Mailman 3 August 2018 - Kwant-discuss

Regarding spin-orbit term in Bilayer graphene
by MS. PRIYANKA SINHA 15 Aug '18

15 Aug '18

Dear Sir, I have two questions. (1) I want to study the intralayer intrinsic spin-orbit coupling in bilayer graphene. For the monolayer case, it is easy to put the nnn hopping by, sys[graphene.neighbors(2)] = spin_orbit But for the bilayer case, as there are two planes and the intralayer coupling which I want to calculate should be in those two planes, Can I use the above code to get the effect. If not, then how can I put the effect in bilayer system. (2) When I am calculating the Hamiltonian submatrix between two sites to see the full matrix without spin-orbit ( only for tight-binding in bilayer where t=1 and interlayer coupling ,t_prep= 0.2) it is showing [[7.+0.j 0.+0.j 0.+0.j 0.+0.j] [0.+0.j 7.+0.j 0.+0.j 0.+0.j] [0.+0.j 0.+0.j 7.+0.j 0.+0.j] [0.+0.j 0.+0.j 0.+0.j 7.+0.j]] where 7 is for onsite element (sys[graphene.shape(rect, (0, 0, 0))] = 7 * sigma_0). Thanks in advance. sincerely, Priyanka Sinha

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Modify the onsite energy of the majorana fermions (example D6 in the paper)
by cqhy1127 13 Aug '18

13 Aug '18

Dear Professors, I want to put a transverse electric field on this example. So Imodify the onsite energy as follows, def onsite(site, p): x, y = site.pos E = 0.15 # the magnitude of electrical field in y direction return tau_z * (p.mu - 2 * p.t) + sigma_z * p.B + tau_x * p.Delta + E* y* s_0 s_0 = numpy.identity(2). However, the program crashed to UserCodeError: Error occurred in user-supplied value function "onsite". The same error also occur when I put a perpendicular magnetic field and modify the hopping energy as def hopping(sitei, sitej, phi, salt): xi, yi = sitei.pos xj, yj = sitej.pos return t0 * exp(-0.5j * phi * (xi - xj) * (yi + yj)) where t0 is the hopping matrix before put magnetic field. Would you like help me in this issue? Happy Kwant! QC HNIE __________The full code _____________________ from matplotlib import pyplot import kwant from kwant.digest import gauss import numpy import tinyarray import scipy.sparse.linalg # Python >= 3.3 provides SimpleNamespace in the # standard library so we can simply import it: # >>> from types import SimpleNamespace # (Kwant does not yet support Python 3.) class SimpleNamespace(object): """A simple container for parameters.""" def __init__(self, **kwargs): self.__dict__.update(kwargs) s_0 = numpy.identity(2) s_z = numpy.array([[1, 0], [0, -1]]) s_x = numpy.array([[0, 1], [1, 0]]) s_y = numpy.array([[0, -1j], [1j, 0]]) tau_z = tinyarray.array(numpy.kron(s_z, s_0)) tau_x = tinyarray.array(numpy.kron(s_x, s_0)) sigma_z = tinyarray.array(numpy.kron(s_0, s_z)) tau_zsigma_x = tinyarray.array(numpy.kron(s_z, s_x)) def onsite(site, p): x, y = site.pos Electric = 0.15 # the magnitude of electrical field in y direction return tau_z * (p.mu - 2 * p.t) + sigma_z * p.B + tau_x * p.Delta + Eeletric * y* s_0 def hopping(site0, site1, p): return tau_z * p.t + 1j * tau_zsigma_x * p.alpha def make_system(l=70): sys = kwant.Builder() lat = kwant.lattice.chain() sys[(lat(x) for x in range(l))] = onsite sys[lat.neighbors()] = hopping return sys.finalized() sys = make_system() # Calculate and plot lowest eigenenergies in B-field. B_values = numpy.linspace(0, 0.6, 80) energies = [] params = SimpleNamespace( t=1, mu=-0.1, alpha=0.05, Delta=0.2) for params.B in B_values: H = sys.hamiltonian_submatrix( args=[params], sparse=True) H = H.tocsc() eigs = scipy.sparse.linalg.eigsh(H, k=20, sigma=0) energies.append(numpy.sort(eigs[0])) pyplot.plot(B_values, energies) pyplot.show()

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Modify the onsite energy and hopping energy
by Q.Chen 13 Aug '18

