Mailman 3 August 2015 - Kwant-discuss

SN junction with repulsive interaction in the normal layer
by abhishek kumar 10 Aug '15

10 Aug '15

Hello, I have been trying to understand the conductance for Normal metal-superconductor proximity system with repulsive interaction in the normal layer numerically. The system I intend to solve is a semi-infinite superconductor, located at x<0, in contact with a semi-infinite normal metal with induced superconducting order parameter up to 0<x<d. Both materials are infinite in the direction transverse to the SN interface. The effect of repulsive interaction is that the sign of induced order parameter in the normal layer is opposite to that in the bulk superconductor. The source code for this system is following: import kwant from matplotlib import pyplot def make_system(a=1, t=1.0, W=10, L=30, barrier=1.5, barrierpos=(14, 15), mu=0.4, Delta_N=0.04, Delta_S=0.1, Deltapos_N=9, Deltapos_S=15): lat_e = kwant.lattice.square(a, name='e') lat_h = kwant.lattice.square(a, name='h') sys = kwant.Builder() #### Define the scattering region. #### sys[(lat_e(x, y) for x in range(L) for y in range(W))] = 4 * t - mu sys[(lat_h(x, y) for x in range(L) for y in range(W))] = mu - 4 * t # hoppings for both electrons and holes sys[lat_e.neighbors()] = -t sys[lat_h.neighbors()] = t for i in range(Deltapos_N, L): for j in xrange(W): if i < barrierpos[0]: sys[lat_e(i, j), lat_h(i, j)] = -Delta_N elif i in range(barrierpos[0], barrierpos[1]): sys[lat_e(i,j)] = 4*t + barrier - mu sys[lat_h(i,j)] = mu - 4*t - barrier else: sys[lat_e(i, j), lat_h(i, j)] = Delta_S #### Define the leads. #### # Symmetry for the left leads. sym_left = kwant.TranslationalSymmetry((-a, 0)) # left electron lead lead0 = kwant.Builder(sym_left) lead0[(lat_e(0, j) for j in xrange(W))] = 4 * t - mu lead0[lat_e.neighbors()] = -t # left hole lead lead1 = kwant.Builder(sym_left) lead1[(lat_h(0, j) for j in xrange(W))] = mu - 4 * t lead1[lat_h.neighbors()] = t # Then the lead to the right # this one is superconducting and thus is comprised of electrons # AND holes sym_right = kwant.TranslationalSymmetry((a, 0)) lead2 = kwant.Builder(sym_right) lead2 += lead0 lead2 += lead1 lead2[((lat_e(0, j), lat_h(0, j)) for j in xrange(W))] = Delta_S #### Attach the leads and return the system. #### sys.attach_lead(lead0) sys.attach_lead(lead1) sys.attach_lead(lead2) return sys def plot_conductance(sys, energies): # Compute conductance data = [] for energy in energies: smatrix = kwant.smatrix(sys, energy) # Conductance is N - R_ee + R_he data.append(smatrix.submatrix(0, 0).shape[0] - smatrix.transmission(0, 0) + smatrix.transmission(1, 0)) pyplot.figure() pyplot.plot(energies, data) pyplot.xlabel("energy [t]") pyplot.ylabel("conductance [e^2/h]") pyplot.show() kwant.plotter.bands(sys.leads[0]) def main(): sys = make_system() # Check that the system looks as intended. kwant.plot(sys) # Finalize the system. sys = sys.finalized() plot_conductance(sys, energies=[0.002 * i +0.00001 for i in xrange(100)]) if __name__ == '__main__': main() I expect a peak in the conductance at zero energy. Now the question I am having here is that I am able to observe the peak when chemical potential (\mu) is of the order of bulk superconducting order parameter (Delta_S) which is unphysical. Also, I must have induced order parameter in the normal layer (Delta_N) much smaller than bulk superconducting order parameter. Can you suggest me something on that? I have analytical results for this type of system and I just want agreement of the same from numerics. Thanks Abhishek -- -- Abhishek Kumar Department of Physical Sciences University of Florida, Gainesville FL 32608 Alternate e-mail ID - kumarabhi(a)ufl.edu Mobile - +1-3522831740 "Life isn't about how to survive the storm, but how to dance in the rain," - Unknown

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stabilized evanescent modes in the lead
by Sergey 10 Aug '15

