Mailman 3 May 2022 - Kwant-discuss

Realistic values of hopping parameters
by Yu Li 19 Oct '23

19 Oct '23

Dear all, Now I’m studying some transport property based on multilayered system, with nonmagnetic layer/ferromagnetic layer (NM/FM) stack. May I ask when creating a tight binding system, and setting hoppings by the following function: syst[(lat(1, 0), lat(1, 1))] = t, how to associate the hopping with a realistic system? Such as hoppings between FM and FM atoms, or between FM and NM atoms? I found in many literatures people just simply put t=1, but I assume the value should depend on the type of atoms. My another question is, is it possible to define more than one type of hopping between two sites? For the tight-binding approximation of p electrons, there are two types of hopping integrals: Vppσ, and Vppπ, so I’m wondering if it’s possible to simulate the effect of both hoppings? Thanks a lot for reading my questions! Cheers, Yu Li

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Defining uniaxial strain in specified region of graphene
by shrushti.tapar07＠gmail.com 21 Jan '23

21 Jan '23

I want to create the graphene strained superlattice-like structure, having uniaxial strain defined at the specified region. Please, someone can suggest to me how to define the strained region and interface between unstrained and strained graphene regions. Thanks in Advance Shrushti

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Re: How the spin is positioned in the Smatrix?
by Diego Bruno 27 Sep '22

27 Sep '22

Can you disponibilize the code?

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Gate-defined Nanowire Quantum Dot
by Jonathan Fields 15 Sep '22

15 Sep '22

Dear Reader, I am new to KWANT and trying to figure out if it is suitable for calculating transport properties of gate-defined quantum dots made out of nanowires, along the lines of the structure used in https://arxiv.org/abs/cond-mat/0609463. Now, I understand that the mailing list is not a place to ask people to do my work for me, and my question is also not for someone to do this. What I am looking for is some insights into if this is possible (and not all that difficult) with the package. At first sight (and going through the tutorials as well as the APS March Meeting material) this does not seem straightforward; what I struggle with is how to define this type of dot in KWANT. Now, one way would of course be to built the entire 3D geometry of the system, but this will be computationally expensive, and probably also rather tricky to do in terms of defining everything, from the hexagonal wire itself to all of the gates and oxide layers and such. Some abstraction would be preferred, perhaps even reducing the dimensionality and making a 2D system, such as often done in the tutorial. Is this a good idea? My problem is that if one does this, then I run into the problem of how to model the 'half wrap-around' type gates typically used in these devices. In the transport through barrier section of the APS March Meeting material there is a section on how to model realistic potentials, but this would not work all that well for these wrap around type gates. On the other hand, in a way they are perhaps not so different from the QPC in that section. One could model the three gates as something like https://i.imgur.com/WZC983c.png as they do essentially form channels in the wire. Apart from if this sacrifices too much of the nanowire nature in favor of a 2DEG system, I do suppose such a system should in principle be able to be treated as a quantum dot. I haven't been able to confirm this as I am not yet sure how one can apply a source-drain voltage in KWANT; I first thought that this would probably be related to the energy of the modes, but then again I have not been able to produce Coulomb diamonds in this way. The question is getting rather lenghty, and also a bit unclear at this point. Perhaps I should finish up by stating it in a concise form; would you think that it is possible to simulate the transport of such a gate defined nanowire quantum dot device with KWANT, and if so, is the approach I am suggesting above a viable one, or would you go about it very differently? Kind regards Jonathan <http://aka.ms/weboutlook>

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How to add random but opposite onsite potential on graphene?
by wilson2048＠outlook.com 26 May '22

26 May '22

Dear community, I want to add random potentials on graphene. Within each unit cell, I want A site have the oppsite value to B site. That is, random across unit cells, but symmetric respect to zero within every unit cell. How to achieve this? I have tried to do so, but cannot find a way. Below is my code: ``` import numpy as np import kwant low = 0 high = 1 def make_syst(a=1): syst = kwant.Builder() lat = kwant.lattice.honeycomb(a, norbs=1, name=['a', 'b']) r = 10 def circle(pos): x, y = pos return x ** 2 + y ** 2 < r ** 2 def onsite(site, low, high): return np.random.uniform(low, high) # first attempt using function, not working, also cannot gurantee a, b are truly opposite in value # syst[lat.a.shape(circle, (0, 0))] = onsite # syst[lat.b.shape(circle, (0, 0))] = -1*onsite # wrong # second attempt, still not right m = np.random.uniform(low, high) syst[lat.a.shape(circle, (0, 0))] = m syst[lat.b.shape(circle, (0, 0))] = -m syst[lat.neighbors()] = 1 return syst.finalized() fsyst = make_syst() # kwant.plot(fsyst) H = fsyst.hamiltonian_submatrix(params=dict(high=high, low=low)) Es = np.linalg.eigvalsh(H) plt.plot(Es, '.') plt.show() ``` Thanks for help!

