Mailman 3 July 2017 - Kwant-discuss

Gate-defined Nanowire Quantum Dot
by Jonathan Fields Sept. 15, 2022

Sept. 15, 2022

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>

4 4

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))

3 3

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

3 3

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

4 3

Current in a closed system
by Abbout Adel Oct. 26, 2017

Oct. 26, 2017

Dear All, I was consulting the example of the current in a *closed system* and I am a little bit confused: The figure showing the current flowing inside a circle [1] is obtained for a magnetic field B=0 ! But we know that for B=0, the Hamiltonian is a real symmetric matrix and thus diagonalized by a real orthogonal matrix, so the eigenvectors are real (any phase is just artificial.) By using the formula giving the current we should find zero ! moreover we can ask why we have a current flowing clockwise and not anticlockwise (I remind that B=0) ! When we put B=0.05, we obtain the figures below for the current and the wave function. the wave function has circular symmetry but not the current. Moreover, x and y play exactly the same role so the current should be the same on x and on y (independently from the used gauge) Am I missing something ? Thank you in advance. Adel [1] https://kwant-project.org/doc/1/tutorial/spectrum

3 3

lead_info
by Prof. CHAN Kwok Sum Sept. 20, 2017

Sept. 20, 2017

Dear Kwant developer, Thank you for your effort in developing Kwant. I have a question about the definition of the direction of momentum in the smatrix.lead_info. Assume a lead lies along the y direction with primitive vector (0,1). The symmetry operation of a lead is (0,1) if the lead goes towards the positive direction and is (0,-1) if the lead goes towards the negative direction. For the momenta contained in smatrix.lead_info for these two leads , do they use the same coordinate system? Positive momenta mean the direction (0,1), negative momenta mean the direction (0,-1). For velocity, in smatrix.lead_info, it has nothing to do with the coordinate system. Positive means outgoing, negative means incoming in the lead. Thank you KS Chan Disclaimer: This email (including any attachments) is for the use of the intended recipient only and may contain confidential information and/or copyright material. If you are not the intended recipient, please notify the sender immediately and delete this email and all copies from your system. Any unauthorized use, disclosure, reproduction, copying, distribution, or other form of unauthorized dissemination of the contents is expressly prohibited.

