[Kwant] Using args in hamiltonian-function
Dear Kwant team, (am using the development version, 1.3) I am trying to plot the potential of my system and I want to use the hamiltonian(ind,ind,*args) function, but I don't understand how to use the args. Normally, I would give a vector with the values of the args as input, but this doesn't work in the case of hamiltonian (it does with hamiltonian_submatrix). What am I doing wrong? I also have a problem using the kwant.plot(sys) after I switched to Linux, I get the error message "NameError: name 'mplot3d' is not defined", is there something I need to install? Sincerely, Camilla
Re: [Kwant] Regarding smatrix and spin
Dear Anton,
sorry for troubling you again.
so I finally got hold of a linux-computer, and managed to run the commands and
install all the things in the notebook. When I try to run the code you have in
your notebook however, I get the following error message:
File "/home/camilla/.local/lib/python3.5/site-packages/kwant/builder.py",
line 1371, in attach_lead
self.leads.append(BuilderLead(lead_builder, tuple(interface)))
File "/home/camilla/.local/lib/python3.5/site-packages/kwant/builder.py",
line 565, in __init__
self.interface = tuple(sorted(interface))
TypeError: unorderable types: tinyarray.ndarray_int() < tinyarray.ndarray_int()
Do you know what the problem could be?
Best,
Camilla
The code if needed:
import kwant
import tinyarray as ta
import numpy as np
from scipy import sparse
from matplotlib import pyplot
import matplotlib
s0 = ta.array([[1, 0], [0, 1]])
sx = ta.array([[0, 1], [1, 0]])
sy = ta.array([[0, 1j], [-1j, 0]])
sz = ta.array([[1, 0], [0, -1]])
# Adapted from https://kwant-project.org/doc/1/tutorial/tutorial2
def make_system(t=1.0, W=10, L=10):
# Now we must specify the number of orbitals per site.
lat = kwant.lattice.square(norbs=2)
syst = kwant.Builder()
syst[(lat(x, y) for x in range(L) for y in range(W))] = \
lambda s, alpha, E_z: 4 * t * s0 + E_z * sz
syst[kwant.builder.HoppingKind((1, 0), lat, lat)] = \
lambda s1, s2, alpha, E_z: -t * s0 - 1j * alpha * sy
syst[kwant.builder.HoppingKind((0, 1), lat, lat)] = \
lambda s1, s2, alpha, E_z: -t * s0 + 1j * alpha * sx
# The new bit: specifying the conservation law.
lead = kwant.Builder(kwant.TranslationalSymmetry((-1, 0)),
conservation_law=-sz, time_reversal=s0)
lead[(lat(0, j) for j in range(W))] = 4 * t * s0
lead[lat.neighbors()] = -t * s0 # Note: no spin-orbit in the lead.
syst.attach_lead(lead)
syst.attach_lead(lead.reversed())
syst = syst.finalized()
return syst
syst = make_system(t=1.0, W=10, L=10)
energies = np.linspace(0, 1, 200)
smatrices = [kwant.smatrix(syst, energy, args=(0.2, 0.05)) for energy in
energies]
fig = pyplot.figure(figsize=(13, 8))
ax = fig.add_subplot(1, 1, 1)
# Like previously smatrix.transmission(lead1, lead0) is transmission from lead0
to lead1
ax.plot(energies, [smatrix.transmission(1, 0) for smatrix in smatrices],
label='total')
# The new bit: smatrix.transmission((lead1, q1), (lead0, q0)) is the
transmission from the
# q0 block of the lead0 into the q1 block of lead1. The subblock ordering is
same as we used
# in set_symmetry.
ax.plot(energies, [smatrix.transmission((1, 0), (0, 0)) for smatrix in
smatrices], label='$G_{↑↑}$')
ax.plot(energies, [smatrix.transmission((1, 1), (0, 0)) for smatrix in
smatrices], label='$G_{↑↓}$')
ax.plot(energies, [smatrix.transmission((1, 0), (0, 1)) for smatrix in
smatrices], label='$G_{↓↑}$')
ax.plot(energies, [smatrix.transmission((1, 1), (0, 1)) for smatrix in
smatrices], label='$G_{↓↓}$')
ax.set_ylabel('$G [e^2/h]$', fontsize='xx-large')
ax.set_xlabel('$E/t$', fontsize='xx-large')
ax.legend(fontsize='x-large');
On 24. jan. 2017 13:18, Anton Akhmerov wrote:
OK, please double-check the remaining simulation parameters.
Anton
On Tue, Jan 24, 2017 at 1:00 PM, Camilla Espedal
<camilla.espe...@ntnu.no> wrote:
Dear Anton,
I triend changing it, but that does not solve the problem.
