Kwant-discuss September 2015

kwant-discuss@python.org

22 participants
33 discussions

Problem with elements of S-matrix not being smooth
by Simon Malzard 28 Sep '15

28 Sep '15

Hello Kwant, The problem I am trying to solve relies on being able to calculate the eigenphases of the scattering matrix for different energies, more precisely it requires the elements of the scattering matrix to be smooth as a function of energy. By examining the elements of the scattering matrix as a function of energy, I have noticed that the elements of the scattering matrix are not smooth and there exists a sign problem. The code I have included below is for a highly(!!) simplified example, where the scattering region is simply two leads attached to a single square. I took the base code from the kwant tutorial page to reduce any possible errors. I have taken a small range of energies and plotted the real parts of the off diagonal elements of the scattering matrix. You will notice that plot included demonstrates that the elements of the scattering matrix are not smooth and a sign change occurs for certain energies (sign changes for both the real and imaginary parts, plotting chosen for simplicity). Note that for the example I take a tiny range of energies, where the conductance is the same and hence the number of active modes is constant as a function of energy. There may be a mistake in understanding on my part, however, I believe this error is due to some sign error in the incoming or outgoing states in the lead as this only effects individual modes (as you will see when you adjust the system size, or move up to the next conductance plateau and the size of the scattering matrix increases. My initial program was looking at graphene for a large rectangular flake and I noticed this effect considerably). I think this is a boundedness problem for certain functions which describes the individual scattering states at certain energies. Is this intentional behaviour for KWANT? As it means I can't perform calculations such as calculating the Wigner-Smith time-delay matrix, among other scattering characteristics. Thank you for your time + best wishes, Simon My code: #### KWANT tutorial code from matplotlib import pyplot as plt import kwant import numpy as np import scipy.linalg as la # First, define the tight-binding system sys = kwant.Builder() # Here, we are only working with square lattices a = 1 lat = kwant.lattice.square(a) t = 1.0 W = 2 L = 2 # Define the scattering region for i in xrange(L): for j in xrange(W): # On-site Hamiltonian sys[lat(i, j)] = 4 * t # Hopping in y-direction if j > 0: sys[lat(i, j), lat(i, j - 1)] = -t # Hopping in x-direction if i > 0: sys[lat(i, j), lat(i - 1, j)] = -t # Then, define and attach the leads: # First the lead to the left # (Note: TranslationalSymmetry takes a real-space vector) sym_left_lead = kwant.TranslationalSymmetry((-a, 0)) left_lead = kwant.Builder(sym_left_lead) for j in xrange(W): left_lead[lat(0, j)] = 4 * t if j > 0: left_lead[lat(0, j), lat(0, j - 1)] = -t left_lead[lat(1, j), lat(0, j)] = -t sys.attach_lead(left_lead) # Then the lead to the right sym_right_lead = kwant.TranslationalSymmetry((a, 0)) right_lead = kwant.Builder(sym_right_lead) for j in xrange(W): right_lead[lat(0, j)] = 4 * t if j > 0: right_lead[lat(0, j), lat(0, j - 1)] = -t right_lead[lat(1, j), lat(0, j)] = -t sys.attach_lead(right_lead) # Plot it, to make sure it's OK kwant.plot(sys) # Finalize the system sys = sys.finalized() # Now that we have the system, we can compute conductance emin, emax = 1.05, 1.06#3.00 points = 21 energies = np.linspace(emin,emax,points) element_0_1, element_1_0 = [], [] for ie in energies: energy = ie # I only consider element 0,1 and 1,0 as 0,0 and 1,1 are vanishingly small and look like floating point errors. #This gets the smartix and looks at the real parts of the off-diagonal elements smatrix = kwant.smatrix(sys, energy).data element_0_1.append(smatrix[0,1].real) element_1_0.append(smatrix[1,0].real) print smatrix[0,1].real print smartix[1,0].real fig2 = plt.figure() ax2 = fig2.add_subplot(1,1,1) ax2.plot(element_0_1, 'ro') ax2.plot(element_1_0, 'bo') plt.show()

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Speed/memory difference btw no hopping and hopping=0.0
by Baris Pekerten 27 Sep '15

27 Sep '15

Dear all, I have a question about speed/memory performance. If I define 100 lattices with hoppings within and in between the lattices, but define most of those hoppings to be 0.0, does this lead to a significantly slower execution than not defining any hoppings at all? (It's related to the code I'm working on that I described in my email with the subject "Dynamic number of lattices"). Thank you all for your concern and time. Cheers, Baris

2 1

Conductance Plot doesn't appear
by Dedi Setiabudidaya 27 Sep '15

27 Sep '15

Can anyone help me why the conductance plot in the enclosed graphene code doesn't appear ?I just copied the codes from the tutorial. Thank you in advance.

