Mailman 3 August 2016 - Kwant-discuss

How the spin is positioned in the Smatrix?
by Qingtian Zhang March 6, 2022

March 6, 2022

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))

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Spin polarized transport calculation
by L.M J March 6, 2022

March 6, 2022

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

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How to caculate hall resistance
by ZHANG Bing Sept. 12, 2021

Sept. 12, 2021

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

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Нow to set the coordinates of the atoms in the "2.5 Beyond square lattices: graphene"
by Матусевич Евгений Aug. 31, 2016

Aug. 31, 2016

Hi, I'm just starting to work with KWANT. I need to calculate conductivity of a graphene layer with defect (watch the picture). I have coordinates of atoms of this layer. As in an example "2.5 Beyond square lattices: graphene" to set the coordinates? -- Евгений Матусевич

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Runnning Kwant computations on parallel machines
by Adrian Nosek Aug. 31, 2016

Aug. 31, 2016

Dear Kwant Community, My name is Adrian Nosek, I am a graduate student at the University of California Riverside in Condensed Matter Physics, and I was wondering whether there are any plans to extend Kwant and let it run on parallel machines, so that systems of bigger sample size could be modeled? I attempted to calculate the conductivity of a sample with 200000 atoms (I believe that's what it was but its been a while since I ran the simulation) and this is where my machine ran out of RAM. I really like the idea of simulating my experiment using Kwant, but is there any advantage to model let's say a 4 by 20 micron size system using Kwant vs a classical approach? I believe the mean free paths of electrons in graphene can easily reach micron-long pathways in high mobility graphene-hBN sandwiches, so that is the reason why I am asking. Also, would it make any sense to implement such a simulation in the context of Big Data Analysis, where analysis is performed on parallel working machines where one could diagonalize such a big Hamiltonian, e.g. using Apache Spark? Thanks for your answers, Adrian

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Help needed: Kwant on the Mac
by Christoph Groth Aug. 30, 2016

Aug. 30, 2016

Hi everyone, Are there any Mac enthusiasts out there who would volunteer to help us to maintain the packaging of Kwant on that important platform? The packaging of Kwant for MacOS X [1] is outdated [2]. Both homebrew [3] and macports [4] seem to be still at the stage of Kwant 1.0. This is because, to my knowledge, none of the devs of Kwant is using a Mac any longer. There’s the Conda packaging by Bas Nijholt. Does this mean that homebrew and macports are no longer needed? Mac users, raise your voice! Christoph [1] https://kwant-project.org/install#mac-os-x [2] https://www.mail-archive.com/kwant-discuss%40kwant-project.org/msg00939.html [3] https://github.com/michaelwimmer/homebrew-kwant [4] https://downloads.kwant-project.org/macports/

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"No module named kwant" when using iPython
by Cheryne Aug. 30, 2016

Aug. 30, 2016

Hi Kwant-Team! I'm having trouble to "import kwant" via iPython interfaces (Spyder). I can run the python script via "python scriptname.py" but when I try "spyder" and then "scriptname.py" I get the error "no module named kwant". Do you know what I have to do so that iPython recognizes the module? Thank you, Cheryne

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Re: [Kwant] Kwant-discuss Digest, Vol 36, Issue 4
by Sumit Ghosh Aug. 25, 2016

