Mailman 3 December 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>

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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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Energy dispersion of MoS2
by Gongwei_Hu Jan. 3, 2018

Jan. 3, 2018

Dear all Kwant workers! My problem is about the calculation of energy dispersion of MoS2 in Ref PRB 92, 195402 (2015). I want to use the tight binding Hamiltonian of MoS2 (Eq (2) in Reference) to obtain energy dispersion in Figure 6(a). Because the honeycomb of monolayer MoS2 is distinct with the graphene, onsite energy of Mo and S is also different. In graphene, the onsite energy of A and B atoms in unit cell is equivalent and thus the hopping energy of nearest and two nearest atom in different direction is same. However, this is not right in MoS2 (A----Mo, B----S). So i choose the code to describe onsite energy in MoS2 as follow def onsite(site): return E_M if (site.family == M) else E_X Is this right? Furthermore, i solve the energy band in y-direction by considering only one lead (abs(y)<Ly, Ly is the width). Is it correct to use the following code to build the system? sym = kwant.TranslationalSymmetry(lat.vec((-1, 0))) sys = kwant.Builder(sym) My Kwant code cannot obtain the result in Figure 6(a). Please help me if you are free, Thanks! My Kwant code: import kwant from matplotlib import pyplot import tinyarray import math import numpy eV, nm=1,1e-9 lamad_M, lamad_X = 0.075*eV, 0.052*eV e0, e2, ep, ez = -1.094*eV, -1.512*eV, -3.560*eV, -6.886*eV V_pdd, V_pdp = 3.689*eV, -1.241*eV V_ddd, V_ddp, V_ddde = -0.895*eV, 0.252*eV, 0.228*eV V_ppd, V_ppp = 1.225*eV, -0.467*eV; a0=0.316*nm; s=1j; sz=+1; sqrt_3=math.sqrt(3) E_M=tinyarray.array([[e0, 0, 0],[0, e2, -s*lamad_M*sz],[0, s*lamad_M*sz, e2]]); E_X=tinyarray.array([[ep+V_ppp, -s*lamad_X/2*sz, 0],[s*lamad_X/2*sz, ep+V_ppp, 0],[0, 0, ez-V_ppd]]); t1_MX=1/7*math.sqrt(2/7)*tinyarray.array([[-9*V_pdp+sqrt_3*V_pdd, 3*sqrt_3*V_pdp-V_pdd, 12*V_pdp+sqrt_3*V_pdd], [5*sqrt_3*V_pdp+3*V_pdd, 9*V_pdp-sqrt_3*V_pdd, -2*sqrt_3*V_pdp+3*V_pdd], [-V_pdp-3*sqrt_3*V_pdd, 5*sqrt_3*V_pdp+3*V_pdd, 6*V_pdp-3*sqrt_3*V_pdd]]) t2_MX=1/7*math.sqrt(2/7)*tinyarray.array([[0, -6*sqrt_3*V_pdp+2*V_pdd, 12*V_pdp+sqrt_3*V_pdd], [0, -6*V_pdp-4*sqrt_3*V_pdd, 4*sqrt_3*V_pdp-6*V_pdd], [14*V_pdp, 0, 0]]) t3_MX=1/7*math.sqrt(2/7)*tinyarray.array([[9*V_pdp-sqrt_3*V_pdd, 3*sqrt_3*V_pdp-V_pdd, 12*V_pdp+sqrt_3*V_pdd], [-5*sqrt_3*V_pdp-3*V_pdd, 9*V_pdp-sqrt_3*V_pdd, -2*sqrt_3*V_pdp+3*V_pdd], [-V_pdp-3*sqrt_3*V_pdd, -5*sqrt_3*V_pdp-3*V_pdd, -6*V_pdp+3*sqrt_3*V_pdd]]) t1_MM=1/4*tinyarray.array([[3*V_ddde+V_ddd, sqrt_3/2*(-V_ddde+V_ddd), -3/2*(V_ddde-V_ddd)], [sqrt_3/2*(-V_ddde+V_ddd), 1/4*(V_ddde+12*V_ddp+3*V_ddd), sqrt_3/4*(V_ddde-4*V_ddp+3*V_ddd)], [-3/2*(V_ddde-V_ddd), sqrt_3/4*(V_ddde-4*V_ddp+3*V_ddd), 