Best,
Camilla
From: Anton Akhmerov [mailto:anton.akhmerov...@gmail.com]
Sent: 24. januar 2017 12:36
To: Camilla Espedal <camilla.espe...@ntnu.no>
Cc: kwant-discuss@kwant-project.org
Subject: Re: [Kwant] Regarding smatrix and spin
Dear Camilla,
Could the difference originate from you using a lattice constant of 2
instead of 1?
Anton
On Tue, Jan 24, 2017, 10:41 Camilla Espedal <camilla.espe...@ntnu.no> wrote:
Dear Anton,
Thanks again for all your help. I will try to do it the linux way. Just one
more thing regarding this. I wrote a script in the old Kwant to find the
total conductance and compare it to the one in your notebook. While the two
plots are qualitatively similar, they are not the same. Am I missing
something, or am I calculating different things?
Best, Camilla
(my code):
# Tutorial 2.3.1. Matrix structure of on-site and hopping elements
#
#
# Physics background
# --
# Gaps in quantum wires with spin-orbit coupling and Zeeman splititng,
# as theoretically predicted in
# http://prl.aps.org/abstract/PRL/v90/i25/e256601
# and (supposedly) experimentally oberved in
# http://www.nature.com/nphys/journal/v6/n5/abs/nphys1626.html
#
# Kwant features highlighted
# --
# - Numpy matrices as values in Builder
import kwant
# For plotting
import matplotlib.pyplot as plt
# For matrix support
import tinyarray
import numpy as np
# define Pauli-matrices for convenience
[Kwant] Question regarding orbitals and scattering matrix
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
Re: [Kwant] Question about lead_info[].wave_functions[]
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
Re: [Kwant] Question about lead_info[].wave_functions[]
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
[Kwant] Question about lead_info[].wave_functions[]
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
Re: [Kwant] Plotting Hamiltonian for overlapping lattices
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
[Kwant] Spatially dependent hopping
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
[Kwant] The reference distance a is too small
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
Re: [Kwant] Hopping between different lattices and families
Thank you! That worked, but I still don't see why the last thing I did didn't work? I added a hopping for two points that were within bounds even if shape_sr started at 1 instead of 0? What am I missing? Best, Camilla From: Bas Nijholt [mailto:basnijh...@gmail.com] Sent: 31. oktober 2016 14:41 To: Camilla Espedal <camilla.espe...@ntnu.no>; Anton Akhmerov <anton.akhme...@gmail.com> Cc: kwant-discuss@kwant-project.org Subject: Re: [Kwant] Hopping between different lattices and families [https://share.polymail.io/v2/z/a/NTgxNzQ5YTNkNTEz/xUmVK-i26NNEAv--i_LM1Plxebyu8uAoC6DbmD79H5dGTrf-kVfHcrHgZTNWF_OjMz4geOWxyljAMWAlegWTqcgJMJI8eMyXr-Ez8eIHo-gW3HG5GbkpLLAdt_w22PY3DobInlRQhU_v_vUt_PJ9RMFO.png] The error message says it all :-) Using `return ((0 <= x < L) and (0 <= y < W)) ` should fix your problem. Best, Bas On Mon, 31 Oct 2016 at 14:29 Camilla Espedal mailto:camilla%20espedal%20%3ccamilla.espe...@ntnu.no%3e> > wrote: Hi again, Thanks, I will try to write it more clearly. So the script I use to make the system is: L = 100 W = 40 a = 1 t = 1 def make_system(W,L,a,t): # Make the lattices # We define two lattices (up and down) with two sublattices A and B 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)],[(0,0),(a,0)], name='down') A_down, B_down = lat_down.sublattices # Define the shape of the scattering region. Must return true where there are sites. def shape_sr(pos): x, y = pos return ((0 < x < L) and (0 < y < W)) sys = kwant.Builder() sys[lat_up.shape(shape_sr, (1,1))] = 2 sys[lat_down.shape(shape_sr, (1,1))] = 2 sys[A_up(1,1), A_down(2,1)] = 2 return sys The error message I get is: KeyError: Site(kwant.lattice.Monoatomic([[1,1], [1,-1]], [0,0]. 'up0'), array([1, 1])) I can not see why the spot should not be created, because it is within the bounds of shapre_sr. Thanks, Best, Camilla -Original Message- From: Anton Akhmerov [mailto:anton.akhme...@gmail.com<mailto:anton.akhme...@gmail.com>] Sent: 31. oktober 2016 12:04 To: Camilla Espedal <camilla.espe...@ntnu.no<mailto:camilla.espe...@ntnu.no>> Cc: kwant-discuss@kwant-project.org<mailto:kwant-discuss@kwant-project.org> Subject: Re: [Kwant] Hopping between different lattices and families Hi Camilla, Please double-check the error message that you see. Your assumption why the code doesn't work is not right: it's possible to add a hopping from any site to any site, regardless of distance or lattices involved. My best guess is that the sites aren't present in the system yet. As a general advice, when describing a problem try to provide complete information required to reproduce this problem. A script and the error message would be usually useful. Best, Anton On Mon, Oct 31, 2016 at 6:58 AM, Camilla Espedal <camilla.espe...