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Kwant-Plot discretize potential with different colours
by Lorenzo BAGNASACCO 17 May '22

17 May '22

Dear Kwant community, I am a physics student and I am approaching to Kwant to solve simple problems of scattering. For example, I created a 2D discrete potential. The potential has two different values: "V0" and "0". When I plot the system, using the command "kwant.plot(syst)", I obtain the plot with only light-blue colour. There is a command to plot the discrete potential with two (or more) different colours (in my case one colour for "V0", and another one for "0")? Yours Sincerely Lorenzo Bagnasacco

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Problems in getting the current
by mondal18＠iitg.ac.in 13 May '22

13 May '22

Dear developers, I was trying to get the plot of currents in a graphene ribbon. I am getting the error "Number of orbitals not defined", which is done by specifying the norbs. However, in my code, I am unable to specify the norbs. Another thing is that the interface between the right lead (and left leads) and the system is not parallel to the y axis. What are the possible ways to solve such problems. The code I am using is the following. #################################################### from math import sqrt import random import itertools as it import tinyarray as ta import numpy as np import matplotlib.pyplot as plt import kwant class Honeycomb(kwant.lattice.Polyatomic): """Honeycomb lattice with methods for dealing with hexagons""" def __init__(self, name=''): prim_vecs = [[0.5, sqrt(3)/2], [1, 0]] # bravais lattice vectors # offset the lattice so that it is symmetric around x and y axes basis_vecs = [[-0.5, -1/sqrt(12)], [-0.5, 1/sqrt(12)]] super(Honeycomb, self).__init__(prim_vecs, basis_vecs, name) self.a, self.b = self.sublattices def hexagon(self, tag): """ Get sites belonging to hexagon with the given tag. Returns sites in counter-clockwise order starting from the lower-left site. """ tag = ta.array(tag) # a-sites b-sites deltas = [(0, 0), (0, 0), (1, 0), (0, 1), (0, 1), (-1, 1)] lats = it.cycle(self.sublattices) return (lat(*(tag + delta)) for lat, delta in zip(lats, deltas)) def hexagon_neighbors(self, tag, n=1): """ Get n'th nearest neighbor hoppings within the hexagon with the given tag. """ hex_sites = list(self.hexagon(tag)) return ((hex_sites[(i+n)%6], hex_sites[i%6]) for i in range(6)) def random_placement(builder, lattice, density): """ Randomly selects hexagon tags where adatoms can be placed. This avoids the edge case where adatoms would otherwise be placed on incomplete hexagons at the system boundaries. """ assert 0 <= density <= 1 system_sites = builder.sites() def hexagon_in_system(tag): return all(site in system_sites for site in lattice.hexagon(tag)) # get set of tags for sites in system (i.e. tags from only one sublattice) system_tags = (s.tag for s in system_sites if s.family == lattice.a) # only allow tags which have complete hexagons in the system valid_tags = list(filter(hexagon_in_system, system_tags)) N = int(density * len(valid_tags)) total_hexagons=len(valid_tags) valuef=random.sample(valid_tags, N) return valuef def ribbon(W, L): def shape(pos): return (-L <= pos[0] <= L and -W <= pos[1] <= W) return shape ## Pauli matrices ## sigma_0 = ta.array([[1, 0], [0, 1]]) # identity sigma_x = ta.array([[0, 1], [1, 0]]) sigma_y = ta.array([[0, -1j], [1j, 0]]) sigma_z = ta.array([[1, 0], [0, -1]]) ## Hamiltonian value functions ## def onsite_potential(site, params): return params['ep'] * sigma_0 def potential_shift(site, params): return params['mu'] * sigma_0 def kinetic(site_i, site_j, params): return -params['gamma'] * sigma_0 def rashba(site_i, site_j, params): d_ij = site_j.pos - site_i.pos rashba = 1j * params['V_R'] * (sigma_x * d_ij[1] - sigma_y * d_ij[0]) return rashba + kinetic(site_i, site_j, params) def spin_orbit(site_i, site_j, params): so = 1j * params['V_I'] * sigma_z return so lat = Honeycomb() A, B = lat.sublattices pv1, pv2 = lat.prim_vecs ysym = kwant.TranslationalSymmetry(pv2 - 2*pv1) # lattice symmetry in -y direction xsym = kwant.TranslationalSymmetry(-pv2) # lattice symmetry in -x direction # adatom lattice, for visualization only adatom_lat = kwant.lattice.Monatomic(lat.prim_vecs, name='adatom') def