1/4*(3*V_ddde+4*V_ddp+9*V_ddd)]]) t2_MM=1/4*tinyarray.array([[3*V_ddde+V_ddd, sqrt_3*(V_ddde-V_ddd), 0], [sqrt_3*(V_ddde-V_ddd), V_ddde+3*V_ddd, 0], [0 , 0,4*V_ddp]]) t3_MM=1/4*tinyarray.array([[3*V_ddde+V_ddd, sqrt_3/2*(-V_ddde+V_ddd), 3/2*(V_ddde-V_ddd)], [sqrt_3/2*(-V_ddde+V_ddd), 1/4*(V_ddde+12*V_ddp+3*V_ddd), -sqrt_3/4*(V_ddde-4*V_ddp+3*V_ddd)], [3/2*(V_ddde-V_ddd), -sqrt_3/4*(V_ddde-4*V_ddp+3*V_ddd), 1/4*(3*V_ddde+4*V_ddp+9*V_ddd)]]) t1_XX=1/4*tinyarray.array([[3*V_ppp+V_ppd, sqrt_3*(V_ppp-V_ppd), 0], [sqrt_3*(V_ppp-V_ppd), V_ppp+3*V_ppd,0], [0, 0, 4*V_ppp]]) t2_XX=tinyarray.array([[V_ppd, 0, 0], [0 ,V_ppp, 0], [0, 0, V_ppp]]) t3_XX=1/4*tinyarray.array([[3*V_ppp+V_ppd, -sqrt_3*(V_ppp-V_ppd), 0], [-sqrt_3*(V_ppp-V_ppd), V_ppp+3*V_ppd, 0], [0, 0 ,4*V_ppp]]) lat = kwant.lattice.honeycomb() M, X = lat.sublattices def make_lead(Lx=1, Ly=48): def Rectangle(pos): x, y = pos return abs(y)<Ly def onsite(site): return E_M if (site.family == M) else E_X #sym = kwant.TranslationalSymmetry((-Lx, 0)) #sym = kwant.TranslationalSymmetry((-3, 0)) sym = kwant.TranslationalSymmetry(lat.vec((-1, 0))) sys = kwant.Builder(sym) #sys = kwant.Builder() sys[lat.shape(Rectangle, (0, 0))] = onsite #hopping_onsit_M=((0, 0),M,M) #hopping_onsit_X=((0, 0),X,X) #sys[kwant.builder.HoppingKind(*hopping_onsit_M)] = E_M########## #sys[kwant.builder.HoppingKind(*hopping_onsit_X)] = E_X######### hopping2_M =((1, 0), M, M) hopping1_M =((-1, 1), M, M) hopping3_M =((0, -1), M, M) sys[kwant.builder.HoppingKind(*hopping1_M)] = t1_MM sys[kwant.builder.HoppingKind(*hopping2_M)] = t2_MM sys[kwant.builder.HoppingKind(*hopping3_M)] = t3_MM hopping2_X =((1, 0), X, X) hopping1_X =((-1, 1), X, X) hopping3_X =((0, -1), X, X) sys[kwant.builder.HoppingKind(*hopping1_X)] = t1_XX sys[kwant.builder.HoppingKind(*hopping2_X)] = t2_XX sys[kwant.builder.HoppingKind(*hopping3_X)] = t3_XX hopping1_MX =((0, 0), M, X) hopping2_MX =((0, 1), M, X) hopping3_MX =((-1, 1), M, X) sys[kwant.builder.HoppingKind(*hopping1_MX)] = t1_MX sys[kwant.builder.HoppingKind(*hopping2_MX)] = t2_MX sys[kwant.builder.HoppingKind(*hopping3_MX)] = t3_MX def family_colors(site): return 0 if (site.family == M) else 1 def hopping_lw(site1, site2): return 0.05 if site1.family == site2.family else 0.1 def hopping_color(site1,site2): return 'g' if site1.family==site2.family else 'b' kwant.plot(sys,site_color=family_colors,site_lw=0.05, hop_lw=hopping_lw,hop_color=hopping_color,colorbar=False) return sys def main(): lead = make_lead().finalized() kwant.plotter.bands(lead, show=False) pyplot.xlabel("momentum [(lattice constant)^-1]") pyplot.ylabel("energy [eV]") pyplot.show() # Call the main function if the script gets executed (as opposed to imported). # See <http://docs.python.org/library/__main__.html>. if __name__ == '__main__': main()

