Mailman 3 November 2016 - Kwant-discuss

How the spin is positioned in the Smatrix?
by Qingtian Zhang 06 Mar '22

06 Mar '22

Dear all, I am trying square lattice with spin-orbit coupling and Zeeman splititng just like the example of Tutorial 2.3.1. Now I want to get the spin-dependent conductance：Guu,Gud,Gdu,and Gdd, where "u" indicates up spin, d indicates down spin. We can have the scattering matrix through Smatrix=kwant.smatrix(sys, energy), but how the spin is positioned in the scattering matrix? I have checked some simple cases, it seems the Smatrix is organized like this: | r t | S= | t' r' | but how the spin is included? Thanks in advance. Qingtiian Zhang The code is: import kwant from matplotlib import pyplot from numpy import matrix import tinyarray sigma_0 = tinyarray.array([[1, 0], [0, 1]]) sigma_x = tinyarray.array([[0, 1], [1, 0]]) sigma_y = tinyarray.array([[0, -1j], [1j, 0]]) sigma_z = tinyarray.array([[1, 0], [0, -1]]) sys=kwant.Builder() lat=kwant.lattice.square() a=1 t=1.0 alpha=0.5 e_z=0.08 W=2 L=2 sys[(lat(x, y) for x in range(L) for y in range(W))] = \ 4 * t * sigma_0 + e_z * sigma_z # hoppings in x-direction sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ -t * sigma_0 - 1j * alpha * sigma_y # hoppings in y-directions sys[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ -t * sigma_0 + 1j * alpha * sigma_x #### Define the left lead. #### lead = kwant.Builder(kwant.TranslationalSymmetry((-a, 0))) lead[(lat(0, j) for j in xrange(W))] = 4 * t * sigma_0 + e_z * sigma_z # hoppings in x-direction lead[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ -t * sigma_0 - 1j * alpha * sigma_y # hoppings in y-directions lead[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ -t * sigma_0 + 1j * alpha * sigma_x #### Attach the leads and return the finalized system. #### sys.attach_lead(lead) sys.attach_lead(lead.reversed()) kwant.plot(sys) sys=sys.finalized() print "Hamiltonian=" print sys.hamiltonian_submatrix() Smatrix=kwant.smatrix(sys, energy=3.) print "The scattering matrix=" print matrix.round((Smatrix.data),2) print "T=",(Smatrix.transmission(1, 0))

3 3

Spin polarized transport calculation
by L.M J 06 Mar '22

06 Mar '22

Dear Kwant users and developers I have two questions related to the spin calculation using kwant. 1. I'm wondering if we can do spin-polarized transport in kwant? For example, can we can get the separate Conductance Vs Energy diagram for spin up and spin down terms. I'm thinking one way of doing this is to set up the Rashba Hamiltonian as a whole. And then manually extract the spin up and spin down hamiltonian and do the transport calculation separately. But this will eliminate some extra terms that I don't know whether this is correct anymore. Any suggestions? 2. How can we set up the spin polarization for a particular site? For example, in some of the topological insulator, can we set up spin polarization on the edge as up and the other side of the edge as down, and then do the transport? Or this question is completely wrong? Thanks for advance. Sincerely, Liming

3 3

How to caculate hall resistance
by ZHANG Bing 12 Sep '21

12 Sep '21

Dear Sir, I am a PhD student of Hong Kong University of Science and Technology. I want to use KWANT to caculate Hall resistance of a Hall bar structure.We can get the conductance between 6 electrodes, but how to get hall resistance? Can you give me some help? Thank you very much. Best Regards, Zhang Bing

4 3

Using Kwant for finding tunneling probability from metal to vacuum
by Kristjan Eimre 14 Feb '17

14 Feb '17

Hello Kwant experts, I have studied Kwant a bit, but before I delve deeper into it, I want to know if it can be applied to my problem. I have a 3d electron potential landscape for a metal-vacuum surface calculated with DFT. (More detailed info and pictures in [1]). Can I use Kwant to calculate the transmission probability of electrons incident on the surface? And if kwant is not suitable for this problem, perhaps you know of any other numerical software or method that would allow this calculation? [1] - http://physics.stackexchange.com/questions/295329/quantum-tunneling-probabi… Best regards, Kristjan

5 9

Question regarding orbitals and scattering matrix
by Camilla Espedal 27 Nov '16

27 Nov '16

Hi again, This question is sort of related to one of mye previous questions (https://www.mail-archive.com/kwant-discuss@kwant-project.org/msg01029.html) but I am writing it as a new one. The questions relates to the sites in the lead unit cell and the scattering matrix. Say I have a system (simple 2D wire), where I have 3 sites in my unit cell (3 orbitals). I then make a system at an energy which is so low that I only have one propagating mode in the system. If I then run smatrix.lead_info[0] it returns a 2x3 matrix (which corresponds to left/right going and number of orbitals). If I then run smatrix.submatrix(0,0) I only get one element, which orbital does this element "belong" to, or how does it relate to these orbitals? Is the scattering matrix the same for all orbitals? Is the probability of scattering from say orbital 1 in one lead to orbital 2 in another the same as from orbital 1 to orbital 1? Hope my question makes sens. Best regards, Camilla