Aug. 25, 2016

Your band structure is correct. When you add magnetic field you change your momentum p to (p-eA), or let's say you push your spectrum. Try it with with a chain with a width of 2 sites and you can see it better. On 25 August 2016 at 11:23, <kwant-discuss-request(a)kwant-project.org> wrote: > Send Kwant-discuss mailing list submissions to > kwant-discuss(a)kwant-project.org > > To subscribe or unsubscribe via the World Wide Web, visit > https://mailman-mail5.webfaction.com/listinfo/kwant-discuss > or, via email, send a message with subject or body 'help' to > kwant-discuss-request(a)kwant-project.org > > You can reach the person managing the list at > kwant-discuss-owner(a)kwant-project.org > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of Kwant-discuss digest..." > > Today's Topics: > > 1. Re: Band structure under B-field (T.C. Wu) > > > ---------- Forwarded message ---------- > From: "T.C. Wu" <tcwu(a)connect.ust.hk> > To: Michael Wimmer <m.t.wimmer(a)tudelft.nl>, < > kwant-discuss(a)kwant-project.org> > Cc: > Date: Wed, 24 Aug 2016 19:50:49 +0800 > Subject: Re: [Kwant] Band structure under B-field > Hi Michael, > > Thanks for your help. I modified the hopping of the vertical leads from -t > to hopping_Ax. Some LL-like flat bands are observed. However, they are > asymmetry about k = 0 (As shown in the attached figures) and it looks a bit > strange to me. Is it making sense? I suspect something is still wrong with > my code. Thanks for your time. > > Best, > Johnny > > On 24 August 2016 at 18:43, Michael Wimmer <m.t.wimmer(a)tudelft.nl> wrote: > >> Dear Johnny, >> >> you simply did not include any magnetic field in the vertical leads, see >> lead_hop_vert(). Passing the parameters as you do is fine. >> >> Best, >> >> Michael >> >> >> On 24-08-16 07:02, T.C. Wu wrote: >> > Dear Kwant users, >> > >> > I would like to plot the band structure of my system under a magnetic >> > field. Based on the code demostrated >> > in http://topocondmat.org/w3_pump_QHE/Laughlinargument.html, I plot the >> > band structure but I cannot observe any Landau level like spectrum. I >> > suspect it has something to do with the line >> > >> > p = SimpleNamespace(t=1.0, mu=0.3, mu_lead=0.3, B=0.5) >> > bands = kwant.physics.Bands(flead,args = [p]) >> > >> > Can the B-field be passed to the Hamiltonian in this way? The complete >> > code is attached below. Thanks for your help. >> > >> > Best, >> > Johnny >> > >> > #------My code-----------# >> > from __future__ import division >> > import numpy as np >> > import kwant >> > from matplotlib import pyplot as plt >> > from math import pi >> > >> > class SimpleNamespace(object): >> > def __init__(self, **kwargs): >> > self.__dict__.update(kwargs) >> > >> > >> > def qhe_corbino(r_out=100, r_in=65, w_lead=10): >> > """Create corbino disk. >> > >> > Square lattice, one orbital per site. >> > Returns kwant system. >> > >> > Arguments required in onsite/hoppings: >> > t, mu, mu_lead, B, phi >> > """ >> > # ring shape >> > def ring(pos): >> > (x, y) = pos >> > rsq = x ** 2 + y ** 2 >> > return (r_in ** 2 < rsq < r_out ** 2) >> > >> > # Onsite and hoppings >> > def onsite(site, p): >> > (x, y) = site.pos >> > return 4 * p.t - p.mu <http://p.mu> >> > >> > def crosses_branchcut(hop): >> > x1, y1 = hop[0].pos >> > x2, y2 = hop[1].pos >> > return y1 < 0 and x1 > 0.5 and x2 < 0.5 >> > >> > def hopping(site1, site2, p): >> > x1, y1 = site1.pos >> > x2, y2 = site2.pos >> > # Check for correctness! >> > return -p.t * np.exp(-0.5j * p.B * (x1 - x2) * (y1 + y2)) >> > >> > def branchcut_hopping(site1, site2, p): >> > return hopping(site1, site2, p) * np.exp(1j * p.phi) >> > >> > # Building system >> > lat = kwant.lattice.square() >> > sys = kwant.Builder() >> > >> > sys[lat.shape(ring, (0, r_in + 1))] = onsite >> > sys[lat.neighbors()] = hopping >> > >> > # adding special hoppings >> > def hops_across_cut(sys): >> > for hop in kwant.builder.HoppingKind((1, 0), lat, lat)(sys): >> > if crosses_branchcut(hop): >> > yield hop >> > sys[hops_across_cut] = branchcut_hopping >> > >> > # Attaching leads >> > sym_lead = kwant.TranslationalSymmetry((-1, 0)) >> > lead = kwant.Builder(sym_lead) >> > >> > def lead_shape(pos): >> > (x, y) = pos >> > return (-w_lead / 2 < y < w_lead / 2) >> > >> > lead[lat.shape(lead_shape, (0, 0))] = lambda site, p: 4 * p.t - >> > p.mu_lead >> > lead[lat.neighbors()] = lambda site1, site2, p: -p.t >> > >> > #### Attach the leads and return the system. #### >> > sys.attach_lead(lead) >> > sys.attach_lead(lead, origin=lat(0, 0)) >> > >> > return sys >> > >> > >> > def total_charge(value_array): >> > determinants = [np.linalg.det(s) for s in value_array] >> > charge = np.cumsum(np.angle(determinants / np.roll(determinants, >> 1))) >> > return charge / (2 * np.pi) >> > >> > >> > def qhe_ribbon(W, periodic=False): >> > """ Creates ribbon system >> > >> > If we have periodic boundary conditions, the flux through a single >> > unit cell is quantized. >> > """ >> > W = 2 * (W // 2) >> > >> > def ribbon_shape(pos): >> > (x, y) = pos >> > return (-W / 2 <= y <= W / 2) >> > >> > def onsite(site, p): >> > (x, y) = site.pos >> > return 4 * p.t - p.mu <http://p.mu> >> > >> > def hopping(site1, site2, p): >> > x1, y1 = site1.pos >> > x2, y2 = site2.pos >> > return -p.t * np.exp(-0.5j * p.B * (x1 - x2) * (y1 + y2)) >> > >> > def hopping_periodic(site1, site2, p): >> > x1, y1 = site1.pos >> > x2, y2 = site2.pos >> > return -p.t * np.exp(-1j * np.pi / (W + 1) * np.round((W + 1) * >> > p.B / (2 * np.pi)) * (x1 - x2) * (y1 + y2)) >> > >> > lat = kwant.lattice.square() >> > sym_sys = kwant.TranslationalSymmetry((-1, 0)) >> > sys = kwant.Builder(sym_sys) >> > >> > sys[lat.shape(ribbon_shape, (0, 0))] = onsite >> > >> > if periodic: >> > sys[lat.neighbors()] = hopping_periodic >> > sys[lat(0, - W / 2), lat(0, + W / 2)] = hopping_periodic >> > else: >> > sys[lat.neighbors()] = hopping >> > >> > return sys >> > >> > # Quantum hall bar codes >> > >> > >> > def qhe_hall_bar(L=50, W=10, w_lead=10, w_vert_lead=None): >> > """Create a hall bar system. >> > >> > Square lattice, one orbital per site. >> > Returns kwant system. >> > >> > Arguments required in onsite/hoppings: >> > t, mu, mu_lead >> > """ >> > >> > L = 2 * (L // 2) >> > W = 2 * (W // 2) >> > w_lead = 2 * (w_lead // 2) >> > if w_vert_lead is None: >> > w_vert_lead = w_lead >> > else: >> > w_vert_lead = 2 * (w_vert_lead // 2) >> > >> > # bar shape >> > def bar(pos): >> > (x, y) = pos >> > return (x >= -L / 2 and x <= L / 2) and (y >= -W / 2 and y <= W >> / 2) >> > >> > # Onsite and hoppings >> > def onsite(site, p): >> > (x, y) = site.pos >> > return 4 * p.t - p.mu <http://p.mu> >> > >> > def hopping_Ax(site1, site2, p): >> > x1, y1 = site1.pos >> > x2, y2 = site2.pos >> > return -p.t * np.exp(-0.5j * p.B * (x1 + x2) * (y1 - y2)) >> > >> > def make_lead_hop_y(x0): >> > def hopping_Ay(site1, site2, p): >> > x1, y1 = site1.pos >> > x2, y2 = site2.pos >> > return -p.t * np.exp(-1j * p.B * x0 * (y1 - y2)) >> > return hopping_Ay >> > >> > def lead_hop_vert(site1, site2, p): >> > return -p.t >> > >> > # Building system >> > lat = kwant.lattice.square() >> > sys = kwant.Builder() >> > >> > sys[lat.shape(bar, (0, 0))] = onsite >> > sys[lat.neighbors()] = hopping_Ax >> > >> > # Attaching leads >> > sym_lead = kwant.TranslationalSymmetry((-1, 0)) >> > lead = kwant.Builder(sym_lead) >> > >> > def lead_shape(pos): >> > (x, y) = pos >> > return (-w_lead / 2 <= y <= w_lead / 2) >> > >> > lead_onsite = lambda site, p: 4 * p.t - p.mu_lead >> > >> > sym_lead_vertical = kwant.TranslationalSymmetry((0, 1)) >> > lead_vertical1 = kwant.Builder(sym_lead_vertical) >> > lead_vertical2 = kwant.Builder(sym_lead_vertical) >> > >> > def lead_shape_vertical1(pos): >> > (x, y) = pos >> > return (-L / 4 - w_vert_lead / 2 <= x <= -L / 4 + w_vert_lead / >> 2) >> > >> > def lead_shape_vertical2(pos): >> > (x, y) = pos >> > return (+L / 4 - w_vert_lead / 2 <= x <= +L / 4 + w_vert_lead / >> 2) >> > >> > lead_vertical1[lat.shape(lead_shape_vertical1, (-L / 4, 0))] = >> > lead_onsite >> > lead_vertical1[lat.neighbors()] = lead_hop_vert >> > lead_vertical2[lat.shape(lead_shape_vertical2, (L / 4, 0))] = >> > lead_onsite >> > lead_vertical2[lat.neighbors()] = lead_hop_vert >> > >> > sys.attach_lead(lead_vertical1) >> > sys.attach_lead(lead_vertical2) >> > >> > sys.attach_lead(lead_vertical1.reversed()) >> > sys.attach_lead(lead_vertical2.reversed()) >> > >> > lead[lat.shape(lead_shape, (-1, 0))] = lead_onsite >> > lead[lat.neighbors()] = make_lead_hop_y(-L / 2) >> > >> > sys.attach_lead(lead) >> > >> > lead = kwant.Builder(sym_lead) >> > lead[lat.shape(lead_shape, (-1, 0))] = lead_onsite >> > lead[lat.neighbors()] = make_lead_hop_y(L / 2) >> > >> > sys.attach_lead(lead.reversed()) >> > >> > return sys >> > >> > >> > def calculate_sigmas(G): >> > # reduce by one dimension G -> G[temp, temp] >> > temp = [0, 1, 3, 4, 5] >> > G = G[temp, :] >> > G = G[:, temp] >> > # invert R = G^-1 >> > # find out whether it is a numpy object >> > r = np.linalg.inv(G) >> > # Voltages follow: V = R I[temp] >> > V = r.dot(np.array([0, 0, 0, 1, -1])) >> > # Completely solved the six terminal system. >> > # Consider the 2x2 conductance now: Use I = sigma U >> > E_x = V[1] - V[0] >> > E_y = V[1] - V[3] >> > # formula above >> > sigma_xx = E_x / (E_x**2 + E_y**2) >> > sigma_xy = E_y / (E_x**2 + E_y**2) >> > return sigma_xx, sigma_xy >> > >> > def plot_bandstructure(flead, momenta): >> > >> > bands = kwant.physics.Bands(flead,args = [p]) >> > energies = [bands(k) for k in momenta] >> > >> > plt.figure() >> > plt.plot(momenta, energies) >> > plt.xlabel(r"$k[a^{-1}]$") >> > plt.ylabel(r"$E [t]$") >> > plt.show() >> > >> > >> > sys = qhe_hall_bar(L=60, W=100, w_lead=90, w_vert_lead=28).finalized() >> > kwant.plot(sys) >> > p = SimpleNamespace(t=1.0, mu=0.3, mu_lead=0.3, B=0.5) >> > Bs = np.linspace(0.02, 0.15, 200) >> > num_leads = len(sys.leads) >> > >> > momenta = [-pi + 0.02 * pi * i for i in range(101)] >> > plot_bandstructure(sys.leads[2], momenta) >> > >> > > > _______________________________________________ > Kwant-discuss mailing list > Kwant-discuss(a)kwant-project.org > https://mailman-mail5.webfaction.com/listinfo/kwant-discuss > > -- Sumit Ghosh Spintronics Theory Group PSE Division KAUST -- ------------------------------ This message and its contents, including attachments are intended solely for the original recipient. 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Band structure under B-field
by T.C. Wu Aug. 24, 2016