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Kwant & Knit
by anil 27 Sep '15

27 Sep '15

Hi, I would like to know whether the algorithm used in ``GreensFunctions`` is the one described in the paper of 2008 by Kazymyrenko & Waintal ; or if it is an other solver ? Thanks in advance, Anil

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Site ordering while plotting wavefunction
by Girish Sharma 27 Sep '15

27 Sep '15

Hi, I have attached a small code, trying to visualize Majorana wavefunctions at the two end points of my 1D wire. The kwant.plotter doesn't really help, so I'm trying basic pyplot. However, due to random ordering of sites, I do not see the wavefunction peaking at the ends (see the last plot). Is there a way out to do this ordering correctly in PYTHON? Thank you for your time ! Best regards, Girish

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Re: [Kwant] quantum well
by Anton Akhmerov 23 Sep '15

23 Sep '15

Dear Dedi, Feel free to use the slides under the creative commons attribution license (Note that the XKCD image is CC-BY-NC though), and the code under the simplified BSD license. The source notebook is over here: antonakhmerov.org/misc/kwant_presentation.ipynb. Best, Anton On Wed, Sep 23, 2015 at 9:10 PM, Dedi Setiabudidaya < setiabudidaya(a)hotmail.com> wrote: > Dear Anton, > > I am interested in using kwant to learn about the magnetic graphene. > I ask your permission to use your slides, including the codes. > Thank you in advance. > > Kind Regards, > > Dedi Setiabudidaya > Lecturer at Sriwijaya University, Indonesia. > > ------------------------------ > From: anton.akhmerov(a)gmail.com > Date: Wed, 23 Sep 2015 18:03:11 +0200 > To: kk_ghosh(a)rediffmail.com > CC: kwant-discuss(a)kwant-project.org > Subject: Re: [Kwant] quantum well > > > Dear Kamal, > > Take a look at these slides, maybe you'll find something useful: > antonakhmerov.org/misc/kwant_presentation.slides.html > > Best, > Anton > > On Wed, Sep 23, 2015 at 6:00 PM, kamal ghosh <kk_ghosh(a)rediffmail.com> > wrote: > > Dear All, > I am interested to calculate the DOS and conductance of graphene quantum > well. I find no previous > guideline on this topic. If this can be done then other nanostructures can > be hopefully analysed I think. > Please help in this regard by giving the appropriate code. > Thanks. > K.K.Ghosh > mail: kk_ghosh(a)rediffmail.com > > <https://sigads.rediff.com/RealMedia/ads/click_nx.ads/www.rediffmail.com/sig…> > Get your own *FREE* website, *FREE* domain & *FREE* mobile app with > Company email. > *Know More >* > <http://track.rediff.com/click?url=___http://businessemail.rediff.com?sc_cid…> > > >

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quantum well
by kamal ghosh 23 Sep '15

23 Sep '15

Dear All, I am interested to calculate the DOS and conductance of graphene quantum well. I find no previous guideline on this topic. If this can be done then other nanostructures can be hopefully analysed I think. Please help in this regard by giving the appropriate code. Thanks. K.K.Ghosh mail: kk_ghosh(a)rediffmail.com

2 1

Calculating the current
by Bahareh Goldozian 23 Sep '15

23 Sep '15

Hi, I am trying to calculate the current (not conductance) as a function of bias, I am wondering if there is any defined way for calculating the current in Kwant or not. Thank you very much, Bahareh

2 1

Package for ubuntu vivid
by David Abergel 17 Sep '15

17 Sep '15

Hi all, firstly, thanks so much for your work in developing and maintaining kwant. Hugely appreciated. Is there any chance you could package it for {,k,x}ubuntu 15.04? I tried installing kwant in that linux today, using the 14.10 package, and I am getting a bunch of errors from Tkinter and matplotlib when I use kwant's inbuilt plotter. Many thanks for your help David

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About hoppingkind and Translational symmetry in hexagonal lattice
by ANANT VIJAY VARMA 17 Sep '15

17 Sep '15

Hello everyone , I am trying to build Hexagonal lattice using general 3-D lattice.I am using the code below: def shape(pos): x, y, z = pos return 0 <= x < a and 0 <= y < b and 0 <= z < c sys = kwant.Builder() sys[lat.shape(shape, (1, 0, 0))] =0 sys[kwant.builder.HoppingKind((0,0,0),a,b)] = t sys[kwant.builder.HoppingKind((-1,1,0),a,b)] = t sys[kwant.builder.HoppingKind((0,1,0),a,b)] = t But it's not working.When I am using neighbors() function instead, its working, but I don't want to use the neighbors() function. But this code is not showing the hoppings but when I use 2-D general lattice with hoppings (0,0),(-1,1),(0,1) it works.Also,it is not showing any error.The lattice I am using is: lat = kwant.lattice.general([(1,0,0),(.5,.5*math.sqrt(3),0),(0,0,3)],[(0,0,0), (0,1 / math.sqrt(3),0)]) a, b = lat.sublattices please tell me how can I use general 3-D lattice, to make graphene, as I want more than one layers,with hoppings not by neighbors() function.Also, I what should I write in Translational geometry.or 2-D general lattice I am using lat.vec((-1,0)).Please clear this a bit Thanks.

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Kwant-discuss September 2015