2 1

Re: [Kwant] About some help to understand Physics
by Sudin Ganguly 24 Nov '16

24 Nov '16

Dear Sir, If I calculate the Rashba term, (S \times d_ij)_z, for one case the Sigma_X terms comes out (in KWANT along (0,0) direction). That's why I have included this term in my system. There is no other reason. It feels that there may be something wrong in my calculation since you have said about the Sigma_z conservation. Can I show you my calculations. It'll not take much time, there are only 5-6 lines. Hope you don't mind. With Regards, Sudin > Dear Sudin, > > 1. I mean the conservation of sigma_z. > > 2. There is no motivation for it, that's just what you have done in your > code. > > Best, > Anton > > On Wed, Nov 23, 2016 at 10:44 PM, Sudin Ganguly <sudin(a)iitg.ernet.in> > wrote: >> Dear Sir, >> >> First of all, I would like to apologize in advance, if this mail bothers >> you. >> >> Today you send me reply about the smatrix for up and down spins in >> graphene. >> That was very much helpful to me. >> >> I would like to ask you about the conservation law in the leads, since >> it >> does not seem right to post this kind of question in KWANT forum. >> >> 1. is this Conservation law meant the current conservation? If this is >> so, >> how do I understand this. >> >> >> 2. Kane-Mele model said that in graphene there is NN Rashba interaction, >> and other is NNN intrinsic SO interaction. Then what is the motivation >> to >> avoid these kind of interactions in the leads. >> >> I'll be eagerly waiting for your reply. >> >> With Regards, >> Sudin >> >> -- >> ==================== >> Sudin Ganguly >> Research Scholar >> Dept. of Physics >> IIT Guwahati >> Assam,India-781039 >> =================== >

1 0

Re: [Kwant] smatrix for up and down spin channels in graphene with KM Hamiltonian
by Sudin Ganguly 24 Nov '16

24 Nov '16

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

2 3

Re: [Kwant] Question about lead_info[].wave_functions[]
by Camilla Espedal 17 Nov '16

17 Nov '16

Hi again, So my final question is then. What is the unit cell? Doesn't a square lattice only have one site per unit cell? Or is it the number of interface sites? Best, Camilla

2 1

Re: [Kwant] Question about lead_info[].wave_functions[]
by Camilla Espedal 16 Nov '16

16 Nov '16

Hi Joe, Thank you. This might be a silly question, but what is the meaning of orbitals here? Is it not only 1? The orbital elements seem to be conjugate of each other. Best, Camilla

2 3

smatrix for up and down spin channels in graphene with KM Hamiltonian
by Sudin Ganguly 16 Nov '16

16 Nov '16

Dear sir, I'm trying to get the transmission coefficients for up and down spin channels in graphene with Kane-Mele Hamiltonian (including Rashba term). So it needs to write the Hamiltonian for up and down spin separately. I started with this, sys=kwant.Builder() lat_u=kwant.lattice.honeycomb() lat_d=kwant.lattice.honeycomb() a,b= lat_u.sublattices c,d= lat_d.sublattices My confusion is that, can I declare these sublattices for up and down spins. With Regards, Sudin

2 4

Question about lead_info[].wave_functions[]
by Camilla Espedal 16 Nov '16

16 Nov '16

Hi all, I have a question regarding the lead_info[x].wave_functions[x]. I am not sure what this is actually returning? I tried to run the function on your quantum_wire_revisited.py-system, like this prop = sm.lead_info[0] print(prop.wave_functions[0]) with W = 2, if that is important. It then returns a 1x2 array or 2x2 matrix depending on the energy. What does this matrix contain? I read about propagatingmodes in the documentation, but I am not sure what it meant. Best, Camilla

2 1

Re: [Kwant] Plotting Hamiltonian for overlapping lattices
by Camilla Espedal 09 Nov '16

09 Nov '16

Hello Antônio, So here is what I want to do. I have a system where I have defined two lattices, lat_up and lat_down, and they overlap spatially (instead of using matrices in the voltage and hopping, so that it is easier to obtain spin-resolved data). They are defined like this: lat_up = kwant.lattice.general([(a,a),(a,-a)],[(0,0),(a,0)], name='up') A_up, B_up = lat_up.sublattices lat_down = kwant.lattice.general([(a,a),(a,-a)],[(0+d,0),(a+d,0+d)], name='down') A_down, B_down = lat_down.sublattices I want to calculate the trace of the dot product between sigma_z and the spinor psi = (psi_up psi_down), and plot it over the system. That is H(lat_up(i,i)) - H(lat_down(i,i)). This was easy to do, when I used matrices for spin, but now that I have implemented it using two lattices instead I don't know how to do it. If I use the same approach as before, I get two values for each (spatial) lattice point, and the result looks completely random. I hope my explanation was understandable. Best, Camilla

