Kwant-discuss

kwant-discuss@python.org

5 participants
900 discussions

How to attach a lead to particular position of honeycomb lattice

by sahu.ajit92＠gmail.com

Dear Sir, I am new to kwant. How to attach a lead to a particular portion(upper side of the square) of the honeycomb structure. sym1 = kwant.TranslationalSymmetry(lat.vec((0,1))) lead1 = kwant.Builder(sym1) def lead2_shape(pos): x, y = pos return 0<x<10 lead1[lat.shape(lead2_shape, (2,0))]=3 lead1[lat.neighbors()] = -1 I used the above code to attach the second lead but it didn’t attach to the correct place. I want to attach the lead to the upper side of the square. main code Wnr=10 lnr=10 a=1 lat=kwant.lattice.honeycomb(a) def rect(pos): x,y=pos return 0<x<lnr and 0<y<Wnr model1 = kwant.Builder() model1[lat.shape(rect,(1,1))] = 3 model1[lat.neighbors()] =-1 ##########lead shape function def lead1_shape(pos): x, y = pos return 0 < y < 10 def lead2_shape(pos): x, y = pos return 0<x<10 ##########1st lead########## sym = kwant.TranslationalSymmetry(lat.vec((-1,0))) #from the left sym.add_site_family(lat.sublattices[0], other_vectors=[(-1, 2)]) sym.add_site_family(lat.sublattices[1], other_vectors=[(-1, 2)]) lead = kwant.Builder(sym) lead[lat.shape(lead1_shape, (1,1))]=3 lead[lat.neighbors()] = -1 model1.attach_lead(lead) ##########problem in 2nd lead, from this below code it attach to other position########## sym1 = kwant.TranslationalSymmetry(lat.vec((0,1))) lead1 = kwant.Builder(sym1) lead1[lat.shape(lead2_shape, (2,0))]=3 lead1[lat.neighbors()] = -1 model1.attach_lead(lead1) kwant.plot(model1) Anyone, please help please see this image in below link, I want to attach the second lead in the red-circled position of the figure https://drive.google.com/file/d/15ORyo4j_tAvgC8jaT5lQxmQNS6e0QoOF/view?usp=…

33 minutes

Elements of a scattering matrix

by Lorenzo BAGNASACCO

Dear Kwant community, I am a physics student and I am approaching to Kwant to solve simple problems of scattering. I am new in Kwant and, for this reason, I'm trying to use Kwnat for basic problems of scattering. The most simple problem in my mind is the scattering of a plane-wave (1 dimension) from the left of a potential barrier. If we now suppose the potential barrier is 'zero' everywhere, the scattering matrix, according to the scattering theory, should be 'S={{0,1},{1,0}}'. If I try to compute the reflection and transmission coefficient, I obtained the correct values (1 for reflection and 0 for transmission). But it occurs only for some energies. For example in the code I attached, if I put the value of '10' in 'S=kwant.solvers.default.smatrix(syst,10)' I obtaine for reflection and transmission the value of '0'. Where is my errors? And, is there a way to print the entire elements of the scattering matrix ? Yours sincerely Lorenzo Bagnasacco

1 hour, 1 minute

Re: How to get Kwant plot data for other use?

by Ajit Kumar Sahu

1 hour, 9 minutes

Add -fPIC flag to linker

by Etienne Fayen

Dear kwant user, I am trying to build kwant and its dependencies from sources. A first build without Mumps succeeded. When adding Mumps however, the linker returns the following error: /usr/bin/ld: /opt/mumps-5.4.1/lib/libzmumps.a(ztools.o): relocation R_X86_64_PC32 against symbol `.gomp_critical_user_critical_old_ooc' can not be used when making a shared object; recompile with -fPIC /usr/bin/ld: final link failed: bad value Here is the content of the build.conf [mumps] include_dirs = /opt/mumps-5.4.1/include /opt/scotch-7.0/include library_dirs = /opt/mumps-5.4.1/lib /opt/mumps-5.4.1/libseq /opt/scotch-7.0/lib libraries = zmumps mumps_common pord esmumps scotch scotcherr mpiseq gfortran Would adding -fPIC flag as suggested by the error message solve the issue ? If so, how can this flag be added with the python build setup ? Best, Etienne F

6 hours, 41 minutes

How to get Kwant plot data for other use?