13 Aug '18

Dear Professors, I want to put a transverse electric field on this example. So Imodify the onsite energy as follows, def onsite(site, p): x, y = site.pos E = 0.15 # the magnitude of electrical field in y direction return tau_z * (p.mu - 2 * p.t) + sigma_z * p.B + tau_x * p.Delta + E* y* s_0 s_0 = numpy.identity(2). However, the program crashed to UserCodeError: Error occurred in user-supplied value function "onsite". The same error also occur when I put a perpendicular magnetic field and modify the hopping energy as def hopping(sitei, sitej, phi, salt): xi, yi = sitei.pos xj, yj = sitej.pos return t0 * exp(-0.5j * phi * (xi - xj) * (yi + yj)) where t0 is the hopping matrix before put magnetic field. Would you like help me in this issue? Happy Kwant! QC HNIE __________The full code _____________________ from matplotlib import pyplot import kwant from kwant.digest import gauss import numpy import tinyarray import scipy.sparse.linalg # Python >= 3.3 provides SimpleNamespace in the # standard library so we can simply import it: # >>> from types import SimpleNamespace # (Kwant does not yet support Python 3.) class SimpleNamespace(object): """A simple container for parameters.""" def __init__(self, **kwargs): self.__dict__.update(kwargs) s_0 = numpy.identity(2) s_z = numpy.array([[1, 0], [0, -1]]) s_x = numpy.array([[0, 1], [1, 0]]) s_y = numpy.array([[0, -1j], [1j, 0]]) tau_z = tinyarray.array(numpy.kron(s_z, s_0)) tau_x = tinyarray.array(numpy.kron(s_x, s_0)) sigma_z = tinyarray.array(numpy.kron(s_0, s_z)) tau_zsigma_x = tinyarray.array(numpy.kron(s_z, s_x)) def onsite(site, p): x, y = site.pos Electric = 0.15 # the magnitude of electrical field in y direction return tau_z * (p.mu - 2 * p.t) + sigma_z * p.B + tau_x * p.Delta + Eeletric * y* s_0 def hopping(site0, site1, p): return tau_z * p.t + 1j * tau_zsigma_x * p.alpha def make_system(l=70): sys = kwant.Builder() lat = kwant.lattice.chain() sys[(lat(x) for x in range(l))] = onsite sys[lat.neighbors()] = hopping return sys.finalized() sys = make_system() # Calculate and plot lowest eigenenergies in B-field. B_values = numpy.linspace(0, 0.6, 80) energies = [] params = SimpleNamespace( t=1, mu=-0.1, alpha=0.05, Delta=0.2) for params.B in B_values: H = sys.hamiltonian_submatrix( args=[params], sparse=True) H = H.tocsc() eigs = scipy.sparse.linalg.eigsh(H, k=20, sigma=0) energies.append(numpy.sort(eigs[0])) pyplot.plot(B_values, energies) pyplot.show()

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About MoS2 ribbon
by cqhy1127 11 Aug '18

11 Aug '18

Dear Professors, When I use kwant to calculate the conductance for MoS2 ribbon, zigzag edge is right, however, for armchair edge ribbon, errors occure as follows, LinAlgError: QZ iteration failed to converge in zgges. I am very comfused about this. Thanks! Q.Chen HNIE

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(no subject)
by Rohit Kumar Srivastav 10 Aug '18

10 Aug '18

I want to apply a voltage on the stadium with three leads in such a way two leads constitute the same current and one lead constitute zero current (Its means voltage is zero in this lead always) for calculating the scattering matrix. Please, suggest me what is the code of voltage. (How to apply the voltage) Best, Rohit

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regarding error message
by shyam lochan bora 10 Aug '18

