Kwant-discuss April 2020

kwant-discuss@python.org

5 participants
9 discussions

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 the spin is positioned in the Smatrix?
by Qingtian Zhang 06 Mar '22

06 Mar '22

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 06 Mar '22

06 Mar '22

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 12 Sep '21

12 Sep '21

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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To to separate spins, electron and hole
by Khani Hosein 22 Jun '21

22 Jun '21

Dear all, I am using Kwant to study a system with both spins and electron and hole, so the hopping matrix is 4X4. Now I want to know how to separate the spins, electron and hole. I study this through the "2.6. Superconductors: orbital degrees of freedom, conservation laws and symmetries" smatrix = kwant.smatrix(syst, energy) data.append(smatrix.submatrix((0, 0), (0, 0)).shape[0] -smatrix.transmission((0, 0), (0, 0)) +smatrix.transmission((0, 1), (0, 0))) I do not find more information about this for kwant. For my system, if I have 3 leads, and the hopping and onsite energy is set in this order: (e↑,0,0,0)- spin up electron,first row of the 4X4matrix (0,e↓,0,0)- spin down electron,second row of the 4X4matrix (0,0, h↑ ,0)- spin up hole,third row of the 4X4matrix (0,0, 0, h ↓ )- spin down hole,fourth row of the 4X4matrix I want to obtain the transmissions from 0 →2. smatrix = kwant.smatrix(syst, energy) The transmission from h↑ to e↑ is: smatrix.transmission((2, 1), (0, 2)) The transmission from h ↓ to e↑ is: smatrix.transmission((2, 1), (0, 3)) Is my understanding correct? Thanks very much in advance! Hosein Khani

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gas adsorption by a crystal
by Marco Di Gennaro (TME) 20 Apr '20

20 Apr '20

Dear everyone, I would like to study gas dynamics and absorption within a transition-metal based crystal. Is possible to realize a simplified Kubas bonding model in tight binding through a simple s-d interaction? Could I distinguish physisorption by chemisorption by Kubas adsorption at this level of theory? Any comment or suggestion would be highly appreciated. Thank you ----------------------------- Marco Di Gennaro Toyota Motor Europe ----------------------------- This e-mail may contain confidential information. If you are not an addressee or otherwise authorised to receive this message, you should not use, copy, disclose or take any action based on this e-mail. If you have received this e-mail in error, please inform the sender promptly and delete this message and any attachments immediately.

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Density of states for a lead
by Jacopo Settino 18 Apr '20

18 Apr '20

Dear all, is it implemented a way to calculate the density or the density of states of a lead (defined as kwant.TranslationalSymmetry ...)? Thank you. Regards, Jacopo

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Re: [Kwant] site value is changing after finalizing the system
by Abbout Adel 17 Apr '20

