Mailman 3 November 2016 - Kwant-discuss

Question about lead_info[].wave_functions[]
by Camilla Espedal Nov. 16, 2016

Nov. 16, 2016

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

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Re: [Kwant] Plotting Hamiltonian for overlapping lattices
by Camilla Espedal Nov. 8, 2016

Nov. 8, 2016

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

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Problem with holoview
by T.C. Wu Nov. 8, 2016

Nov. 8, 2016

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

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Plotting Hamiltonian for overlapping lattices
by Camilla Espedal Nov. 8, 2016

Nov. 8, 2016

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

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Hopping between different lattices and families
by Camilla Espedal Nov. 4, 2016

Nov. 4, 2016

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

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Spatially dependent hopping
by Camilla Espedal Nov. 3, 2016

Nov. 3, 2016

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

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The tight-binding Hamiltonian in real space and momentum space
by T.C. Wu Nov. 1, 2016

Nov. 1, 2016

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

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The reference distance a is too small
by Camilla Espedal Nov. 1, 2016

Nov. 1, 2016

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

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