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parallel mumps
by Benoit Gaury Dec. 29, 2017

Dec. 29, 2017

Hi, I wanted to know what kwant does if the parallel version of the MUMPS library is installed instead of the sequential version. Will it be ignored? Benoit

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Energy dispersion of MoS2
by Gongwei_Hu Dec. 27, 2017

Dec. 27, 2017

Dear all Kwant workers! My problem is about the calculation of energy dispersion of MoS2 in Ref PRB 92, 195402 (2015). I want to use the tight binding Hamiltonian of MoS2 (Eq (2) in Reference) to obtain energy dispersion in Figure 6(a). Because the honeycomb of monolayer MoS2 is distinct with the graphene, onsite energy of Mo and S is also different. In graphene, the onsite energy of A and B atoms in unit cell is equivalent and thus the hopping energy of nearest and two nearest atom in different direction is same. However, this is not right in MoS2 (A----Mo, B----S). So i choose the code to describe onsite energy in MoS2 as follow def onsite(site): return E_M if (site.family == M) else E_X Is this right? Furthermore, i solve the energy band in y-direction by considering only one lead (abs(y)<Ly, Ly is the width). Is it correct to use the following code to build the system? sym = kwant.TranslationalSymmetry(lat.vec((-1, 0))) sys = kwant.Builder(sym) My Kwant code cannot obtain the result in Figure 6(a). Please help me if you are free, Thanks! My Kwant code: import kwant from matplotlib import pyplot import tinyarray import math import numpy eV, nm=1,1e-9 lamad_M, lamad_X = 0.075*eV, 0.052*eV e0, e2, ep, ez = -1.094*eV, -1.512*eV, -3.560*eV, -6.886*eV V_pdd, V_pdp = 3.689*eV, -1.241*eV V_ddd, V_ddp, V_ddde = -0.895*eV, 0.252*eV, 0.228*eV V_ppd, V_ppp = 1.225*eV, -0.467*eV; a0=0.316*nm; s=1j; sz=+1; sqrt_3=math.sqrt(3) E_M=tinyarray.array([[e0, 0, 0],[0, e2, -s*lamad_M*sz],[0, s*lamad_M*sz, e2]]); E_X=tinyarray.array([[ep+V_ppp, -s*lamad_X/2*sz, 0],[s*lamad_X/2*sz, ep+V_ppp, 0],[0, 0, ez-V_ppd]]); t1_MX=1/7*math.sqrt(2/7)*tinyarray.array([[-9*V_pdp+sqrt_3*V_pdd, 3*sqrt_3*V_pdp-V_pdd, 12*V_pdp+sqrt_3*V_pdd], [5*sqrt_3*V_pdp+3*V_pdd, 9*V_pdp-sqrt_3*V_pdd, -2*sqrt_3*V_pdp+3*V_pdd], [-V_pdp-3*sqrt_3*V_pdd, 5*sqrt_3*V_pdp+3*V_pdd, 6*V_pdp-3*sqrt_3*V_pdd]]) t2_MX=1/7*math.sqrt(2/7)*tinyarray.array([[0, -6*sqrt_3*V_pdp+2*V_pdd, 12*V_pdp+sqrt_3*V_pdd], [0, -6*V_pdp-4*sqrt_3*V_pdd, 4*sqrt_3*V_pdp-6*V_pdd], [14*V_pdp, 0, 0]]) t3_MX=1/7*math.sqrt(2/7)*tinyarray.array([[9*V_pdp-sqrt_3*V_pdd, 3*sqrt_3*V_pdp-V_pdd, 12*V_pdp+sqrt_3*V_pdd], [-5*sqrt_3*V_pdp-3*V_pdd, 9*V_pdp-sqrt_3*V_pdd, -2*sqrt_3*V_pdp+3*V_pdd], [-V_pdp-3*sqrt_3*V_pdd, -5*sqrt_3*V_pdp-3*V_pdd, -6*V_pdp+3*sqrt_3*V_pdd]]) t1_MM=1/4*tinyarray.array([[3*V_ddde+V_ddd, sqrt_3/2*(-V_ddde+V_ddd), -3/2*(V_ddde-V_ddd)], [sqrt_3/2*(-V_ddde+V_ddd), 