3 3

virtual lead
by Patrik Arvoy July 31, 2017

July 31, 2017

Dear users and developers, I would like to attach Büttiker’s virtual lead (the leads with zero net currents) to all sites in the scattering region to mimic dephasing processes. The attached code works fine as long as the switch 'vl=False' (without attaching any virtual lead). I get equal conductance for up and down spin. As I understood, attaching virtual leads can be done via the following builder class in kwant: https://kwant-project.org/doc/1/reference/generated/kwant. builder.SelfEnergyLead#kwant.builder.SelfEnergyLead I have the retarded self energy of each virtual lead (- 1j*0.0025) that I can replace with '*selfenergy_func*' in this builder class (am I right?). Now if I change 'vl=True' : 1- I get an error message, related to symmetry but there is no argument to define symmetry... 2- how can I ensure zero net currents through these virtual leads? Thanks in advance for any help Patrik -------------------------------------------------- from mpl_toolkits.mplot3d import Axes3D from scipy.spatial import * from matplotlib import rcParams from numpy import * from numpy.linalg import * import pickle import sys import os import string import heapq import kwant import tinyarray from matplotlib import pyplot chiral=True if chiral: p = pi/5 #phi t = 0.66 #theta a = 0.34 x = 1.4 e1 = 0 e2 = 0.3 t2=0.1 t1=-x*t2 t0 = 2 lam=-0.08 t_so1 = 0.01 #spin-orbit coupling param t_so2 = x*t_so1 #spin-orbit coupling param tl=tr=0.3 gd = 0.005 #the gamma_d, dephasing parameter N = 30 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]]) no=2 #number of orbitals def sigma_v1(ap): # pauli metrix along the vertical axis value=sigma_z*cos(t)+sin(t)*(sigma_x*sin(ap)-sigma_y*cos(ap)) return value def sigma_v2(ap): # pauli metrix along the vertical axis value=sigma_z*cos(t)-sin(t)*(sigma_x*sin(ap)-sigma_y*cos(ap)) return value def family_color(sites): return 'black' #if site.family == sites def hopping_lw(site1, site2): return 0.08 class Amorphous(kwant.builder.SiteFamily): def __init__(self, coords): self.coords = coords super(Amorphous, self).__init__("amorphous", "",no) def normalize_tag(self, tag): try: tag = int(tag[0]) except: raise KeyError if 0 <= tag < len(coords): return tag else: raise KeyError def pos(self, tag): return self.coords[tag] coords=[(0.0000000000, 0.0000000000, 0.0000000000), (-0.1336881039, 0.4114496766, 0.3400000000), (-0.4836881039, 0.6657395614, 0.6800000000), (-0.9163118961, 0.6657395614, 1.0200000000), (-1.2663118961, 0.4114496766, 1.3600000000), (-1.4000000000, 0.0000000000, 1.7000000000), (-1.2663118961, -0.4114496766, 2.0400000000), (-0.9163118961, -0.6657395614, 2.3800000000), (-0.4836881039, -0.6657395614, 2.7200000000), (-0.1336881039, -0.4114496766, 3.0600000000), (0.0000000000, -0.0000000000, 3.4000000000), (-0.1336881039, 0.4114496766, 3.7400000000), (-0.4836881039, 0.6657395614, 4.0800000000), (-0.9163118961, 0.6657395614, 4.4200000000), (-1.2663118961, 0.4114496766, 4.7600000000), (-1.4000000000, 0.0000000000, 5.1000000000), (-1.2663118961, -0.4114496766, 5.4400000000), (-0.9163118961, -0.6657395614, 5.7800000000), (-0.4836881039, -0.6657395614, 6.1200000000), (-0.1336881039, -0.4114496766, 6.4600000000), (0.0000000000, -0.0000000000, 6.8000000000), (-0.1336881039, 0.4114496766, 7.1400000000), (-0.4836881039, 0.6657395614, 7.4800000000), (-0.9163118961, 0.6657395614, 7.8200000000), (-1.2663118961, 0.4114496766, 8.1600000000), (-1.4000000000, 0.0000000000, 8.5000000000), (-1.2663118961, -0.4114496766, 8.8400000000), (-0.9163118961, -0.6657395614, 9.1800000000), (-0.4836881039, -0.6657395614, 9.5200000000), (-0.1336881039, -0.4114496766, 9.8600000000), (-1.4000000000, 0.0000000000, 0.0000000000), (-1.2663118961, -0.4114496766, 