Mailman 3 July 2019 - Kwant-discuss

Re: [Kwant] Periods for kwant.TranslationalSymmetry
by Barış Özgüler 06 Jul '19

06 Jul '19

Hi Ousmane, I'm trying different geometries of junctions. I've added Code 1 and 2 below. Code 1 produces 2 separate leads attached to horizontal and vertical surfaces. Using Code 2 (just TranslationalSymmetry and lead_shape() is different than Code 1), I tried to produce a single lead which is attached horizontally and vertically but it failed. How should I play with kwant.TranslationalSymmetry or lead_shape() to create such a lead? ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ # Code 1 import kwant import matplotlib.pyplot as plt def make_system(a, W, L): def shape(pos): (x, y) = pos if x <= 0: return (-L <= x <= 0 and -L <= y <= 0) elif x >0: return (0 <= x <= L and -L <= y <= L) def onsite(site, par): return 4 * par.t - par.mu def hopx(site1, site2, par): return -par.t def hopy(site1, site2, par): return -par.t lat = kwant.lattice.square(a, norbs=1) syst = kwant.Builder() syst[lat.shape(shape, (0, 0))] = onsite syst[kwant.builder.HoppingKind((1, 0), lat, lat)] = hopx syst[kwant.builder.HoppingKind((0, 1), lat, lat)] = hopy # attach lead to horizontal normal surface lead = kwant.Builder(kwant.TranslationalSymmetry((-a, a))) def lead_shape(pos): (x, y) = pos return -L <= x <= -5 def lead_hopx(site1, site2, par): return -par.t def lead_onsite(site, par): return 4 * par.t - par.mu lead[lat.shape(lead_shape, (-7, 0))] = lead_onsite lead[kwant.builder.HoppingKind((1, 0), lat, lat)] = lead_hopx lead[kwant.builder.HoppingKind((0, 1), lat, lat)] = hopy syst.attach_lead(lead) # attach lead to vertical normal surface lead = kwant.Builder(kwant.TranslationalSymmetry((-2*a, a))) def lead_shape(pos): (x, y) = pos return 5 <= y <= L def lead_hopx(site1, site2, par): return -par.t def lead_onsite(site, par): return 4 * par.t - par.mu lead[lat.shape(lead_shape, (0, 7))] = lead_onsite lead[kwant.builder.HoppingKind((1, 0), lat, lat)] = lead_hopx lead[kwant.builder.HoppingKind((0, 1), lat, lat)] = hopy syst.attach_lead(lead) syst = syst.finalized() return syst a = 5 number_of_sites = 20 L=number_of_sites*a number_of_sites2 = 50 L2=number_of_sites2*a syst = make_system(a=a, W=L2, L=L) kwant.plot(syst) ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Code 2 import kwant import matplotlib.pyplot as plt def make_system(a, W, L): def shape(pos): (x, y) = pos if x <= 0: return (-L <= x <= 0 and -L <= y <= 0) elif x >0: return (0 <= x <= L and -L <= y <= L) def onsite(site, par): return 4 * par.t - par.mu def hopx(site1, site2, par): return -par.t def hopy(site1, site2, par): return -par.t lat = kwant.lattice.square(a, norbs=1) syst = kwant.Builder() syst[lat.shape(shape, (0, 0))] = onsite syst[kwant.builder.HoppingKind((1, 0), lat, lat)] = hopx syst[kwant.builder.HoppingKind((0, 1), lat, lat)] = hopy # works but does not plot the lead attached to vertical surface lead = kwant.Builder(kwant.TranslationalSymmetry((-a, a))) #, time_reversal=1) # doesn't work #lead = kwant.Builder(kwant.TranslationalSymmetry((-2*a, a))) #, time_reversal=1) # doesn't work #lead = kwant.Builder(kwant.TranslationalSymmetry((-a, 2*a))) #, time_reversal=1) def lead_shape(pos): (x, y) = pos return -L <= x <= 0 or 5 <= y <= L """ if x < 0: return -L <= x <= 0 #or 5 <= y <= L else: return 0 <= y <= L """ def lead_hopx(site1, site2, par): return -par.t def lead_onsite(site, par): return 4 * par.t - par.mu lead[lat.shape(lead_shape, (0, 0))] = lead_onsite lead[kwant.builder.HoppingKind((1, 0), lat, lat)] = lead_hopx lead[kwant.builder.HoppingKind((0, 1), lat, lat)] = hopy syst.attach_lead(lead) syst = syst.finalized() return syst a = 5 number_of_sites = 20 L=number_of_sites*a number_of_sites2 = 50 L2=number_of_sites2*a syst = make_system(a=a, W=L2, L=L) kwant.plot(syst) ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Thanks, -- A. Barış Özgüler PhD Candidate in Physics https://home.physics.wisc.edu/ozguler/ University of Wisconsin–Madison Madison, Wisconsin 53706, USA