1/4*(V_ddde+12*V_ddp+3*V_ddd), sqrt_3/4*(V_ddde-4*V_ddp+3*V_ddd)], [-3/2*(V_ddde-V_ddd), sqrt_3/4*(V_ddde-4*V_ddp+3*V_ddd), 1/4*(3*V_ddde+4*V_ddp+9*V_ddd)]]) t2_MM=1/4*tinyarray.array([[3*V_ddde+V_ddd, sqrt_3*(V_ddde-V_ddd), 0], [sqrt_3*(V_ddde-V_ddd), V_ddde+3*V_ddd, 0], [0 , 0,4*V_ddp]]) t3_MM=1/4*tinyarray.array([[3*V_ddde+V_ddd, sqrt_3/2*(-V_ddde+V_ddd), 3/2*(V_ddde-V_ddd)], [sqrt_3/2*(-V_ddde+V_ddd), 1/4*(V_ddde+12*V_ddp+3*V_ddd), -sqrt_3/4*(V_ddde-4*V_ddp+3*V_ddd)], [3/2*(V_ddde-V_ddd), -sqrt_3/4*(V_ddde-4*V_ddp+3*V_ddd), 1/4*(3*V_ddde+4*V_ddp+9*V_ddd)]]) t1_XX=1/4*tinyarray.array([[3*V_ppp+V_ppd, sqrt_3*(V_ppp-V_ppd), 0], [sqrt_3*(V_ppp-V_ppd), V_ppp+3*V_ppd,0], [0, 0, 4*V_ppp]]) t2_XX=tinyarray.array([[V_ppd, 0, 0], [0 ,V_ppp, 0], [0, 0, V_ppp]]) t3_XX=1/4*tinyarray.array([[3*V_ppp+V_ppd, -sqrt_3*(V_ppp-V_ppd), 0], [-sqrt_3*(V_ppp-V_ppd), V_ppp+3*V_ppd, 0], [0, 0 ,4*V_ppp]]) lat = kwant.lattice.honeycomb() M, X = lat.sublattices def make_lead(Lx=1, Ly=48): def Rectangle(pos): x, y = pos return abs(y)<Ly def onsite(site): return E_M if (site.family == M) else E_X #sym = kwant.TranslationalSymmetry((-Lx, 0)) #sym = kwant.TranslationalSymmetry((-3, 0)) sym = kwant.TranslationalSymmetry(lat.vec((-1, 0))) sys = kwant.Builder(sym) #sys = kwant.Builder() sys[lat.shape(Rectangle, (0, 0))] = onsite #hopping_onsit_M=((0, 0),M,M) #hopping_onsit_X=((0, 0),X,X) #sys[kwant.builder.HoppingKind(*hopping_onsit_M)] = E_M########## #sys[kwant.builder.HoppingKind(*hopping_onsit_X)] = E_X######### hopping2_M =((1, 0), M, M) hopping1_M =((-1, 1), M, M) hopping3_M =((0, -1), M, M) sys[kwant.builder.HoppingKind(*hopping1_M)] = t1_MM sys[kwant.builder.HoppingKind(*hopping2_M)] = t2_MM sys[kwant.builder.HoppingKind(*hopping3_M)] = t3_MM hopping2_X =((1, 0), X, X) hopping1_X =((-1, 1), X, X) hopping3_X =((0, -1), X, X) sys[kwant.builder.HoppingKind(*hopping1_X)] = t1_XX sys[kwant.builder.HoppingKind(*hopping2_X)] = t2_XX sys[kwant.builder.HoppingKind(*hopping3_X)] = t3_XX hopping1_MX =((0, 0), M, X) hopping2_MX =((0, 1), M, X) hopping3_MX =((-1, 1), M, X) sys[kwant.builder.HoppingKind(*hopping1_MX)] = t1_MX sys[kwant.builder.HoppingKind(*hopping2_MX)] = t2_MX sys[kwant.builder.HoppingKind(*hopping3_MX)] = t3_MX def family_colors(site): return 0 if (site.family == M) else 1 def hopping_lw(site1, site2): return 0.05 if site1.family == site2.family else 0.1 def hopping_color(site1,site2): return 'g' if site1.family==site2.family else 'b' kwant.plot(sys,site_color=family_colors,site_lw=0.05, hop_lw=hopping_lw,hop_color=hopping_color,colorbar=False) return sys def main(): lead = make_lead().finalized() kwant.plotter.bands(lead, show=False) pyplot.xlabel("momentum [(lattice constant)^-1]") pyplot.ylabel("energy [eV]") pyplot.show() # Call the main function if the script gets executed (as opposed to imported). # See <http://docs.python.org/library/__main__.html>. if __name__ == '__main__': main()