0.3400000000), (-0.9163118961, -0.6657395614, 0.6800000000), (-0.4836881039, -0.6657395614, 1.0200000000), (-0.1336881039, -0.4114496766, 1.3600000000), (0.0000000000, -0.0000000000, 1.7000000000), (-0.1336881039, 0.4114496766, 2.0400000000), (-0.4836881039, 0.6657395614, 2.3800000000), (-0.9163118961, 0.6657395614, 2.7200000000), (-1.2663118961, 0.4114496766, 3.0600000000), (-1.4000000000, 0.0000000000, 3.4000000000), (-1.2663118961, -0.4114496766, 3.7400000000), (-0.9163118961, -0.6657395614, 4.0800000000), (-0.4836881039, -0.6657395614, 4.4200000000), (-0.1336881039, -0.4114496766, 4.7600000000), (0.0000000000, -0.0000000000, 5.1000000000), (-0.1336881039, 0.4114496766, 5.4400000000), (-0.4836881039, 0.6657395614, 5.7800000000), (-0.9163118961, 0.6657395614, 6.1200000000), (-1.2663118961, 0.4114496766, 6.4600000000), (-1.4000000000, 0.0000000000, 6.8000000000), (-1.2663118961, -0.4114496766, 7.1400000000), (-0.9163118961, -0.6657395614, 7.4800000000), (-0.4836881039, -0.6657395614, 7.8200000000), (-0.1336881039, -0.4114496766, 8.1600000000), (0.0000000000, -0.0000000000, 8.5000000000), (-0.1336881039, 0.4114496766, 8.8400000000), (-0.4836881039, 0.6657395614, 9.1800000000), (-0.9163118961, 0.6657395614, 9.5200000000), (-1.2663118961, 0.4114496766, 9.8600000000)] amorphous_lat = Amorphous(coords) syst = kwant.Builder() for i in range(N): syst[amorphous_lat(i)] = e1*sigma_0 syst[amorphous_lat(N+i)] = e2*sigma_0 syst[amorphous_lat(i), amorphous_lat(N+i)] = lam*sigma_0 if i > 0: syst[amorphous_lat(i), amorphous_lat(i-1)] = t1*sigma_0 + 1j*t_so1*(sigma_v1(i*p)+sigma_v1((i-1)*p)) syst[amorphous_lat(N+i),amorphous_lat(N+i-1)] = t2*sigma_0 + 1j*t_so2*(sigma_v2(i*p)+sigma_v2((i-1)*p)) #the section that cause the problem vl=False if vl: def mount_vlead(syst, vlead_interface, norbs): """Mounts virtual lead to interfaces provided. :sys: kwant.builder.Builder An unfinalized system to mount leads :vlead_interface: sequence of kwant.builder.Site Interface of lead :norb: integer Number of orbitals in system hamiltonian. """ dim = len(vlead_interface)*norbs sea = zeros((dim, dim), dtype=float) - 1j*0.5*gd def selfenergy_func(energy, args=()): return sea vlead = kwant.builder.SelfEnergyLead(selfenergy_func, vlead_interface) syst.leads.append(vlead) #attaching virtual lead to all sites vli = syst.sites() mount_vlead(syst, vli, norbs=no) lat=kwant.lattice.cubic(a, norbs=no) syst[lat(0, 0, -1)] = e1*sigma_0 syst[amorphous_lat(0), lat(0, 0, -1)] = tl*sigma_0 sym = kwant.TranslationalSymmetry([0, 0, -a]) dn_lead = kwant.Builder(sym, conservation_law=-sigma_z) dn_lead[lat(0, 0, -2)] = e1*sigma_0 dn_lead[lat.neighbors()] = t0*sigma_0 syst.attach_lead(dn_lead) prim_vecs=tinyarray.array([(a,0.,0.),(0.,a,0.),(0.,0.,a)]) offset=tinyarray.array((-1.2663118961, 0.4114496766,0.0)) lat2=kwant.lattice.Monatomic(prim_vecs, offset, norbs=no) syst[lat2(0, 0, N)] = e1*sigma_0 syst[amorphous_lat(2*N-1), lat2(0, 0, N)] = tr*sigma_0 sym1 = kwant.TranslationalSymmetry([0, 0, a]) up_lead = kwant.Builder(sym1, conservation_law=-sigma_z) up_lead[lat2(0, 0, N+1)] = e1*sigma_0 up_lead[lat2.neighbors()] = t0*sigma_0 syst.attach_lead(up_lead) system=kwant.plot(syst, site_lw=0.1, site_color=family_color, hop_lw=hopping_lw) trans=True if trans: syst = syst.finalized() energies = [] datau = [] datad = [] for ie in range(-320,520): energy = ie * 0.001 smatrix = kwant.smatrix(syst, energy=energy) energies.append(energy) Gu=smatrix.transmission((1, 0), 0) Gd=smatrix.transmission((1, 1), 0) datau.append(Gu) datad.append(Gd) fig = pyplot.figure() pyplot.plot(energies, datau, 'r--') pyplot.plot(energies, datad, 'b:') pyplot.legend(['Gu', 'Gd'], loc='upper left') pyplot.xlim([-0.4,0.65]) pyplot.ylim([-0.03,1.0]) pyplot.show()