@ntnu.no<mailto:camilla.espe...@ntnu.no>> wrote: > Hi again, > > I tried to add > > sys[A_up(2,2), B_down(2,2)] = 2 > > This does not work, and I think it is because A_up and B_down are not > only on different sublattices, but on different lattices as well. In > the tutorial on superconductors > (https://kwant-project.org/doc/1.0/tutorial/tutorial5#lattice-descript > ion-using-different-lattices) they define the hopping as > > sys[((lat_e(x, y), lat_h(x, y)) for x in range(Deltapos, L) > for y in range(W))] = Delta > > between the lattices but on the same spatial point. But I want to hop between > two different lattices from one point in space to another, if that makes > sense. > > Best, > Camilla > > -Original Message- > From: Anton Akhmerov > [mailto:anton.akhme...@gmail.com<mailto:anton.akhme...@gmail.com>] > Sent: 31. oktober 2016 11:48 > To: Camilla Espedal <camilla.espe...@ntnu.no<mailto:camilla.espe...@ntnu.no>> > Cc: kwant-discuss@kwant-project.org<mailto:kwant-discuss@kwant-project.org> > Subject: Re: [Kwant] Hopping between different lattices and families > > Hi Camilla, > > It's exactly like you would expect: syst[A_up(i, j), B_down(i, j)] = > value. See e.g. https://kwant-project.org/doc/1/tutorial/tutorial4 > > Best, > Anton > > On Mon, Oct 31, 2016 at 6:43 AM, Camilla Espedal > <camilla.espe...@ntnu.no<mailto:camilla.espe...@ntnu.no>> wrote: >> 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 = >> kw
Re: [Kwant] Hopping between different lattices and families
Hi again, I tried to add sys[A_up(2,2), B_down(2,2)] = 2 This does not work, and I think it is because A_up and B_down are not only on different sublattices, but on different lattices as well. In the tutorial on superconductors (https://kwant-project.org/doc/1.0/tutorial/tutorial5#lattice-description-using-different-lattices) they define the hopping as sys[((lat_e(x, y), lat_h(x, y)) for x in range(Deltapos, L) for y in range(W))] = Delta between the lattices but on the same spatial point. But I want to hop between two different lattices from one point in space to another, if that makes sense. Best, Camilla -Original Message- From: Anton Akhmerov [mailto:anton.akhme...@gmail.com] Sent: 31. oktober 2016 11:48 To: Camilla Espedal <camilla.espe...@ntnu.no> Cc: kwant-discuss@kwant-project.org Subject: Re: [Kwant] Hopping between different lattices and families Hi Camilla, It's exactly like you would expect: syst[A_up(i, j), B_down(i, j)] = value. See e.g. https://kwant-project.org/doc/1/tutorial/tutorial4 Best, Anton On Mon, Oct 31, 2016 at 6:43 AM, Camilla Espedal <camilla.espe...@ntnu.no> wrote: > 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
Re: [Kwant] Family-dependent onsite potential
Thanks, I now changed the order, but I still get the same error message. So now the code reads kwant.plotter.map(sys, V) sys = sys.finalized() but now it seems to be in a different place the error message is now 'int' object has no attribute 'site', and the V-function is still def V(sys): Hd = onsite(site) return (Hd[0,0] - Hd[1,1]).real Best, Camilla
Re: [Kwant] Family-dependent onsite potential
The problem occurs when I try to plot a map of the voltage on the sample, to check that everything is working. The problem does not seem to occur when assigning it to a builder element sys[lattice.shape(shape_sr, (1,1))] = onsite gives no error messages. This is what I am trying to do, I write a function that calculates the voltage (I followed one of your tutorials) def V(sys): Hd = onsite(site) return (Hd[0,0] - Hd[1,1]).real and then sys = sys.finalized() kwant.plotter.map(sys, V) to try to plot it, but then I get the error. -Original Message- From: Christoph Groth [mailto:christoph.gr...@cea.fr] Sent: 27. oktober 2016 12:15 To: Camilla Espedal <camilla.espe...@ntnu.no> Cc: kwant-discuss@kwant-project.org Subject: Re: [Kwant] Family-dependent onsite potential Camilla Espedal wrote: > (...) > but it does not work. I get error message: ‘int’ object has no > attribute ‘family’. How can I solve this, or what am I doing > wrong? This shouldn’t be. Can you provide a complete script that demostrates the problem? Christoph
[Kwant] Family-dependent onsite potential
Hello, I am making a system with 2 sublattices, so they belong to different families (a and b), and I wish to define a sublattice-dependent onsite energy. I tried using the following code for the onsite function. def onsite(site): onsite_a = 2 onsite_b = 2 return onsite_a if site.family == a else onsite_b but it does not work. I get error message: 'int' object has no attribute 'family'. How can I solve this, or what am I doing wrong? Best, Camilla
