='down') c,d = lat_d.sublattices =============================================== Now I have another problem. I was trying to build up the KaneMele Hamiltonian on graphene. Case I: Followed by the example "https://kwantproject.org/doc/1.0/tutorial/tutorial2", I've included Rashba term, and got the two terminal conductance. Case II: Now I want the transmission coefficients from different spin species. So I build up the Hamiltonian for up and down spins. If I want to compare case I and case II, one needs to calculate for case I smatrix(1,0) and for case II smatrix(2,0) + smatrix(3,0) + smatrix(2,1) + smatrix(3,1). But these two are not coming same, which should be. When Rashba strength is zero, It's ok. I am not getting any clue why these two results are not coming out the same. I've appended two codes for case I and case II. With regards, Sudin
Dear sir,
I've implemented the same on square lattice, and the conductance is coming out as expected. But when I did the same on graphene, the expected result is not coming.
With Regards, Sudin
 ==================== Sudin Ganguly Research Scholar Dept. of Physics IIT Guwahati Assam,India781039 ===================
Hi Sudin, Since transmission is quantized in one case and isn't quantized in the other, it seems that in case II the Hamiltonian of the leads is different from the Hamiltonian of the scattering region. Moreover I see that in case I you have a term that is also present in the leads and that is proportional to sigma_x. This term cannot be added to case II since there it would be a hopping term between different leads (and that's not allowed by Kwant). Physically, in case I you don't have a conservation law in the leads, so you cannot separate the lead Hamiltonian into that of different spins. Hope that helps, Anton On Wed, Nov 23, 2016 at 6:06 AM, Sudin Ganguly <sudin@iitg.ernet.in> wrote:
Dear Sir,
Now I found the solution, I should have named the different kinds of lattices, like
================================================ lat_u = kwant.lattice.honeycomb(1, name='up') a,b = lat_u.sublattices
lat_d = kwant.lattice.honeycomb(1, name='down') c,d = lat_d.sublattices ===============================================
Now I have another problem.
I was trying to build up the KaneMele Hamiltonian on graphene.
Case I: Followed by the example "https://kwantproject.org/doc/1.0/tutorial/tutorial2", I've included Rashba term, and got the two terminal conductance.
Case II: Now I want the transmission coefficients from different spin species. So I build up the Hamiltonian for up and down spins.
If I want to compare case I and case II, one needs to calculate
for case I smatrix(1,0) and for case II smatrix(2,0) + smatrix(3,0) + smatrix(2,1) + smatrix(3,1).
But these two are not coming same, which should be. When Rashba strength is zero, It's ok.
I am not getting any clue why these two results are not coming out the same.
I've appended two codes for case I and case II.
With regards, Sudin
Dear sir,
I've implemented the same on square lattice, and the conductance is coming out as expected. But when I did the same on graphene, the expected result is not coming.
With Regards, Sudin
 ==================== Sudin Ganguly Research Scholar Dept. of Physics IIT Guwahati Assam,India781039 ===================
Dear Sir, That was a great help to me. Thank you very much. With Regards, Sudin
Hi Sudin,
Since transmission is quantized in one case and isn't quantized in the other, it seems that in case II the Hamiltonian of the leads is different from the Hamiltonian of the scattering region. Moreover I see that in case I you have a term that is also present in the leads and that is proportional to sigma_x. This term cannot be added to case II since there it would be a hopping term between different leads (and that's not allowed by Kwant). Physically, in case I you don't have a conservation law in the leads, so you cannot separate the lead Hamiltonian into that of different spins.
Hope that helps, Anton
On Wed, Nov 23, 2016 at 6:06 AM, Sudin Ganguly <sudin@iitg.ernet.in> wrote:
Dear Sir,
Now I found the solution, I should have named the different kinds of lattices, like
================================================ lat_u = kwant.lattice.honeycomb(1, name='up') a,b = lat_u.sublattices
lat_d = kwant.lattice.honeycomb(1, name='down') c,d = lat_d.sublattices ===============================================
Now I have another problem.
I was trying to build up the KaneMele Hamiltonian on graphene.
Case I: Followed by the example "https://kwantproject.org/doc/1.0/tutorial/tutorial2", I've included Rashba term, and got the two terminal conductance.
Case II: Now I want the transmission coefficients from different spin species. So I build up the Hamiltonian for up and down spins.
If I want to compare case I and case II, one needs to calculate
for case I smatrix(1,0) and for case II smatrix(2,0) + smatrix(3,0) + smatrix(2,1) + smatrix(3,1).
But these two are not coming same, which should be. When Rashba strength is zero, It's ok.
I am not getting any clue why these two results are not coming out the same.
I've appended two codes for case I and case II.
With regards, Sudin
Dear sir,
I've implemented the same on square lattice, and the conductance is coming out as expected. But when I did the same on graphene, the expected result is not coming.
With Regards, Sudin
 ==================== Sudin Ganguly Research Scholar Dept. of Physics IIT Guwahati Assam,India781039 ===================
 ==================== Sudin Ganguly Research Scholar Dept. of Physics IIT Guwahati Assam,India781039 ===================
participants (2)

Anton Akhmerov

Sudin Ganguly