Kwant-discuss July 2020

kwant-discuss@python.org

14 participants
13 discussions

by ZHANG Bing

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 months, 1 week

To to separate spins, electron and hole

by Khani Hosein

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

7 months

Migrating spin_orbit.py to real unit system

by Nathaniel Gregory Seil

Hello, I would like to model a 2DEG under a magnetic field and have been investigating the spin_orbit.py code. I would like to modify this code so that it utilises real units and models upon a to-scale lattice. However, I am a little bit unclear as to how to progress. I noticed in the base code we have a = 1, t = 1 and hbar = 2 (seen from the Pauli spin matrices which normally have hbar/2 as a coefficient in front). To represent the real life scenario of a lattice with constant a = 5E-10 m, would we do the following: * a = 5E-10 m * hbar = 1.05457E-34 J s (standard SI units) * m_electron = 9.109E-31 kg (standard SI units) * t = hbar ^ 2 / (2 * m_electron * a^2) and then just substitute these values into the rest of the code? I get the result of 0 conductivity for the lead voltages -0.046 to 0.105V (code shows "energies=[0.01 * i*t - 0.3*t for i in range(100)]"). I also get this for -0.0046 to 0.0105V and for -0.46 - 1.05V. Do these results seem right? I have attached my code with these substitutions and the results. Many thanks, Nathaniel Seil

1 year, 5 months

Peierls phase from kwant.physics.magnetic_gauge

by Paweł Wójcik

Dear KWANT community, Recently I have used KWANT to simulate electronic transport in T-junction with the perpendicular magnetic field applied to the nanostructure. As well known, the inclusion of the orbital effects in this case (by the peierls substitution) is not easy due to appropriate gauge which should be applied for the vertical leads. So I decided to use the newest functionality of KWANT included in kwant.physics.magnetic_gauge. I started testing this function from a simple nanowire (NW) with two leads applied on both sides of NW and the magnetic field perpendicular to NW. When calling ham=sys.hamiltonian_submatrix(params=params), similarly as in documentation, everything works OK. The problem appears when I am trying to calculate transport and call the function smatrix = kwant.smatrix(sys, energy=energy, params=params). Then, an following error occurs i = syst.id_by_site[a] j = syst.id_by_site[b]# We only store *either* (i, j) *or* (j, i). If not presentKeyError: Site(kwant.lattice.Monatomic([[75.58904535685008, 0.0], [0.0, 75.58904535685008]], [0.0, 0.0], '', None), array([-1, -9])) The above exception was the direct cause of the following exception: And I don't know how is the reason of this error. Below I paste my code nw = SimpleNamespace(\ W = 10, L = 100, dx = nm2au(4), m = 0.015, B = T2au(.5), ) def make_system_transport_gauge(nw): W=nw.W L=nw.L dx=nw.dx m=nw.m B=nw.B def onsite(sitei,peierls): x,y=sitei.pos t=1.0/(2.0*nw.m*nw.dx*nw.dx) return 4*t def hopping(sitei, sitej, peierls): xi,yi=sitei.pos xj,yj=sitej.pos t=1.0/(2.0*nw.m*nw.dx*nw.dx) return -t*peierls(sitei,sitej) lat=kwant.lattice.square(dx) sys = kwant.Builder() sys[(lat(i,j) for i in range(L) for j in range(-W+1,W))]=onsite sys[lat.neighbors()] = hopping syml = kwant.TranslationalSymmetry((-dx, 0)) l_lead=kwant.Builder(syml) l_lead[(lat(0,y) for y in range(-W+1,W))]=onsite l_lead[lat.neighbors()]=hopping l_lead.substituted(peierls='peierls_llead') sys.attach_lead(l_lead) symr = kwant.TranslationalSymmetry((dx, 0)) r_lead=kwant.Builder(symr) r_lead[(lat(0,y) for y in range(-W+1,W))]=onsite r_lead[lat.neighbors()]=hopping r_lead.substituted(peierls='peierls_rlead') sys.attach_lead(r_lead) sys = sys.finalized() return sys def B_syst(pos): return nw.B sys=make_system_transport_gauge(nw) gauge = kwant.physics.magnetic_gauge(sys) peierls_sys, peierls_llead, peierls_rlead = gauge(B_syst, B_syst, B_syst) params = dict(t=1, peierls=peierls_sys, peierls_llead=peierls_llead, peierls_rlead=peierls_rlead) ham=sys.hamiltonian_submatrix(params=params) #this works #I tried to calculate transport energy=eV2au(3e-3) smatrix = kwant.smatrix(sys, energy=energy, params=params) #this generates an error I would be grateful for any help or hint what is wrong. Best regards, Pawel Wojcik