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Conservation law
by Antonio Lucas Rigotti Manesco Dec. 17, 2017

Dec. 17, 2017

Dear Kwant users, I have two questions: 1) Specifying conservation laws is necessary only when transport calculations are done? If I am trying to compute ldos and bands should I bother with properly defining the conservation laws? 2) I was trying to implement a system with leads along the x-direction. However, along the y-direction, half of it is superconducting and the other half is not. How can I define the conservation law in such case since it is not possible to use a conservation law for all y values in the lead? Best, -- Antônio Lucas Rigotti Manesco PhD fellow - University of São Paulo, Brazil

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How to build a phosphorene lattice
by cqhy1127 Dec. 16, 2017

Dec. 16, 2017

Dear Professors, I want to build a phosphorene lattice and I used the following code _________________________________________________________ ax = 0.443 ay = 0.327 alpha = 98.15*(np.pi/180) beta = 103.69*(np.pi/180) theta = np.arccos(-np.cos(beta)/np.cos(alpha/2)) s = 0.5*ax-a*np.cos(alpha/2) h = b*np.sin(theta) # (ax,0) and (0, ay) are primitive vectors of the phosphorene vectors # (-s/2,-ay/2,h),(s/2,-ay/2,0.0),(ax/2-s/2,0,0.0),(ax/2+s/2,h) are corrdinates of four basis atoms. lat=kwant.lattice.general([(ax,0),(0,ay)], [(-s/2,-ay/2,h),(s/2,-ay/2,0.0),(ax/2-s/2,0,0.0),(ax/2+s/2,h)] ) a,b,c,d=lat.sublattices___________________________________________________________________________It report an error like this File "D:\Users\gongcheng5\Anaconda3\lib\site-packages\kwant\lattice.py", line 95, in __init__ basis = ta.array(basis, float) ValueError: Input has irregular shape. Would you like to help me to find the bug? Thank you! Regards, Qiao Chen University of Antwerp Condensed Matter Theory Department of Physics

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making systems with translational symmetry perpendicular to the direction of transport
by Maurer, Leon Dec. 13, 2017

Dec. 13, 2017

Hi all, This is a follow up to my post yesterday (where I put a Si tight binding model into Kwant). My goal is to create a 3D system with translational symmetries in a plane so that I can look at transport perpendicular to that (infinite) plane. So, there wouldn’t be a translational symmetry in the direction of transport, but there will be translational symmetry in the two dimensions perpendicular to transport. It’s a little difficult to explain how I’m trying to do this, but hopefully the below explanation mostly conveys the idea. The attached jupyter notebook uses a standard Si primitive cell as the unit cell, and for simplicity, I’ve chosen the axis of the system to be along the first Si primitive vector as defined in the code (1/2, 1/2, 0). There is translational symmetry along the other two primitive vectors (set in “In [5]” of the notebook). Everything seems to work basically as expected. The axis of the system does lie along the first Si primitive vector; I can attach leads with the same symmetries; and the leads have the right band structure: the band structure down the axis of the leads is the band structure between the gamma and L points (calculated in “In [8]”– compare with the full band structure in “In [10]”). I could calculate the transmission down the axis of the structure with something like kwant.smatrix(syst, energy, args=(0,0)).transmission(1, 0), which isn’t shown in the notebook. (I’d also be putting different potentials in the different sites so that the structure isn’t uniform. There’s not much point calculating transport thru the system in the notebook.) Two questions: 1. Can I calculate transport in other directions --- such as the (1,0,0) direction --- using this system? 2. The primitive lattice vectors are not orthogonal, so I don’t really have translational symmetry perpendicular to the axis of the system. Does anyone have an idea for how to fix that? I could create a (larger) non-primitive unit cell with orthogonal primitive vectors by having a bunch of basis vectors (that sounds weird, but I think that the terminology is right), but I like having my unit cell be simple. (I have tried effectively building a larger unit cell from the primitive cells, but I’ve run into problems – a topic for a different email.) -Leon

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