10 Aug '15

Dear Developers, I am a bit surprised that for my system with 16 sites and 9 hoppings between the unit cells I get lead.modes(E, args =[...] ) returning stabilized modes which are 9 vectors of length 9 . I understand that my hopping is degenerate and what I hoped to get from calling lead.modes(E, args =[...] ) is evanescent mode vectors of length 16 with corresponding complex momenta and some extra vectors spanning the non-propagating subspace. Could you clarify how to get what I want, please. Best wishes, Sergey

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Extracting data from each lattice (spin up and down)
by Gerson 10 Aug '15

10 Aug '15

I'm trying to reproduce the data from PRB 74, 205307 (2006) with Kwant. I'm having trouble extracting data from the spin up and spin down lattices. This is how I do it: Define two square lattices with names "up" and "down". Here's the code for the local energies: lat_up = kwant.lattice.square(1, name="up") lat_dw = kwant.lattice.square(1, name="dw") delta=1.1*Ny; sys[(lat_up(x, y) for x in range(Nx) for y in range(Ny))] = 4*t sys[(lat_dw(x, y+delta) for x in range(Nx) for y in range(Ny))] = 4*t I'm using this "delta" so that the kwant.plot(sys) show then separately. Define separate leads for the spin up and down lattices. So I can investigate the injection of each kind of spin. To reproduce Fig.1, panels (b) and (c), of the paper above I run rho0=np.abs(wf(0).sum(axis=0))**2 This gives me the spin up and down projections of the wave-function injected via lead 0 (up lead). But the spin up projection is on one lattice, while the spin down is on the other lattice. When I plot using kwant's map plot (command below), I do see exactly Fig.1(b) and (c), one in each lattice. kwant.plotter.map(sys, rho0); But I don't know how to extract from rho0 (or from kwant's wave-function command) the data from a given lattice. When I try to implement a spin-orbit Hamiltonian using matrices instead of separate lattices, it is easy to split the spin up and down data using something like ldos[0::2] and ldos[1::2], since the up and down data alternate in the array. But with matrices I have no control over the spin up or down injection. So it seems that I do have to use separate lattices. So, with separate lattices... how do I extract the data from each lattice to separate arrays? Thanks in advance, Best regards, Gerson

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Python 3 support
by Joseph Weston 10 Aug '15

10 Aug '15

Dear Kwant users, I am looking to port Kwant 1.0.4 to Python 3 ahead of the development work on Kwant 2.0, which will begin soon. Kwant 2.0 will be fully Python 3 from the start, and so it will be useful to have the existing Kwant 1.x as Python 3 to serve as a base for Kwant 2.0. In addition, any users who want to use Python 3 straight away (a requested feature in the survey) would be able to do so without having to wait for Kwant 2.0. I would like to start a discussion about which version of Python 3 Kwant should support. Below I will outline the the status of support for Python 3 on various platforms, as well as my proposal. The status of Python 3 ---------------------- Python 3 is the preferred [1] version of the Python programming language for applications in current development. The current stable version of Python 3 is version 3.4, and was released in March 2014. Windows and Mac OS X installers for this version have been available since release [2], in addition the Anaconda distribution has been shipping installers for Python 3.4 since version 2.0. For popular Linux distributions the Python 3 package is already version 3.4 by default, even in releases more than a year old[3-6]. The notable exception is Debian old-stable (Wheezy) which still has Python 3.2. Proposal -------- I propose that Kwant 1.x (and subsequently Kwant 2.x) depend on Python version 3.4, as opposed to 3.2 or some even older version. For Windows and OS X the current standard download proposed on python.org is version 3.4, so any users on those platforms will just have to choose the default. For users who are still on Debian old-stable (e.g. users who don't control their computing environment where the admins have not yet updated to stable) this would mean that they cannot use the Python 3 version of Kwant or Kwant 2. I think this is a reasonable trade off. The Python 3 release of Kwant 1.x will not add any new features or bug fixes, so users on old-stable will not be inconvenienced; they will just have to keep using the Python 2 version of Kwant 1.x. The development of Kwant 2.0 will in any case take some time, which will give any users on old-stable the chance to upgrade to current stable. In any case old-stable becomes unsupported in less than a year. Anyone with a strong preference either way is encouraged to reply to this thread. Happy kwanting, Joe References ---------- [1]: https://wiki.python.org/moin/Python2orPython3 [2]: https://www.python.org/downloads/ [3]: For ubuntu, since 14.04 http://packages.ubuntu.com/search?keywords=python3.4 [4]: For Debian, on current stable (Jessie) https://packages.debian.org/eo/jessie/python3 [5]: For OpenSuse since 13.2, for Fedora since 21 http://rpmfind.net/linux/rpm2html/search.php?query=python3

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simplify kwant installation on OS X
by Bas Nijholt 10 Aug '15