2 3

small correction in the documentation
by Abbout Adel July 31, 2017

July 31, 2017

Dear all, In the section "Computing local quantities: densities and currents", the function field_direction(pos,r0,delta) is defined with the condition: if r==0: m_i=[0,0,1] This should be m_i =[0,0,-1] This explains why we get some strange pattern in the present figures on the online documentation. With this minor correction, the result will be better and more physical. Adel

2 1

up/down conductance
by Patrik Arvoy July 21, 2017

July 21, 2017

Dear kwant users and developers, I am trying to calculate the up and down conductance in the following system, separately, to calculate spin polarization. I followed some of the steps suggested in the mailing list before (wavefuncation or current operator). I know for this system I should get the same conductance for up and down spins. I first calculate the total conductance But then 1- The wave function approach does not give the the up/down conductance similar to total. 2- the current-operator approach gives the error 'kwant.graph.core.EdgeDoesNotExistError'. I have attached the code in the following. If one runs the code it plot the system with leads correctly the first conductance plot is what one expects (if trans:) then the second plot is incorrect (if strans1:) and then gives the error (if strans:). I appreciate any help Patrik ----------------------------------------------------------------- from mpl_toolkits.mplot3d import Axes3D from scipy.spatial import * from matplotlib import rcParams from numpy import * from numpy.linalg import * import pickle import sys import os import string import heapq import kwant import tinyarray from matplotlib import pyplot chiral=True if chiral: p = pi/5 #phi t = 0.66 #theta a = 0.34 x = 1.4 e1 = 0 e2 = 0.3 t2=0.1 t1=-x*t2 t0 = 2 lam=-0.08 t_so1 = 0.01 #spin-orbit coupling param t_so2 = x*t_so1 #spin-orbit coupling param tl=tr=0.3 N = 30 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]]) no=2 #number of orbitals def sigma_v1(ap): # pauli metrix along the vertical axis value=sigma_z*cos(t)+sin(t)*(sigma_x*sin(ap)-sigma_y*cos(ap)) return value def sigma_v2(ap): # pauli metrix along the vertical axis value=sigma_z*cos(t)-sin(t)*(sigma_x*sin(ap)-sigma_y*cos(ap)) return value def family_color(sites): return 'black' #if site.family == sites def hopping_lw(site1, site2): return 0.08 class Amorphous(kwant.builder.SiteFamily): def __init__(self, coords): self.coords = coords super(Amorphous, self).__init__("amorphous", "",no) def normalize_tag(self, tag): try: tag = int(tag[0]) except: raise KeyError if 0 <= tag < len(coords): return tag else: raise KeyError def pos(self, tag): return self.coords[tag] coords=[(0.0000000000, 0.0000000000, 0.0000000000), (-0.1336881039, 0.4114496766, 0.3400000000), (-0.4836881039, 0.6657395614, 0.6800000000), (-0.9163118961, 0.6657395614, 1.0200000000), (-1.2663118961, 0.4114496766, 1.3600000000), (-1.4000000000, 0.0000000000, 1.7000000000), (-1.2663118961, -0.4114496766, 2.0400000000), (-0.9163118961, -0.6657395614, 2.3800000000), (-0.4836881039, -0.6657395614, 2.7200000000), (-0.1336881039, -0.4114496766, 3.0600000000), (0.0000000000, -0.0000000000, 3.4000000000), (-0.1336881039, 0.4114496766, 3.7400000000), (-0.4836881039, 0.6657395614, 4.0800000000), (-0.9163118961, 0.6657395614, 4.4200000000), (-1.2663118961, 0.4114496766, 4.7600000000), (-1.4000000000, 0.0000000000, 5.1000000000), (-1.2663118961, -0.4114496766, 5.4400000000), (-0.9163118961, -0.6657395614, 5.7800000000), (-0.4836881039, -0.6657395614, 6.1200000000), (-0.1336881039, -0.4114496766, 6.4600000000), (0.0000000000, -0.0000000000, 6.8000000000), (-0.1336881039, 0.4114496766, 7.1400000000), (-0.4836881039, 0.6657395614, 7.4800000000), (-0.9163118961, 0.6657395614, 7.8200000000), (-1.2663118961, 0.4114496766, 8.1600000000), (-1.4000000000, 0.0000000000, 8.5000000000), (-1.2663118961, -0.4114496766, 8.8400000000), (-0.9163118961, -0.6657395614, 9.1800000000), (-0.4836881039, -0.6657395614, 9.5200000000), (-0.1336881039, -0.4114496766, 9.8600000000), (-1.4000000000, 0.0000000000, 0.0000000000), (-1.2663118961, -0.4114496766, 0.3400000000), (-0.9163118961, -0.6657395614, 0.6800000000), (-0.4836881039, -0.6657395614, 1.0200000000), (-0.1336881039, -0.4114496766, 1.3600000000), (0.0000000000, -0.0000000000, 1.7000000000), (-0.1336881039, 0.4114496766, 2.0400000000), (-0.4836881039, 0.6657395614, 2.3800000000), (-0.9163118961, 