by sahu.ajit92＠gmail.com

Dear all, I am new to kwant. I want numerical data from Kwant for e.g. numerical data that is used to plot the honeycomb structure. Thanking you Ajit Kumar Sahu

1 week, 1 day

Problems in calculating conductivity using the KPM method

by 674657065＠qq.com

Dear all： I am a PHD student and i am using the kwant to calculate the conductivity of the graphene. Excuse me, I'd like to ask you a question that in the kwant documentation, you used the KPM method to calculate the conductivity of graphene. Does the disorder strength take a value of 0 or approach 0? If the disorder strength is 0, why is the conductivity not diverging at points where the energy is not zero? Thank you for your answer. Best wishes Hanlin Liu

1 week, 4 days

Solving CIP - GMR in Kwant is tricky? doesn't work? or my code in wrong?

by chris stats

Dear all, To test kwant as a beginner I wanted to solve a CIP GMR system (not CPP). Usual config. is 2 FMs separated by a NM; however because it is CIP, then the leads are partially connected to the 3 layers My system extends from the quantum wire problem adding Pauli matrices and the conservation law sigma_z I added impurities using a random function; however, my output sometimes shows a larger conductance for the antiparallel case (rather than the parallel one). No integration involved, simple conductance calculation using: "smatrix.transmission(1, 0))". From a code perspective, my only concern is on the leads, for instance I have for one ferromagnet: leftlead[(lat(0, j) for j in range(W))] = Jxc * (sigma_x*mx + sigma_y*my + sigma_z*mz ) I do not add impurities on the leads. the 4t term is not taken as i shifted the bandwidth. Is this a good "oversimplified approach? From a kwant perspective, As I said, sometimes the AP case is larger than the P config. Because of this I performed a random distribution average over 10000 loops and my result shows that in 25% of the cases AP is larger than P. Why it is not possible to get a solution to this system with low error? Is it because the quantum wire conductance problem is too simple to give proper results for CIP GMR? Shall I avoid using the conductance and focus instead on current out of equlibrium? Or CIP-GMR has particular constraints that I'm omitting in Kwant. Thanks a lot for a response...

4 weeks, 1 day

New to Kwant. Basic bias voltage in quantum wire?

by statsconchris＠gmail.com

Dear all, In the quantum wire set up I naively considered (oversimplfied) : left_lead[(lat(0, j) for j in range(W))] = (+0.5) right_lead[(lat(0, j) for j in range(W))] = (- 0.5) I wanted to have a bias voltage, muL > muR (0.5 eV in my case). I computed the conductance expecting to have different values for electrons flowing from left to right and right to left, i.e., smatrix.transmission(1, 0)) different from smatrix.transmission(0, 1)) but the results are identical! So my question is how do I actually construct a bias voltage and get the current from left to right different than from right to left. To oversimplify the problem I'm not interested in energy integration, let's assume that all the physics is dominated by electrons with a fixed energy value. Thank you for your answer

4 weeks, 1 day

How to get higher plateaus in quantum Hall conductivity?

