Kwant-discuss November 2019

kwant-discuss@python.org

12 participants
18 discussions

SIS Junction
by Denise Puglia 20 Nov '19

20 Nov '19

Dear community, I am trying to simulate the current in a JJ with kwant. So far current oscillates with a phase rate that scales with bias. However, the averaged current does not depend on bias, as show in the plots below. Any idea what might be causing this? For simplicity, I do not consider any bound states in my calculations. Any suggestions are welcome! Best, Denise Parameters: t=1 mu=t Delta=0.02 # superconducting gap N=1 #size of the N region S=10 #size of the S region barrier=1 #barrier in the N region [image: barrier_1_V_1.5.png] Same parameters but with barrier =2 [image: barrier_2_V_1.5.png] [image: barrier_2_V_0.2.png]

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Attaching two different lattice
by tavakkolidjawad 14 Nov '19

14 Nov '19

Hello everyone I'm Javad Tavakkoli and I'm a master student in condensed matter physics. I recently received a thesis that I want to use Kwant for its simulations. I have a question : Can I use this package to attaching two different system with different structure and different dimension? Can you explain briefly? Thank you.

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Non-equilibrium Green's functions and Current in tkwant
by Rudolf 13 Nov '19

13 Nov '19

Hello, The kwant documentation on kwant.solvers.common.GreensFunction() states that calling this method will return the retarded Green's function. Does this method evaluate the equilibrium or non-equilibrium retarded Green's function? I am interested in the time-dependent non-equilibrium density matrix, which can be written as the kinetic lesser NE Green's function G_<(t,t') rho_neq (t) = -iG_<(t,t')|t=t'. Thank you in advance. Cheers, Rudolf

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Josephson Junctions using tkwant
by Denise Puglia 13 Nov '19

13 Nov '19

Dear tkwant community, Has anyone recently tried to simulate Josephson Junctions using tkwant? I tried to follow the examples and tutorials, but several of them do not work in the last tkwant version. I am sending attached and you can find below the code that I am running but the current does not oscillate as a function of time and the IV curve is linear. Any suggestions on what may be wrong? Any help or comment is appreciated. Here is the code: import kwant import tkwant import tinyarray import numpy as np import matplotlib.pyplot as plt import scipy.constants as ct import time as comp_time from mpi4py import MPI comm=MPI.COMM_WORLD start = comp_time.time() tau_x = tinyarray.array([[0, 1], [1, 0]]) tau_y = tinyarray.array([[0, -1j], [1j, 0]]) tau_z = tinyarray.array([[1, 0], [0, -1]]) tau_0 = tinyarray.array([[1, 0], [0, 1]]) c_e = tinyarray.array([[1, 0], [0, 0]], complex) c_h = tinyarray.array([[0, 0], [0, -1]], complex) ### parameters Delta=0.02 #superconducting gap barrier=0.9 #barrier in the N region N=3 #size of the N region S=10 #size of the S region t=1 mu=t I_time_avg=[] V_values = np.linspace(-1.5*Delta, 1.5*Delta, 31) def make_system(a=1): lat = kwant.lattice.square(norbs=2) syst = kwant.Builder() #### Define junction. #### ### S syst[(lat(x, 0) for x in range(-S, 0))] = (2 * t - mu) * tau_z + Delta * tau_x #### N syst[(lat(x, 0) for x in range(0, N))] = (2 * t - mu + barrier) * tau_z ### S syst[(lat(x, 0) for x in range(N, N+S))] = (2 * t - mu) * tau_z + Delta * tau_x # Hoppings syst[lat.neighbors()] = -t * tau_z ### add JJ phase syst[(lat(-1,0),lat(0,0))] = -t*np.exp(1j*phase(time))*c_e -t*np.exp(-1j*phase(time))*c_h ### JJ phase #### Define the leads. #### lead_left = kwant.Builder(kwant.TranslationalSymmetry((-1, 0))) lead_left[lat(0, 0)] = (2 * t - mu) * tau_z + Delta * tau_x lead_left[lat.neighbors()] = -t * tau_z lead_right = lead_left.reversed() syst.attach_lead(lead_left) syst.attach_lead(lead_right) return syst def phase(time): ### int_{0}^{t}A(1-cos(pi*t'/tau))dt' def g(time,tau,A): return A*time-A*tau/np.pi*np.sin(np.pi*time/tau) if time<0: return 0 elif time<tau: return g(time, tau=tau, A=V/2) else: return V*(time-tau) for V in V_values: tau=0.01/(np.abs(0.04*np.pi*Delta)) tmax=4.01/(np.abs(0.04*np.pi*Delta)) syst = make_system() lat = kwant.lattice.square(norbs=2) # Finalize the system. fsyst = syst.finalized() #bondaries condition boundaries=[tkwant.leads.MonomialAbsorbingBoundary(strength=8,degree=3,num_cells=1300)] #kwant.plot(fsyst) left_lead_interface = [(lat(1, 0), lat(0, 0))] current_operator = kwant.operator.Current(fsyst,where=left_lead_interface) # occupation -- for each lead occupation_l = tkwant.manybody.make_occupation(mu) occupation_r = tkwant.manybody.make_occupation(mu+V) occupation = [occupation_l, occupation_r] # Create the solver solver = tkwant.manybody.State(fsyst, tmax, occupation) I_time = [] #get the current as a function of time real_time = np.linspace(0, tmax, 200) for time in real_time: solver.evolve(time) result = solver.evaluate(current_operator) I_time.append(result) data = np.column_stack((real_time, I_time)) I_time_avg.append(np.mean(I_time)) end = comp_time.time() print('Execution time is: '+str((end - start)/60)+' minutes') # check current as a function of time plt.figure() plt.plot(real_time, I_time) #plot IV curve plt.figure() plt.plot(V_values, np.asarray(I_time_avg)/(2*barrier*Delta), 'o') data = np.column_stack((V_values, I_time_avg)) np.savetxt('IV_curve.txt', data) Best regards, Denise