10 Aug '15

Hi all, Upon experimenting with Joe’s python3 version of kwant on OS X I found that mumps has a well maintained homebrew formula of its own in the homebrew/science tap: https://github.com/Homebrew/homebrew-science/blob/master/mumps.rb I think it might be useful to simplify the kwant installation on OS X. Also the tinyarray and kwant version are outdated on https://github.com/michaelwimmer/homebrew-kwant Updating tinyarray via pip doesn’t work: bnijholt:~> pip install tinyarray -U Collecting tinyarray Installing collected packages: tinyarray Found existing installation: tinyarray 1.0.2 DEPRECATION: Uninstalling a distutils installed project (tinyarray) has been deprecated and will be removed in a future version. This is due to the fact that uninstalling a distutils project will only partially uninstall the project. Uninstalling tinyarray-1.0.2: Successfully uninstalled tinyarray-1.0.2 Rolling back uninstall of tinyarray Exception: Traceback (most recent call last): File "/usr/local/lib/python2.7/site-packages/pip/basecommand.py", line 223, in main status = self.run(options, args) File "/usr/local/lib/python2.7/site-packages/pip/commands/install.py", line 299, in run root=options.root_path, File "/usr/local/lib/python2.7/site-packages/pip/req/req_set.py", line 646, in install **kwargs File "/usr/local/lib/python2.7/site-packages/pip/req/req_install.py", line 813, in install self.move_wheel_files(self.source_dir, root=root) File "/usr/local/lib/python2.7/site-packages/pip/req/req_install.py", line 1008, in move_wheel_files isolated=self.isolated, File "/usr/local/lib/python2.7/site-packages/pip/wheel.py", line 339, in move_wheel_files clobber(source, lib_dir, True) File "/usr/local/lib/python2.7/site-packages/pip/wheel.py", line 317, in clobber shutil.copyfile(srcfile, destfile) File "/usr/local/Cellar/python/2.7.10_2/Frameworks/Python.framework/Versions/2.7/lib/python2.7/shutil.py", line 83, in copyfile with open(dst, 'wb') as fdst: IOError: [Errno 13] Permission denied: '/usr/local/lib/python2.7/site-packages/tinyarray.so' Changing the kwant tarball to the 1.0.4 file on the brew formula also doesn’t work (https://github.com/basnijholt/homebrew-kwant/blob/master/kwant.rb): bnijholt:~> brew install kwant ==> Installing kwant from basnijholt/homebrew-kwant ==> Using Homebrew-provided fortran compiler. This may be changed by setting the FC environment variable. ==> Building with an alternative Fortran compiler This is unsupported. Warning: No Fortran optimization information was provided. You may want to consider setting FCFLAGS and FFLAGS or pass the `--default-fortran-flags` option to `brew install` if your compiler is compatible with GCC. If you like the default optimization level of your compiler, ignore this warning. ==> Downloading pypi.python.org/packages/source/k/kwant/kwant-1.0.4.tar.gz Already downloaded: /Library/Caches/Homebrew/kwant-1.0.4.tar.gz ==> Patching patching file build.conf ==> python setup.py install --prefix=/usr/local/Cellar/kwant/1.0.4 Build configuration was: User-configured LAPACK and BLAS User-configured MUMPS ********************************************************************** error: command 'clang' failed with exit status 1 READ THIS: https://git.io/brew-troubleshooting If reporting this issue please do so at (not Homebrew/homebrew): https://github.com/basnijholt/homebrew-kwant/issues Best Bas

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Nearest neighbor Hamiltonian elements (Current density maps)
by LaGasse, Samuel 01 Aug '15

01 Aug '15

Hi All, I am currently trying to implement the advice given by Joseph in https://www.mail-archive.com/kwant-discuss@kwant-project.org/msg00075.html? to write a code which generates the current density going into each site in my graphene system. My issue is with returning the nearest neighbor hopping elements in graphene. In the example Joseph posted for a square lattice, there is an obvious coordinate for the nearest neighbor sites. It seems to me that in graphene (or any honeycomb lattice), this is not so obvious. I have been looking for a function built into Kwant that would give me what I need, but haven't had much luck. I've figured out lots of ways (for example, using sys_leads_sites on my finalized system) to generate the number assigned to each site and the corresponding position, but not a good way to determine which are nearest neighbors. I'm guessing the answer is very simple using some of the machinery built into Kwant, I'm just not seeing it. Does anyone have any tips they would be willing to give me? I am not looking for a complete current density code, just a nudge in the right direction. ? Thanks very much! Sam

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