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Re: [Kwant] Periods for kwant.TranslationalSymmetry
by Ousmane LY 05 Jul '19

05 Jul '19

Hi Bariş, it’s possible to attach the lead in that direction. However it’s unclear to me why do you want to do this. Please provide more details about your system. Regards, Ousmane

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Re: [Kwant] Periods for kwant.TranslationalSymmetry
by Barış Özgüler 04 Jul '19

04 Jul '19

Thanks, Ousmane. I have attached another figure. Orange is the lead, blue is the scattering region. Instead of attaching two different leads horizontally and vertically, is it possible to attach a single lead (like the orange one in the figure) which is connected to the scattering region both horizontally and vertically? Barış

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Re: [Kwant] Periods for kwant.TranslationalSymmetry
by Ousmane LY 04 Jul '19

04 Jul '19

Hi Bariş, what you are saying is correct. Considering the leads as perpendicular to the plane at the interface sites, wouldn’t alter the transport properties of the system. You should look at the leads as probes. Even if they seem to cross, there is no real crossing. regards, Ousmane

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Re: [Kwant] Periods for kwant.TranslationalSymmetry
by Barış Özgüler 03 Jul '19

03 Jul '19

Thanks, Ousmane, for your answer. Yes, there is no trouble with horizontal attachment. Actually, that's why my question is not about it. I need to attach the lead vertically. *A related question*: I've attached a system figure in this e-mail . There are vertical and horizontal leads. I try to choose that period (b = 1, c = 1) for the vertical attachment because I don't want the horizontal and vertical leads to cross each other. I am not sure if I have to care about crossing between the leads if Kwant does not consider physical structure of the leads and how they intersect. Can I consider the leads as perpendicular to the plane? Barış

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Periods for kwant.TranslationalSymmetry
by Ousmane LY 03 Jul '19

03 Jul '19

Dear Bariş, I don’t know why kwant doesn’t attach the lead as you want. However, it works quite fine if you attach it transversally. You may try the program bellow, in case this is helpful. I just added the transversal lead to your code. Regards, Ousmane ############################################## import kwant import matplotlib.pyplot as plt def make_system(a, W, L): def shape(pos): (x, y) = pos return (-L <= x <= 0 and -L <= y <= L) def onsite(site, par): return 4 * par.t - par.mu def hopx(site1, site2, par): return -par.t def hopy(site1, site2, par): return -par.t lat = kwant.lattice.square(a, norbs=1) syst = kwant.Builder() syst[lat.shape(shape, (0, 0))] = onsite syst[kwant.builder.HoppingKind((1, 0), lat, lat)] = hopx syst[kwant.builder.HoppingKind((0, 1), lat, lat)] = hopy # (b = 2, c = 1) works, (b = 1, c = 1) does not work b = 2 c = 1 lead = kwant.Builder(kwant.TranslationalSymmetry((b*a, c*a))) #, #time_reversal=1) lead2 = kwant.Builder(kwant.TranslationalSymmetry((a, a))) def lead_shape(pos): (x, y) = pos return -L/2<= y <=L/2 #return -2*L<= x <=-L def lead_shape2(pos): (x, y) = pos #return -L/2<= y <=L/2 return -2*L<= x <=-L def lead_hopx(site1, site2, par): return -par.t def lead_onsite(site, par): return 4 * par.t - par.mu lead[lat.shape(lead_shape, (0, 0))] = lead_onsite lead2[lat.shape(lead_shape2, (-L, 0))] = lead_onsite lead[kwant.builder.HoppingKind((1, 0), lat, lat)] = lead_hopx lead[kwant.builder.HoppingKind((0, 1), lat, lat)] = hopy lead2[kwant.builder.HoppingKind((1, 0), lat, lat)] = " " lead2[kwant.builder.HoppingKind((0, 1), lat, lat)] = " " syst.attach_lead(lead) syst.attach_lead(lead2) syst = syst.finalized() return syst lat = kwant.lattice.honeycomb() sym = kwant.TranslationalSymmetry(lat.a.vec((-2, 1))) lead = kwant.Builder(sym) lead[lat.wire((0, -5), 5)] = 0 lead[lat.neighbors()] = 1 a = 5 number_of_sites = 20 L=number_of_sites*a number_of_sites2 = 50 L2=number_of_sites2*a syst = make_system(a=a, W=L2, L=L) kwant.plot(syst) ##############################################

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