by Jerry xhm

Hello Kwant community, I am using the KPM method to calculate conductivities in the simplest QHE system -- square lattice nearest hopping gas. The goal is to see well-quantized plateaus up to n=5. I use local vectors at the center of the system. But it seems not available at all as far as I've tried increasing system size (like 80*80) and number of moments (like 500). I doubt if it really needs so demanding computational resources in order to get n=5. Hopefully I missed something basic here. Thank you! from cmath import exp import numpy as np import time import sys import kwant #from matplotlib import pyplot from matplotlib import pyplot as plt L_sys = [50, 50] E_F=0.4 def make_system(a=1, t=1): lat = kwant.lattice.square(a, norbs=1) syst = kwant.Builder() def fluxx(site1, site2, Bvec): pos = [(site1.pos[i]+site2.pos[i]-L_sys[i])/2.0 for i in range(2)] return exp(-1j * Bvec * pos[1] ) def fluxy(site1, site2, Bvec): pos = [(site1.pos[i]+site2.pos[i]-L_sys[i])/2.0 for i in range(2)] return 1 #exp(-1j * (-Bvec * pos[0])) def hopx(site1, site2, Bvec): # The magnetic field is controlled by the parameter Bvec return fluxx(site1, site2, Bvec) * t def hopy(site1, site2, Bvec): # The magnetic field is controlled by the parameter Bvec return fluxy(site1, site2, Bvec) * t def onsite(site): return 4*t #### Define the scattering region. #### syst[(lat(x, y) for x in range(L_sys[0]) for y in range(L_sys[1]))] = onsite # hoppings in x-direction syst[kwant.builder.HoppingKind((1, 0), lat, lat)] = hopx # hoppings in y-directions syst[kwant.builder.HoppingKind((0, 1), lat, lat)] = hopy # Finalize the system. syst = syst.finalized() return lat, syst def cond(lat, syst, random_vecs_flag=False): center_pos = [x/2 for x in L_sys] center0 = lambda s: np.linalg.norm(s.pos-center_pos) < 2 num_mmts = 800; if random_vecs_flag: center_vecs = kwant.kpm.RandomVectors(syst, where=center0) one_vec = next(center_vecs) num_vecs = 10 # len(center_vecs) else: center_vecs = np.array(list(kwant.kpm.LocalVectors(syst, where=center0))) one_vec = center_vecs[0] num_vecs = len(center_vecs) area_per_orb = np.abs(np.cross(*lat.prim_vecs)) norm = area_per_orb * np.linalg.norm(one_vec) ** 2 Binvfields = np.arange(3.01, 26.2, 1) params = dict(Bvec=0) dataxx = [] dataxy = [] for Binv in Binvfields: params['Bvec'] = 1/Binv cond_xx = kwant.kpm.conductivity(syst, params=params, alpha='x', beta='x', mean=True, num_moments=num_mmts, num_vectors=num_vecs, vector_factory=center_vecs) cond_xy = kwant.kpm.conductivity(syst, params=params, alpha='x', beta='y', mean=True, num_moments=num_mmts, num_vectors=num_vecs, vector_factory=center_vecs) dataxx.append(5*cond_xx(mu=E_F, temperature=0.0)/norm) dataxy.append(-cond_xy(mu=E_F, temperature=0.0)/norm) print(dataxx) print(dataxy) plot_curves( [ (r'$\sigma_{xx}\times5$',(Binvfields,dataxx)), (r'$\sigma_{xy}$',(Binvfields,dataxy)), ] ) def plot_curves(labels_to_data): plt.figure(figsize=(12,10)) for label, (x, y) in labels_to_data: plt.plot(x, y, label=label, linewidth=2) plt.legend(loc=2, framealpha=0.5) plt.xlabel("1/B") plt.ylabel(r'$\sigma [e^2/h]$') plt.show() plt.clf() def main(): lat, syst = make_system() cond(lat, syst) if __name__ == '__main__': main()