site_size(s): return 0.25 if s.family in lat.sublattices else 0.3 def site_color(s): if s.family==lat.sublattices[0]: return 'w' elif s.family==lat.sublattices[1]: return 'k' else: return 'g' def create_lead_h(W, sym1, axis=(0, 0)): lead = kwant.Builder(sym1) lead[lat.wire(axis, W)] = 0. * sigma_0 lead[lat.neighbors(1)] = kinetic return lead def create_ribbon(W, L, adatom_density=0.2, show_adatoms=False): ## scattering region ## sys = kwant.Builder() sys[lat.shape(ribbon(W, L), (0, 0))] = onsite_potential sys[lat.neighbors(1)] = kinetic adatoms = random_placement(sys, lat, adatom_density) sys[(lat.hexagon(a) for a in adatoms)] = potential_shift sys[(lat.hexagon_neighbors(a, 1) for a in adatoms)] = rashba sys[(lat.hexagon_neighbors(a, 2) for a in adatoms)] = spin_orbit if show_adatoms: # no hoppings are added so these won't affect the dynamics; purely cosmetic sys[(adatom_lat(*a) for a in adatoms)] = 0 ## leads ## leads = [create_lead_h(W, xsym)] leads += [lead.reversed() for lead in leads] # right lead for lead in leads: sys.attach_lead(lead) return sys def plot_currents(syst, currents): fig, axes = plt.subplots(1, len(currents)) if not hasattr(axes, '__len__'): axes = (axes,) for ax, (title, current) in zip(axes, currents): kwant.plotter.current(syst, current, ax=ax, colorbar=False) ax.set_title(title) plt.show() def currents(sys, params): syst = sys.finalized() wf = kwant.wave_function(syst, energy=-1, args=(params,)) psi = wf(0)[0] # even (odd) indices correspond to spin up (down) up, down = psi[::2], psi[1::2] print(psi.shape) density = np.abs(up)**2 + np.abs(down)**2 # spin down components have a minus sign spin_z = np.abs(up)**2 - np.abs(down)**2 # spin down components have a minus sign spin_y = 1j * (down.conjugate() * up - up.conjugate() * down) rho = kwant.operator.Density(syst) rho_sz = kwant.operator.Density(syst, sigma_z) rho_sy = kwant.operator.Density(syst, sigma_y) # calculate the expectation values of the operators with 'psi' density = rho(psi) spin_z = rho_sz(psi) spin_y = rho_sy(psi) plot_densities(syst, [ ('$σ_0$', density), ('$σ_z$', spin_z), ('$σ_y$', spin_y), ]) J_0 = kwant.operator.Current(syst) J_z = kwant.operator.Current(syst, sigma_z) J_y = kwant.operator.Current(syst, sigma_y) # calculate the expectation values of the operators with 'psi' current = J_0(psi) spin_z_current = J_z(psi) spin_y_current = J_y(psi) plot_currents(syst, [ ('$J_{σ_0}$', current), ('$J_{σ_z}$', spin_z_current), ('$J_{σ_y}$', spin_y_current), ]) if __name__ == '__main__': params = dict(gamma=1., ep=0, mu=0., V_I=0.007, V_R=0.0165) # In adatoms W=11 L=32 adatom_density=0.1 sys = create_ribbon(W, L, adatom_density, show_adatoms=True) # fig = plt.figure() ax = plt.subplot() ax = kwant.plot(sys, site_color=site_color, site_lw=0.05, site_size=site_size,lead_site_lw=0, dpi = 150) # ax.savefig('system2.png', bbox_inches = 'tight', dpi = 200) currents(sys, params) ################################################### I shall look forward to your kind reply. Thanking you. Sincerely yours, Sayan Mondal, Research scholar, IIT Guwahati, India

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Help: Inputting Random Potential on Graphene
by Blackwell, Raymond 12 May '22

12 May '22

Hello, My name is Raymond Blackwell and I am attempting to use Kwant to simulate some experimental data. Our data involves dopant atoms intercalated under graphene, so I would like to simulate the LDOS but with a potential that randomly varies at several points within the system. I am trying to modify the code for the kernel_polynominal_method, but I cannot seem to get a random potential. I have used a similar method to randomly select a few points and modify the hopping parameter, but I am struggling with the seemingly more simple case where the potential varies. The relevant portion of my code is below. def make_syst(r=30, t=-1, a=1): syst = kwant.Builder() lat = kwant.lattice.honeycomb(a, norbs=1) def circle(pos): x, y = pos return x ** 2 + y ** 2 < r ** 2 sites2 = list(syst.sites()) Random_sites= random.choices(sites2, k=10) def onsite(site, salt): return 0.5 * kwant.digest.gauss(repr(Random_sites), salt) syst[lat.shape(circle, (0, 0))] = onsite(bytes(3),bytes(3)) Any help is greatly appreciated! Best, -Raymond

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