10 Aug '18

Dear Sir, I am using kwant in windows with the help of notepad++. when I run the following program import matplotlib from matplotlib import pyplot from mpl_toolkits import mplot3d import numpy as np from wraparound import wraparound import kwant def momentum_to_lattice(k): B = np.array(graphene.prim_vecs).T A = B.dot(np.linalg.inv(B.T.dot(B))) return np.linalg.solve(A, k) def dispersion_2D(syst, args=None, lim=1.5*np.pi, num_points=200): """A simple plot of 2D band structure.""" if args is None: args = [] momenta = np.linspace(-lim, lim, num_points) energies = [] for kx in momenta: for ky in momenta: lattice_k = momentum_to_lattice([kx, ky]) h = syst.hamiltonian_submatrix(args=(list(args) + list(lattice_k))) energies.append(np.linalg.eigvalsh(h)) energies = np.array(energies).reshape(num_points, num_points, -1) emin, emax = np.min(energies), np.max(energies) kx, ky = np.meshgrid(momenta, momenta) fig = pyplot.figure() axes = fig.add_subplot(1, 1, 1, projection='3d') for band in range(energies.shape[-1]): axes.plot_surface(kx, ky, energies[:, :, band], cstride=2, rstride=2, cmap=matplotlib.cm.RdBu_r, vmin=emin, vmax=emax, linewidth=0.1) graphene = kwant.lattice.general([[1, 0], [1/2, np.sqrt(3)/2]], # lattice vectors [[0, 0], [0, 1/np.sqrt(3)]]) # Coordinates of the sites a, b = graphene.sublattices bulk_graphene = kwant.Builder(kwant.TranslationalSymmetry(*graphene.prim_vecs)) bulk_graphene[graphene.shape((lambda pos: True), (0, 0))] = 0 bulk_graphene[graphene.neighbors(1)] = 1 dispersion_2D(wraparound(bulk_graphene).finalized()) zigzag_ribbon = kwant.Builder(kwant.TranslationalSymmetry([1, 0])) zigzag_ribbon[graphene.shape((lambda pos: abs(pos[1]) < 9), (0, 0))] = 0 zigzag_ribbon[graphene.neighbors(1)] = 1 kwant.plotter.bands(zigzag_ribbon.finalized()) armchair_ribbon = kwant.Builder(kwant.TranslationalSymmetry([0, np.sqrt(3)])) armchair_ribbon[graphene.shape((lambda pos: abs(pos[0]) < 9), (0, 0))] = 0 armchair_ribbon[graphene.neighbors(1)] = 1 kwant.plotter.bands(armchair_ribbon.finalized(), fig_size=(12, 8)) zigzag_ribbon = kwant.Builder(kwant.TranslationalSymmetry([1, 0])) zigzag_ribbon[a.shape((lambda pos: abs(pos[1]) < 9), (0, 0))] = 0.2 zigzag_ribbon[b.shape((lambda pos: abs(pos[1]) < 9), (0, 0))] = -0.2 zigzag_ribbon[graphene.neighbors(1)] = 1 kwant.plotter.bands(zigzag_ribbon.finalized(), fig_size=(12, 8)) The following error message appeared.. File "C:\Users\Shyam Lochan Bora\Desktop\new 1.py", line 5, in <module> from wraparound import wraparound ModuleNotFoundError: No module named 'wraparound' Help me in this regard

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Voltage
by Rohit Kumar Srivastav 10 Aug '18

10 Aug '18

Is this code correct for the voltage applied in the 3rd lead?

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error message
by shyam lochan bora 09 Aug '18

09 Aug '18

Dear Sir, I am running Kwant in windows using notepad ++. import matplotlib from matplotlib import pyplot from mpl_toolkits import mplot3d import numpy as np from wraparound import wraparound import kwant def momentum_to_lattice(k): B = np.array(graphene.prim_vecs).T A = B.dot(np.linalg.inv(B.T.dot(B))) return np.linalg.solve(A, k) def dispersion_2D(syst, args=None, lim=1.5*np.pi, num_points=200): """A simple plot of 2D band structure.""" if args is None: args = [] momenta = np.linspace(-lim, lim, num_points) energies = [] for kx in momenta: for ky in momenta: lattice_k = momentum_to_lattice([kx, ky]) h = syst.hamiltonian_submatrix(args=(list(args) + list(lattice_k))) energies.append(np.linalg.eigvalsh(h)) energies = np.array(energies).reshape(num_points, num_points, -1) emin, emax = np.min(energies), np.max(energies) kx, ky = np.meshgrid(momenta, momenta) fig = pyplot.figure() axes = fig.add_subplot(1, 1, 1, projection='3d') for band in range(energies.shape[-1]): axes.plot_surface(kx, ky, energies[:, :, band], cstride=2, rstride=2, cmap=matplotlib.cm.RdBu_r, vmin=emin, vmax=emax, linewidth=0.1) graphene = kwant.lattice.general([[1, 0], [1/2, np.sqrt(3)/2]], # lattice vectors [[0, 0], [0, 1/np.sqrt(3)]]) # Coordinates of the sites a, b = graphene.sublattices bulk_graphene = kwant.Builder(kwant.TranslationalSymmetry(*graphene.prim_vecs)) bulk_graphene[graphene.shape((lambda pos: True), (0, 0))] = 0 bulk_graphene[graphene.neighbors(1)] = 1 dispersion_2D(wraparound(bulk_graphene).finalized()) zigzag_ribbon = kwant.Builder(kwant.TranslationalSymmetry([1, 0])) zigzag_ribbon[graphene.shape((lambda pos: abs(pos[1]) < 9), (0, 0))] = 0 zigzag_ribbon[graphene.neighbors(1)] = 1 kwant.plotter.bands(zigzag_ribbon.finalized()) armchair_ribbon = kwant.Builder(kwant.TranslationalSymmetry([0, np.sqrt(3)])) armchair_ribbon[graphene.shape((lambda pos: abs(pos[0]) < 9), (0, 0))] = 0 armchair_ribbon[graphene.neighbors(1)] = 1 kwant.plotter.bands(armchair_ribbon.finalized(), fig_size=(12, 8)) zigzag_ribbon = kwant.Builder(kwant.TranslationalSymmetry([1, 0])) zigzag_ribbon[a.shape((lambda pos: abs(pos[1]) < 9), (0, 0))] = 0.2 zigzag_ribbon[b.shape((lambda pos: abs(pos[1]) < 9), (0, 0))] = -0.2 zigzag_ribbon[graphene.neighbors(1)] = 1 kwant.plotter.bands(zigzag_ribbon.finalized(), fig_size=(12, 8)) This error message is appeared.. Please help me in this regard