1 month, 3 weeks

Surprising (?) behaviour of attach leads

by maciej.zwierzycki＠ifmpan.poznan.pl

Dear Kwant Authors and Users, Greetings and thank you for a wonderful tool. While trying to force Kwant to accept the unit cell of the lead in a particular, connected form, I've encountered somewhat puzzling situation illustrated in the attached piece of code. The described procedure does not make sense physically, but its purpose is to illustrate the behaviour which may possibly (?) lead to problems, at least for newbies like me. ;) Let's say I define two honeycomb lattices, differing in the choice of basis, but entirely equivalent (i.e. they overlap) prime=np.array([[sqrt(3)/2,sqrt(3)],[1.5,0.0]])*a basis_at=np.array([[0.0,0.0],[-0.5,0.5]])*a lat = kwant.lattice.general([prime[:,0],prime[:,1]],[basis_at[:,0],basis_at[:,1]]) and basis2=np.array([[0.0,sqrt(3)/2],[-0.5,-1.0]])*a lat2 = kwant.lattice.general([prime[:,0],prime[:,1]],[basis2[:,0],basis2[:,1]]) I'm using numpy so that vector algebra works. The rectangular scattering region and the left lead (same width) are populated with "lat". Now I'm adding a few atoms from lat2 to the right edge of the scattering region, e.g. a single hexagon for i in range (0,1): # changing the range we can generate also the full layer of lat2 sites syst[lat2.sublattices[0](0+2*i,9-i)]=0.0 syst[lat2.sublattices[1](0+2*i,8-i)]=0.0 syst[lat2.sublattices[0](1+2*i,8-i)]=0.0 syst[lat2.sublattices[1](1+2*i,8-i)]=0.0 and then attach the lead, also populated with "lat2". I know, that's not how it's described in tutorial. ;) The filling algorithm generates the system which to naked eye looks like the perfect nanowire. The transmission however is not perfect i.e. T < N (number of modes). If the full layer of lat2 sites is added to the right edge, than everything is as it should be, i.e. perfect transmission. I'm not sure if it's a bug - I'm doing things not in the manual - but I find it strange. A perfect system, however generated, should lead to perfect transmission. What gives? Also I noticed that neighbours() method called for one of the lattices tends to pick up the sites from the other lattice, if they belong to he sublattice generated from (0,-0.5a), i.e. from the common basis. Try commenting out one of the lines 53-54. Is it intentional or not? It's quite likely that the described situation never arises in real-world situations especially if one does the right thing and pads the interface with the full principal layer before attaching the leads. I've stumbled upon it only thanks to my laziness. But it might also illustrate some fragility of the algorithm, possibly worth eliminating. In any case I'd be grateful for some illumination. Why isn't the "perfect" wire behaving as it should? Where is the imperfection if it's not visible in the structure? With Kind Regards Maciej Zwierzycki import kwant import numpy as np from numpy import sin, cos,tan,sqrt from matplotlib import pyplot def make_system(a, t, W, L1): prime=np.array([[sqrt(3)/2,sqrt(3)],[1.5,0.0]])*a basis_at=np.array([[0.0,0.0],[-0.5,0.5]])*a lat = kwant.lattice.general([prime[:,0],prime[:,1]],[basis_at[:,0],basis_at[:,1]]) syst = kwant.Builder() #### Define the scattering region. #### def scatt_shape(pos): (x, y) = pos return (-L1 < x < L1) and ( -W <y < W) syst[lat.shape(scatt_shape,basis_at[:,0])]=0 syst[lat.neighbors()] = t #### Left lead. #### def lead_shape(pos): (x, y) = pos return (-W < y < W ) lsym=kwant.TranslationalSymmetry(lat.vec((0,-1))) lsym.add_site_family(lat.sublattices[0], other_vectors=[(-2,1)]) lsym.add_site_family(lat.sublattices[1], other_vectors=[(-2,1)]) llead = kwant.Builder(lsym) llead[lat.shape(lead_shape,basis_at[:,0])] = 0 llead[lat.neighbors()] = t #### Right lead. #### ### Define a hexagonal lattice with different - but equivalent! - basis basis2=np.array([[0.0,sqrt(3)/2],[-0.5,-1.0]])*a lat2 = kwant.lattice.general([prime[:,0],prime[:,1]],[basis2[:,0],basis2[:,1]]) #### Extra hexagon of lat2 on the right edge of the scattering region: #### -- range(0,1) - single hexagon ##### -- range(-2,3) - full width for i in range (0,1): syst[lat2.sublattices[0](0+2*i,9-i)]=0.0 syst[lat2.sublattices[1](0+2*i,8-i)]=0.0 syst[lat2.sublattices[0](1+2*i,8-i)]=0.0 syst[lat2.sublattices[1](1+2*i,8-i)]=0.0 syst[lat2.neighbors()]=t syst[lat.neighbors()]=t kwant.plot(syst) lsym=kwant.TranslationalSymmetry(lat2.vec((0,1))) lsym.add_site_family(lat2.sublattices[0], other_vectors=[(2,-1)]) lsym.add_site_family(lat2.sublattices[1], other_vectors=[(2,-1)]) rlead= kwant.Builder(lsym) rlead[lat2.shape(lead_shape,basis_at[:,0])] = 0 rlead[lat2.neighbors()] =t syst.attach_lead(llead) syst.attach_lead(rlead) syst=syst.finalized() return syst syst = make_system(a=1.42,t=3.0,W=10.5,L1=20) kwant.plot(syst) data1 = [] data2 = [] params = dict(a=1.42, t=-3.0) energies=[0.2*i+0.01 for i in range(20)] for energy in energies: print('En=',energy) smatrix = kwant.smatrix(syst, energy,params=params) data1.append(smatrix.transmission(1, 0)) data2.append(smatrix.num_propagating(0)) pyplot.figure() pyplot.plot(energies, data1, 'r--', label='T') pyplot.plot(energies, data2,'r>', label='N') legend = pyplot.legend(loc='upper left') pyplot.xlabel("energy") pyplot.ylabel("conductance [e^2/h]") pyplot.show()

1 month, 3 weeks

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