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Non-equilibrium Green's functions and Current in tkwant
by Ousmane LY 05 Nov '19

05 Nov '19

Hi Rudolf, In tkwant the wavefunction approach is used instead of non-equilibrium Green functions. This provides better scalability in both time and system size. Non-equilibrium densities and currents can be obtained by evolving kwant operators in time. The Green functions (if needed) can be also obtained by integrating the wavefunctions over energy. For more details you can have a look to the Weston’s thesis (book) [1] (mainly Chapter 2 and 3) as well as the tkwant tutorials. Regards, * J. Weston, Numerical Methods for Time-Resolved Quantum Nanoelectronics, Springer (2017)

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armchair nanoribbon with defect
by Nafise Nouri 04 Nov '19

04 Nov '19

Dear Joseph At first thank you for kwant team. My problem for zigzag nanoribbon with defect (hole) was solved with your help. Now I have a bit problem with armchair nanoribbon. I have changed zigzag nanoribbon according to making the armchair nanoribbon. It is OK when we have no defect on the system but when I try to make hole on the scattering region and leads I have a problem. The shape of holes on the scattering region and leads are not same. My code is as the following. That is very king of you if you help me where is the problem. Thanks In advance for your help. Beat wishes, Nafise import kwant from math import sqrt import matplotlib.pyplot as plt import tinyarray import numpy as np import math import cmath #import scipy.linalg as la import matplotlib d=1.42; a1=d*math.sqrt(3); #on-site energy................................................... t=-2.7; latt = kwant.lattice.general([(0,a1),(a1*math.sqrt(3)/2,a1*0.5)], [(-d/2,a1/2),(d/2,a1/2)]) a,b = latt.sublattices syst= kwant.Builder() def rectangle(pos): x, y = pos z=x**2+y**2 return -2.4*a1<x<2.4*a1 and -5*d<y<5*d syst[latt.shape(rectangle,(1,1))]=0 def delet(pos): x, y = pos z=x**2+y**2 return z<(2*a1)**2 del syst[latt.shape(delet, (1,1))] #nearest neighbors............................................................. syst[[kwant.builder.HoppingKind((0,0),a,b)]] =t syst[[kwant.builder.HoppingKind((0,1),a,b)]] =t syst[[kwant.builder.HoppingKind((-1,1),a,b)]] =t ax=kwant.plot(syst); sym = kwant.TranslationalSymmetry(latt.vec((-2,4))) lead = kwant.Builder(sym) def lead_shape(pos): x, y = pos return -5*d<y<5*d lead[latt.shape(lead_shape, (1,1))]=0 def delet_lead(pos): x, y = pos z=x**2+y**2 return z<(2*a1)**2 del lead[latt.shape(delet_lead, (1,1))] lead[[kwant.builder.HoppingKind((0,0),a,b)]]=t lead[[kwant.builder.HoppingKind((0,1),a,b)]]=t lead[[kwant.builder.HoppingKind((-1,1),a,b)]]=t syst.attach_lead(lead,add_cells=0) syst.attach_lead(lead.reversed(),add_cells=0) ax=kwant.plot(syst);