Aug. 24, 2016

Dear Kwant users, I would like to plot the band structure of my system under a magnetic field. Based on the code demostrated in http://topocondmat.org/w3_pump_QHE/Laughlinargument.html, I plot the band structure but I cannot observe any Landau level like spectrum. I suspect it has something to do with the line p = SimpleNamespace(t=1.0, mu=0.3, mu_lead=0.3, B=0.5) bands = kwant.physics.Bands(flead,args = [p]) Can the B-field be passed to the Hamiltonian in this way? The complete code is attached below. Thanks for your help. Best, Johnny #------My code-----------# from __future__ import division import numpy as np import kwant from matplotlib import pyplot as plt from math import pi class SimpleNamespace(object): def __init__(self, **kwargs): self.__dict__.update(kwargs) def qhe_corbino(r_out=100, r_in=65, w_lead=10): """Create corbino disk. Square lattice, one orbital per site. Returns kwant system. Arguments required in onsite/hoppings: t, mu, mu_lead, B, phi """ # ring shape def ring(pos): (x, y) = pos rsq = x ** 2 + y ** 2 return (r_in ** 2 < rsq < r_out ** 2) # Onsite and hoppings def onsite(site, p): (x, y) = site.pos return 4 * p.t - p.mu def crosses_branchcut(hop): x1, y1 = hop[0].pos x2, y2 = hop[1].pos return y1 < 0 and x1 > 0.5 and x2 < 0.5 def hopping(site1, site2, p): x1, y1 = site1.pos x2, y2 = site2.pos # Check for correctness! return -p.t * np.exp(-0.5j * p.B * (x1 - x2) * (y1 + y2)) def branchcut_hopping(site1, site2, p): return hopping(site1, site2, p) * np.exp(1j * p.phi) # Building system lat = kwant.lattice.square() sys = kwant.Builder() sys[lat.shape(ring, (0, r_in + 1))] = onsite sys[lat.neighbors()] = hopping # adding special hoppings def hops_across_cut(sys): for hop in kwant.builder.HoppingKind((1, 0), lat, lat)(sys): if crosses_branchcut(hop): yield hop sys[hops_across_cut] = branchcut_hopping # Attaching leads sym_lead = kwant.TranslationalSymmetry((-1, 0)) lead = kwant.Builder(sym_lead) def lead_shape(pos): (x, y) = pos return (-w_lead / 2 < y < w_lead / 2) lead[lat.shape(lead_shape, (0, 0))] = lambda site, p: 4 * p.t - p.mu_lead lead[lat.neighbors()] = lambda site1, site2, p: -p.t #### Attach the leads and return the system. #### sys.attach_lead(lead) sys.attach_lead(lead, origin=lat(0, 0)) return sys def total_charge(value_array): determinants = [np.linalg.det(s) for s in value_array] charge = np.cumsum(np.angle(determinants / np.roll(determinants, 1))) return charge / (2 * np.pi) def qhe_ribbon(W, periodic=False): """ Creates ribbon system If we have periodic boundary conditions, the flux through a single unit cell is quantized. """ W = 2 * (W // 2) def ribbon_shape(pos): (x, y) = pos return (-W / 2 <= y <= W / 2) def onsite(site, p): (x, y) = site.pos return 4 * p.t - p.mu def hopping(site1, site2, p): x1, y1 = site1.pos x2, y2 = site2.pos return -p.t * np.exp(-0.5j * p.B * (x1 - x2) * (y1 + y2)) def hopping_periodic(site1, site2, p): x1, y1 = site1.pos x2, y2 = site2.pos return -p.t * np.exp(-1j * np.pi / (W + 1) * np.round((W + 1) * p.B / (2 * np.pi)) * (x1 - x2) * (y1 + y2)) lat = kwant.lattice.square() sym_sys = kwant.TranslationalSymmetry((-1, 0)) sys = kwant.Builder(sym_sys) sys[lat.shape(ribbon_shape, (0, 0))] = onsite if periodic: sys[lat.neighbors()] = hopping_periodic sys[lat(0, - W / 2), lat(0, + W / 2)] = hopping_periodic else: sys[lat.neighbors()] = hopping return sys # Quantum hall bar codes def qhe_hall_bar(L=50, W=10, w_lead=10, w_vert_lead=None): """Create a hall bar system. Square lattice, one orbital per site. Returns kwant system. Arguments required in onsite/hoppings: t, mu, mu_lead """ L = 2 * (L // 2) W = 2 * (W // 2) w_lead = 2 * (w_lead // 2) if w_vert_lead is None: w_vert_lead = w_lead else: w_vert_lead = 2 * (w_vert_lead // 2) # bar shape def bar(pos): (x, y) = pos return (x >= -L / 2 and x <= L / 2) and (y >= -W / 2 and y <= W / 2) # Onsite and hoppings def onsite(site, p): (x, y) = site.pos return 4 * p.t - p.mu def hopping_Ax(site1, site2, p): x1, y1 = site1.pos x2, y2 = site2.pos return -p.t * np.exp(-0.5j * p.B * (x1 + x2) * (y1 - y2)) def make_lead_hop_y(x0): def hopping_Ay(site1, site2, p): x1, y1 = site1.pos x2, y2 = site2.pos return -p.t * np.exp(-1j * p.B * x0 * (y1 - y2)) return hopping_Ay def lead_hop_vert(site1, site2, p): return -p.t # Building system lat = kwant.lattice.square() sys = kwant.Builder() sys[lat.shape(bar, (0, 0))] = onsite sys[lat.neighbors()] = hopping_Ax # Attaching leads sym_lead = kwant.TranslationalSymmetry((-1, 0)) lead = kwant.Builder(sym_lead) def lead_shape(pos): (x, y) = pos return (-w_lead / 2 <= y <= w_lead / 2) lead_onsite = lambda site, p: 4 * p.t - p.mu_lead sym_lead_vertical = kwant.TranslationalSymmetry((0, 1)) lead_vertical1 = kwant.Builder(sym_lead_vertical) lead_vertical2 = kwant.Builder(sym_lead_vertical) def lead_shape_vertical1(pos): (x, y) = pos return (-L / 4 - w_vert_lead / 2 <= x <= -L / 4 + w_vert_lead / 2) def lead_shape_vertical2(pos): (x, y) = pos return (+L / 4 - w_vert_lead / 2 <= x <= +L / 4 + w_vert_lead / 2) lead_vertical1[lat.shape(lead_shape_vertical1, (-L / 4, 0))] = lead_onsite lead_vertical1[lat.neighbors()] = lead_hop_vert lead_vertical2[lat.shape(lead_shape_vertical2, (L / 4, 0))] = lead_onsite lead_vertical2[lat.neighbors()] = lead_hop_vert sys.attach_lead(lead_vertical1) sys.attach_lead(lead_vertical2) sys.attach_lead(lead_vertical1.reversed()) sys.attach_lead(lead_vertical2.reversed()) lead[lat.shape(lead_shape, (-1, 0))] = lead_onsite lead[lat.neighbors()] = make_lead_hop_y(-L / 2) sys.attach_lead(lead) lead = kwant.Builder(sym_lead) lead[lat.shape(lead_shape, (-1, 0))] = lead_onsite lead[lat.neighbors()] = make_lead_hop_y(L / 2) sys.attach_lead(lead.reversed()) return sys def calculate_sigmas(G): # reduce by one dimension G -> G[temp, temp] temp = [0, 1, 3, 4, 5] G = G[temp, :] G = G[:, temp] # invert R = G^-1 # find out whether it is a numpy object r = np.linalg.inv(G) # Voltages follow: V = R I[temp] V = r.dot(np.array([0, 0, 0, 1, -1])) # Completely solved the six terminal system. # Consider the 2x2 conductance now: Use I = sigma U E_x = V[1] - V[0] E_y = V[1] - V[3] # formula above sigma_xx = E_x / (E_x**2 + E_y**2) sigma_xy = E_y / (E_x**2 + E_y**2) return sigma_xx, sigma_xy def plot_bandstructure(flead, momenta): bands = kwant.physics.Bands(flead,args = [p]) energies = [bands(k) for k in momenta] plt.figure() plt.plot(momenta, energies) plt.xlabel(r"$k[a^{-1}]$") plt.ylabel(r"$E [t]$") plt.show() sys = qhe_hall_bar(L=60, W=100, w_lead=90, w_vert_lead=28).finalized() kwant.plot(sys) p = SimpleNamespace(t=1.0, mu=0.3, mu_lead=0.3, B=0.5) Bs = np.linspace(0.02, 0.15, 200) num_leads = len(sys.leads) momenta = [-pi + 0.02 * pi * i for i in range(101)] plot_bandstructure(sys.leads[2], momenta)

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Kwant installation for Python 3 on MacOS
by KLOSS Thomas Aug. 12, 2016

Aug. 12, 2016

Dear All, I would like to install Kwant using Python 3 under OS X (on my Macbook Pro, OS X 10.6). For Mac OS X however, the guidelines on the Kwant webside cover only the Python 2 installation. Is there a way to install Kwant using Python 3 on a Mac? Kind Regards, Thomas Kloss

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