0.6657395614, 2.7200000000), (-1.2663118961, 0.4114496766, 3.0600000000), (-1.4000000000, 0.0000000000, 3.4000000000), (-1.2663118961, -0.4114496766, 3.7400000000), (-0.9163118961, -0.6657395614, 4.0800000000), (-0.4836881039, -0.6657395614, 4.4200000000), (-0.1336881039, -0.4114496766, 4.7600000000), (0.0000000000, -0.0000000000, 5.1000000000), (-0.1336881039, 0.4114496766, 5.4400000000), (-0.4836881039, 0.6657395614, 5.7800000000), (-0.9163118961, 0.6657395614, 6.1200000000), (-1.2663118961, 0.4114496766, 6.4600000000), (-1.4000000000, 0.0000000000, 6.8000000000), (-1.2663118961, -0.4114496766, 7.1400000000), (-0.9163118961, -0.6657395614, 7.4800000000), (-0.4836881039, -0.6657395614, 7.8200000000), (-0.1336881039, -0.4114496766, 8.1600000000), (0.0000000000, -0.0000000000, 8.5000000000), (-0.1336881039, 0.4114496766, 8.8400000000), (-0.4836881039, 0.6657395614, 9.1800000000), (-0.9163118961, 0.6657395614, 9.5200000000), (-1.2663118961, 0.4114496766, 9.8600000000)] amorphous_lat = Amorphous(coords) syst = kwant.Builder() #adding the onsite and hopping to the system for i in range(N): syst[amorphous_lat(i)] = e1*sigma_0 syst[amorphous_lat(N+i)] = e2*sigma_0 syst[amorphous_lat(i), amorphous_lat(N+i)] = lam*sigma_0 if i > 0: syst[amorphous_lat(i), amorphous_lat(i-1)] = t1*sigma_0 + 1j*t_so1*(sigma_v1(i*p)+sigma_v1((i-1)*p)) syst[amorphous_lat(N+i),amorphous_lat(N+i-1)] = t2*sigma_0 + 1j*t_so2*(sigma_v2(i*p)+sigma_v2((i-1)*p)) # If we want to attach to vertical 1D chains to the system # we first add a site of the down lead to the scattering region lat=kwant.lattice.cubic(a, norbs=no) syst[lat(0, 0, -1)] = e1*sigma_0 syst[amorphous_lat(0), lat(0, 0, -1)] = tl*sigma_0 # We make a regular down lead and attach it to the system dn_lead = kwant.Builder(kwant.TranslationalSymmetry((0, 0, -a))) dn_lead[lat(0, 0, -2)] = e1*sigma_0 dn_lead[lat.neighbors()] = t0*sigma_0 syst.attach_lead(dn_lead) prim_vecs=tinyarray.array([(a,0.,0.),(0.,a,0.),(0.,0.,a)]) offset=tinyarray.array((-1.2663118961, 0.4114496766,0.0)) lat2=kwant.lattice.Monatomic(prim_vecs, offset, norbs=no) syst[lat2(0, 0, N)] = e1*sigma_0 syst[amorphous_lat(2*N-1), lat2(0, 0, N)] = tr*sigma_0 up_lead = kwant.Builder(kwant.TranslationalSymmetry((0, 0, a))) up_lead[lat2(0, 0, N+1)] = e1*sigma_0 up_lead[lat2.neighbors()] = t0*sigma_0 syst.attach_lead(up_lead) system=kwant.plot(syst, site_lw=0.1, site_color=family_color, hop_lw=hopping_lw) trans=True if trans: syst = syst.finalized() energies = [] data = [] for ie in range(-320,520): energy = ie * 0.001 smatrix = kwant.smatrix(syst, energy=energy) energies.append(energy) data.append(0.5*smatrix.transmission(1, 0)) fig = pyplot.figure(figsize=(6,2)) pyplot.plot(energies, data) pyplot.xlim([-0.32,0.52]) pyplot.ylim([-0.03,1.25]) pyplot.xlabel("energy [eV]") pyplot.ylabel("conductance [e^2/h]") pyplot.show() strans1=True if strans1: #syst = syst.finalized() energies = [] data = [] def oscle(ene, lead_nr): wfs=kwant.wave_function(syst, ene, check_hermiticity=True)(lead_nr) spin_current_z = 0 for psi in wfs: psi_start = psi[0 : 2] psi_end = psi[2 * 61: 2 * 61 + 2] #spin_current_z += -2 * imag(psi_end.conjugate().dot(sigma_z).dot(psi_start)) spin_current_z += abs(imag(psi_end.conjugate().dot(sigma_z).dot(psi_start))) return spin_current_z for ie in range(-320,520): energy = ie * 0.001 energies.append(energy) data.append(oscle(ene=energy, lead_nr=1)) fig = pyplot.figure(figsize=(6,2)) pyplot.plot(energies, data) pyplot.show() strans=True if strans: #syst = syst.finalized() J_spin = kwant.operator.Current(syst, sigma_z, where=[(amorphous_lat(0), amorphous_lat(N-2))], sum=True) all_wfs = kwant.wave_function(syst, energy=0.25)(1) spin_current_list = sum(J_spin(wf) for wf in all_wfs) print(spin_current_list)

2 4

installation problem
by Prof. CHAN Kwok Sum July 18, 2017

July 18, 2017

Dear Kwant developer, I solved my problem in installation. I forgot to install packages which are required by matplotlib. After installing them, the problem is solved. KS Chan Disclaimer: This email (including any attachments) is for the use of the intended recipient only and may contain confidential information and/or copyright material. If you are not the intended recipient, please notify the sender immediately and delete this email and all copies from your system. Any unauthorized use, disclosure, reproduction, copying, distribution, or other form of unauthorized dissemination of the contents is expressly prohibited.

1 0