1 year, 5 months

Conductivity in 2D system with Zeeman and Rashba spin-orbit interaction

by anna.krzyzewska＠amu.edu.pl

Dear Kwant community, I would like to calculate the DOS and conductivity in 2D system with Zeeman and Rashba spin-orbit interaction in a square lattice. Regarding the chapter 2.3.1 in KWANT tutorial I defined the function make_system(). Then, according to the chapter 2.9 in the tutorial, I used the kwant.kpm.conductivity() method to calculate the longitudinal and transverse conductivity in the system. But I see that my results are wrong and I do not understand some things: 1. question: in chapter 2.3.1 we did not need to define the norbs parameter but I suppose that KWANT "knows" that we have here two orbitals per site (considering the spin) because we use the Pauli matrices. But, to obtain some results using function kwant.kpm.conductivity(), I see that the argument norbs=2 in the system deifinition is required (without it I get the error: 'NoneType' object cannot be interpreted as an integer). Thus, my quesion is: how does KWANT interpret my system if I add or not this argument (nobrs=2)? I think this could be the problem causing my wrong results. 2. question: To use the method kwant.kpm.conductivity() we don't need to attach the leads. Maybe it is obvious and trivial quesion, but I do not understand how we can calculate the conductivity (eg. induced by the external electric field) in a closed system? And what about the boundary conditions? Below I present the whole code. #-------------------------------------------------------------------------------------- #-------------------------------------------------------------------------------------- import kwant from matplotlib import pyplot import tinyarray # we define the identity matrix and Pauli matrices 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]]) def make_system(t=1.8, alpha=0.1, e_z=0.0018, W=30, L=30, a=1): lat = kwant.lattice.square(norbs=2) # norbs - the number of orbitals per site syst = kwant.Builder() syst[(lat(x,y) for x in range(L) for y in range(W))] = 4*t*sigma_0 + e_z*sigma_z # Zeeman energy adds to the on-site term syst[kwant.builder.HoppingKind((a,0), lat, lat)] = -t*sigma_0 - 1j*alpha*sigma_y/(2*a) # hoppings in x-direction; (a,0) means hopping form (i,j) to (i+1,j) syst[kwant.builder.HoppingKind((0,a), lat, lat)] = -t*sigma_0 + 1j*alpha*sigma_x/(2*a) # hoppings in y-direction; (0,a) means hopping form (i,j) to (i,j+1) return syst def plot_dos_and_curves(dos, labels_to_data): pyplot.figure() pyplot.fill_between(dos[0], dos[1], label="DoS [a.u.]", alpha=0.5, color='gray') for label, (x, y) in labels_to_data: pyplot.plot(x, y, label=label, linewidth=2) pyplot.legend(loc=2, framealpha=0.5) pyplot.xlabel("energy [t]") pyplot.ylabel("$\sigma [e^2/h]$") pyplot.show() def main(): syst = make_system() kwant.plot(syst); # check if the system looks as intended syst = syst.finalized() spectrum = kwant.kpm.SpectralDensity(syst, rng=0, num_vectors=30) # object that represents the density of states for the system energies, densities = spectrum() # component 'xx' cond_xx = kwant.kpm.conductivity(syst, alpha='x', beta='x', rng=0) # component 'xy' cond_xy = kwant.kpm.conductivity(syst, alpha='x', beta='y', rng=0) energies = cond_xx.energies cond_array_xx = np.array([cond_xx(e, temperature=0.01) for e in energies]) cond_array_xy = np.array([cond_xy(e, temperature=0.01) for e in energies]) plot_dos_and_curves( (spectrum.energies, spectrum.densities * 8), # why multiplied by 8? [ (r'Longitudinal conductivity $\sigma_{xx} / 4$', (energies, cond_array_xx.real / 4)), (r'Hall conductivity $\sigma_{xy}$', (energies, cond_array_xy.real))], ) # standard Python construct to execute 'main' if the program is used as a script if __name__ == '__main__': main() #-------------------------------------------------------------------------------------- #-------------------------------------------------------------------------------------- Regards, Anna Krzyzewska

1 year, 5 months

(no subject)

by Prof. CHAN Kwok Sum

Dear Kwant developer, I want to define a spatially varying current operator which depends on the two sites of a bond. Can this be done giving the “onsite” a function in the current operator definition. According to the manual, the function for onsite has the signature of a Hamiltonian on-site function, does it mean the function can only have one site as its input and cannot have two sites of a bond as input? If “onsite” cannot do the job, any suggestion of how to solve the problem? Regards, 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 year, 5 months

Changing color limits with kwant.plotter.plot

by Jannis

Dear kwant community, Is there any way to change the color limits in kwant.plotter.plot? I use the site_color in kwant.plotter.plot to map my data on a 3D system. In contrast to kwant.plotter.map, there is no vmin/vmax option. I know that I can assign the figure to a subplot with ax. But I haven't found a way to create a colorbar or set the color limits with this option, because I lack a mappable. Has anyone figured out how to do this? (or if it is possible) Thanks, Jannis

1 year, 6 months

Phonon transmission in Kwant

by Ran Mutc

Dear Kwant developers, I wonder whether it is possible to calculate phonon transmission via NEGF formalism in Kwant. For example within the force constant model, is it possible to construct the dynamical matrix and calculate phonon self energies via surface Green's functions? Or do you recommend any other way to implement the phonon transmission in Kwant? Best, Ran

1 year, 6 months

Re: Phonon transmission in Kwant

by Ousmane LY

Hi Ran, the problem you described seems to be more adapted to tkwant or its extension tkwantOperator which computes energy and heat transport. So, you may give it a try. Regards, Ousmane

1 year, 6 months

Hamiltonian - Self energy matrix dimension mismatch

by mutc1r2595＠gmail.com

Dear Kwant developers, I am trying to calculate the retarded Green's function for a simple 2D square lattice with two leads. Rather than using the following: G = kwant.greens_function(sys, energy) Gr10=G.submatrix(1,0) I need to calculate Green's function by Gr = (EI-H-Sigma_L-Sigma_R)^-1. But apparently I coudn't properly construct it in Kwant: Gr2=Np.linalg.inv(energy*Np.identity(W)-H-Sigma_Lr-Sigma_Rr) H = sys.hamiltonian_submatrix() The problem is dimensions of self energy matrices are WxW, where W is the width sites. However the Hamiltonian matrix I get above has the dimensions of NxN, where N is the number of sites in the scattering region. Do I use the wrong Hamiltonian? How should I implement Gr = (EI-H-Sigma_L-Sigma_R)^-1 correctly in Kwant? Thanks for your time, Ran

1 year, 6 months

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Kwant-discuss July 2020