3 2

Problem with holoview
by T.C. Wu 08 Nov '16

08 Nov '16

Dear Kwant developers, I encounter problems with running the code in [1]. I guess it is not quite related to kwant but caused by matplotlib and holoview. Since part of the code relies on the function "spectrum", I appreciate any idea for tackling the error, which is shown in the attached figure. Thanks. [1] https://github.com/topocm/topocm_content/blob/master/w2_majorana/nanowire.i… Best, Johnny

3 2

Plotting Hamiltonian for overlapping lattices
by Camilla Espedal 08 Nov '16

08 Nov '16

Dear all, I need some help trying to plot the onsite energy of my system. The problem is that I have two overlapping lattices, one for spin up and one for spin down. From before, I had the following function: def V(i): ham = sys.hamiltonian(i,i) ham = 0.5*np.trace(np.dot(ham,s_z)).real return ham kwant.plotter.map(sys,V) which worked fine when I only had one lattice (and I used pauli matrices to express the spin degrees of freedom instead of having two lattices). What I would like is a function that does the same as V(i) for my system. Plotted H(1,1) - H(2,2) at position (1,1) etc. I am not sure how to do this. I was considering doing it manually and looping through the whole H, but how do I know its size? If you have any better/easier suggestions I would appreciate it. Best, Camilla

2 1

Hopping between different lattices and families
by Camilla Espedal 04 Nov '16

04 Nov '16

Hi, To explain what I mean. I have a system where I have separated spin-up and spin-down into two lattices (like electron and hole in the example at the kwant site) so that it is would be easier to extract spin-resolved information (G_up/up, Gup/down etc.). In addition, these two lattices consists of two sublattices (A and B). The code is like this lat_up = kwant.lattice.general([(1,0),(s,c)],[(0,0),(0,1/sqrt(3))], name='up') A_up, B_up = lat_up.sublattices lat_down = kwant.lattice.general([(1,0),(s,c)],[(0,0),(0,1/sqrt(3))], name='down') A_down, B_down = lat_down.sublattices What I want to do now, is to add a hopping term between say A_up (i,j) and B_down (i.j). So a hopping term between the two different lattices and sublattices. How can I implement this? Or is there a better way to achieve what I want? Best Camilla Espedal

6 16

Spatially dependent hopping
by Camilla Espedal 03 Nov '16

03 Nov '16

Hi again, I was wondering if there is an easy way to define different regions with different hoppings? E.g. what I want to achieve is to make system where the hopping from one of the leads into the scattering region is different from the hopping within the lead and the scattering region. How can this be achieved? On a more general note, if I have two scattering regions in the system. It is easy and efficient to define different onsite energies for the two regions using shape. Is there a similarly easy way to define the hopping differently (using neighbors() within a shape)? And how are these two regions connected, does the connection have to be added "manually"? I hope my question makes sense. Best, Camilla

2 1

The tight-binding Hamiltonian in real space and momentum space
by T.C. Wu 01 Nov '16

01 Nov '16

Dear Kwant users, I recently reading the course materials about topological insulator at http://topocondmat.org/w7_defects/ti_majoranas.html. However, the Kwant code which simulates the majoranas on the quantum spin-Hall edge is not quite transparent to me. In particular, the hoppings defined in Kwant are def onsite(site, p): (x, y) = site.pos return (p.M - 4 * p.B) * s0szsz - 4 * p.D * s0s0sz + p.gaps(x, y)[1] * mysz + p.gaps(x, y)[0] * s0s0sx def hopx(site1, site2, p): return p.B * s0szsz + p.D * s0s0sz + 0.5j * p.A * szsxsz def hopy(site1, site2, p): return p.B * s0szsz + p.D * s0s0sz - 0.5j * p.A * s0sysz I got a bit lost since I don't quite understand why should hopx and hopy be defined in this way. Maybe a silly question, but how should one obtain the hoppings by looking at the momentum space BdG Hamiltonian? Thanks for your help. Best, Johnny

2 1

The reference distance a is too small
by Camilla Espedal 01 Nov '16

01 Nov '16

Hi again, I am trying to make sense of the error message I get when trying to plot using kwant.plotter map(). The error message is "the reference distance a is too small", and a is the lattice spacing. What is the meaning of this error message? Best, Camilla

2 1