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Re: [Kwant] Calculating valley polarized conductances using Kwant
by Kevin Ryczko 01 Aug '18

01 Aug '18

Thanks Anton! > On Aug 1, 2018, at 2:16 PM, Anton Akhmerov <anton.akhmerov+kd(a)gmail.com> wrote: > > Hi Kevin, > >> I just wanted to verify that the indices of the modes I am finding match up with the indices of the submatrix. > > This is indeed correct. The sort order of the scattering matrix > elements matches the sort order of the modes in the lead_info. > > Best, > Anton

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Re: [Kwant] Calculating valley polarized conductances using Kwant
by Kevin Ryczko 01 Aug '18

01 Aug '18

Hi Joe, Thanks for getting back so quickly! I realized after sending my initial email that I made a mistake in the ordering of the Python functions. You are indeed correct that I should be summing after taking the modulus squared of the transmission coefficient matrix elements. Before we finish the discussion, I just wanted to verify that the indices of the modes I am finding match up with the indices of the submatrix. You mentioned that I had the right idea, but did not comment on that. I just want to be sure. Thanks again, Kevin > On Aug 1, 2018, at 7:45 AM, Joseph Weston <joseph.weston08(a)gmail.com> wrote: > > Hi Kevin, > > Thanks for the well-posed and focused question! > >> I would like to calculate the valley polarized conductance for a graphene nanoribbon with 2 leads (let’s say in the x-direction). My current approach is this: >> >> 1) Get the S-matrix for a certain energy >> 2) Find the indices of the modes with positive velocities >> 3) Separate these modes by positive and negative momenta >> 4) Get the sub matrix from the S-matrix >> 5) Sum the transmission coefficients for positive and negative momenta > > This is the right idea. > >> 2) Find the indices of the modes with positive velocities > > We only care about selecting (by their valley) the correct *incoming* > modes. In Kwant's convention these are the modes with *negative*, not > positive, velocity. > > This is in an obscure part of the documentation [1], where we say > >> positive velocity and momentum directions are defined with respect to > the translational symmetry direction of the [lead] > > When leads are attached to a scattering region, their symmetry direction > points *away* from the scattering region "towards infinity", which means > that the incoming modes have negative velocity in Kwant's convention. > > >> The code below illustrates these 5 steps: >> >> import progressbar >> def valleyPolarizability(syst, energies, lead_start=0, lead_end=1): >> KPs = [] >> Ks = [] >> bar = progressbar.ProgressBar() >> for energy in bar(energies): >> smatrix = kwant.smatrix(syst, energy, params={'phi': phi}) >> positives = np.where(smatrix.lead_info[lead_start].velocities >= 0)[0] >> momentas = smatrix.lead_info[lead_start].momenta[positives] >> K_prime_indices = np.where(momentas < 0)[0] >> K_indices = np.where(momentas >= 0)[0] >> submatrix = smatrix.submatrix(lead_end, lead_start) >> K_prime_T = np.absolute(np.sum(submatrix[:, K_prime_indices]))**2 >> K_T = np.absolute(np.sum(submatrix[:, K_indices]))**2 >> KPs.append(K_prime_T) >> Ks.append(K_T) >> return KPs, Ks > > This is almost correct except for a couple of things. Firstly we should > select the modes that have negative velocity, as already discussed. > Secondly: > >> K_prime_T = np.absolute(np.sum(submatrix[:, K_prime_indices]))**2 > > Here you're summing the scattering *amplitudes*, when you really want to > sum the scattering *probabilities*: > >> K_prime_T = np.sum(np.abs(submatrix[:, K_prime_indices]))**2 > > i.e. you need to take the absolute square before summing. > > > Happy Kwanting, > > Joe > > > [1]: > https://kwant-project.org/doc/1.3/reference/generated/kwant.physics.Propaga… > >

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