17 Apr '20

Dear Sudin, Your code seems to work fine for me. Why don't you just use an onsite function as below? (you can put a condition as you wish) sys_2[site] returns a function so you need to add the argument of hat function: sys_2[site](site) (be careful, this will not work if the leads add some sites to the central system: in the lead, the potential is given by scalars, in the system by a function. a small modification is required) I hope this helps, Adel ############################################################################# def make_system(W, L, lim): ## scattering region ## def Onsite(site): x,y=site.pos if y< lim: return x else: return 0 sys = kwant.Builder() sys[lat.shape(cross(W,L), (0,0))] = Onsite sys[lat.neighbors(1)] = -1. leads = [create_lead_h(W, xsym1,axis=(0,0)),create_lead_h(W, xsym2,axis=(0,0))] for lead in leads: sys.attach_lead(lead) return sys def main(): sys_2 = make_system(W=3.5, L=3, lim=-1) kwant.plotter.plot(sys_2,site_color=lambda site:sys_2[site](site),colorbar=True, cmap=None) if __name__ == '__main__': main() On Fri, Apr 17, 2020 at 7:06 AM SUDIN GANGULY <sudinganguly(a)gmail.com> wrote: > Dear Sir, > > Thank you for your reply. The problem I am facing is that if I assign the > site values like (1,2,3,...) along the bottom line, the colormap of the > site values are changing whenever I compile the code. > ############################ > import kwant > from pylab import * > import matplotlib.pyplot as plt > from random import * > import numpy as np > > > class Honeycomb(kwant.lattice.Polyatomic): > 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 > > sys=kwant.Builder() > lat = Honeycomb() > a,b= lat.sublattices > > > def cross(W, L): > def shape(pos): > return ((-W <= pos[1] <= W and -L <= pos[0] <= L)) > return shape > > pv1, pv2 = lat.prim_vecs > > > xsym1 = kwant.TranslationalSymmetry((-pv2)) # lattice symmetry in -x > direction > xsym1.add_site_family(lat.sublattices[0], other_vectors=[(-2, 1)]) > xsym1.add_site_family(lat.sublattices[1], other_vectors=[(-2, 1)]) > > xsym2=kwant.TranslationalSymmetry((pv2)) > xsym2.add_site_family(lat.sublattices[0], other_vectors=[(-2, 1)]) > xsym2.add_site_family(lat.sublattices[1], other_vectors=[(-2, 1)]) > > def create_lead_h(W, symmetry, axis): > lead = kwant.Builder(symmetry) > lead[lat.wire(axis, W)] = 0. > lead[lat.neighbors(1)] = -1. > return lead > > > def make_system(W, L, no_of_line): > > ## scattering region ## > sys = kwant.Builder() > sys[lat.shape(cross(W,L), (0,0))] = 0 > sys[lat.neighbors(1)] = -1. > > > line=[] > for site in sys.expand(lat.shape(cross(W,L), (0, 0))): > line.append(site.pos[1]) > > > line=set(line) > line=list(line) > line=sort(line) > my_list=[] > i=1 > for site in sys.expand(lat.shape(cross(W,L), (0, 0))): > for j in range(0,no_of_line+1,2): > line_no=j > if (site.pos[1]==line[line_no] or > site.pos[1]==line[line_no+1]): > my_list.append(site) > sys[site]=i > i=i+1 > > ## leads ## > > leads = [create_lead_h(W, xsym1,axis=(0,0))] > leads += [create_lead_h(W, xsym2,axis=(0,0))] > > for lead in leads: > sys.attach_lead(lead) > > > #============================================================================= > return {'sys': sys } > > def main(): > sys_2 = make_system(W=3.5, L=5, no_of_line=1) > kwant.plotter.plot(sys_2['sys'],site_color=lambda > site:sys_2['sys'][site],colorbar=True, cmap=None) > > if __name__ == '__main__': > main() > ################################# > > I can resolve this issue by collecting the site positions from the array > named my_list in the given code and then assign the site values > accordingly. However, this procedure is a bit lengthy. If there is any > other way to do that with less coding, that will be very helpful. > With Regards, > Sudin > > On Fri, Apr 17, 2020 at 1:36 AM Abbout Adel <abbout.adel(a)gmail.com> wrote: > >> Dear Sudin, >> >> Please post the code giving the error or explain better your concern. >> >> Could you just do it by defining an on site function? >> >> def Onsite(site): >> x,y=site.pos() >> i,_=site.tag >> if y=y0: return Values[i] >> else: return V0 >> >> >> sys[(........)]=Onsite >> >> I hope this helps, >> Adel >> >> On Wed, Apr 15, 2020 at 3:45 PM SUDIN GANGULY <sudinganguly(a)gmail.com> >> wrote: >> >>> Dear Sir, >>> >>> I want to assign a particular sequence of site values on a particular >>> line (a number of lines) of a zigzag graphene nanoribbon. For example, the >>> bottom zigzag line. >>> >>> let's say, from the left to right there are 10 sites and I want to put >>> the onsite values as [1,2,3,...]. >>> >>> I was able to get the information about the sites that are in the bottom >>> line and have assigned the site values accordingly. But the problem is that >>> each time I finalize the system, I get different onsite values along the >>> bottom line. Is there any way to resolve this? Or maybe this approach is >>> not the right way to do that. >>> >>> A part of my code is given below >>> ======================== >>> def make_system(W, L, no_of_line): >>> >>> ## scattering region ## >>> sys = kwant.Builder() >>> sys[lat.shape(cross(W,L), (0,0))] = 0 >>> sys[lat.neighbors(1)] = -1. >>> #######INFO of the line######### >>> line=[] >>> for site in sys.expand(lat.shape(cross(W,L), (0, 0))): >>> #print (site.pos[0],site.pos[1]) >>> line.append(site.pos[1]) >>> >>> line=set(line) >>> line=list(line) >>> line=sort(line) >>> >>> >>> i=1 >>> for site in sys.expand(lat.shape(cross(W,L), (0, 0))): >>> for j in range(0,no_of_line+1,2): >>> line_no=j >>> if (site.pos[1]==line[line_no] or site.pos[1]==line[line_no+1]): >>> sys[site]=i >>> i=i+1 >>> ######################## >>> >>> With Regards, >>> Sudin >>> >> >> >> -- >> Abbout Adel >> > > > -- > সুদিন > -- Abbout Adel

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site value is changing after finalizing the system
by SUDIN GANGULY 16 Apr '20

16 Apr '20

Dear Sir, I want to assign a particular sequence of site values on a particular line (a number of lines) of a zigzag graphene nanoribbon. For example, the bottom zigzag line. let's say, from the left to right there are 10 sites and I want to put the onsite values as [1,2,3,...]. I was able to get the information about the sites that are in the bottom line and have assigned the site values accordingly. But the problem is that each time I finalize the system, I get different onsite values along the bottom line. Is there any way to resolve this? Or maybe this approach is not the right way to do that. A part of my code is given below ======================== def make_system(W, L, no_of_line): ## scattering region ## sys = kwant.Builder() sys[lat.shape(cross(W,L), (0,0))] = 0 sys[lat.neighbors(1)] = -1. #######INFO of the line######### line=[] for site in sys.expand(lat.shape(cross(W,L), (0, 0))): #print (site.pos[0],site.pos[1]) line.append(site.pos[1]) line=set(line) line=list(line) line=sort(line) i=1 for site in sys.expand(lat.shape(cross(W,L), (0, 0))): for j in range(0,no_of_line+1,2): line_no=j if (site.pos[1]==line[line_no] or site.pos[1]==line[line_no+1]): sys[site]=i i=i+1 ######################## With Regards, Sudin

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Kwant-discuss April 2020