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(no subject)
by Khani Hosein 04 Nov '19

04 Nov '19

Dear all, I am using kwant to calculate the transmission of a bulk system. I use " sys = kwant.wraparound.wraparound(sys) and lead = kwant.wraparound.wraparound(lead, keep=0)" to change my tight-binding ribbon system to a bulk system. The transmission is obtained using: kys = np.arange(-0.5, 0.5, 0.001) for ky in kys: smatrix = kwant.smatrix(sys, energy, [ky]) transmission.append(smatrix.transmission(1, 0)) I want to obtain the Transmission vs the incident angle of an electron, and I also need to do the integration ∫T(ky, E) dky or ∫T(θ,E)cosθdθ. I do not undstand the ky in the system with kwant.wraparoun, what is the unit of ky, what is k here for the system. Can you give me some advices on this?Thanks in advance. The definition of incident angle is shown in the attached Fig.1， the band structure for my bulk system is shown in attached Fig.2 and the Tranmission vs ky is shown in Fig.3 (I do not know how the set the values for ky). Regards, Hosein Khani

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Re: [Kwant] Armchair nanoribbon with defect
by Nafise Nouri 04 Nov '19

04 Nov '19

Dear Joseph Thank you for your response. My problem for zigzag nanoribbon with defect (hole) was solved with your help. Now I have a bit problem with armchair nanoribbon. I have changed zigzag nanoribbon according to making the armchair nanoribbon. It is OK when we have no defect on the system but when I try to make hole on the scattering region and leads I have a problem. The shape of holes on the scattering region and leads are not same. My code is as the following. That is very king of you if you help me where is the problem. Thanks In advance for your help. Beat wishes, Nafise import kwant from math import sqrt import matplotlib.pyplot as plt import tinyarray import numpy as np import math import cmath #import scipy.linalg as la import matplotlib d=1.42; a1=d*math.sqrt(3); #on-site energy................................................... t=-2.7; latt = kwant.lattice.general([(0,a1),(a1*math.sqrt(3)/2,a1*0.5)], [(-d/2,a1/2),(d/2,a1/2)]) a,b = latt.sublattices syst= kwant.Builder() def rectangle(pos): x, y = pos z=x**2+y**2 return -2.4*a1<x<2.4*a1 and -5*d<y<5*d syst[latt.shape(rectangle,(1,1))]=0 def delet(pos): x, y = pos z=x**2+y**2 return z<(2*a1)**2 del syst[latt.shape(delet, (1,1))] #nearest neighbors............................................................. syst[[kwant.builder.HoppingKind((0,0),a,b)]] =t syst[[kwant.builder.HoppingKind((0,1),a,b)]] =t syst[[kwant.builder.HoppingKind((-1,1),a,b)]] =t ax=kwant.plot(syst); sym = kwant.TranslationalSymmetry(latt.vec((-2,4))) lead = kwant.Builder(sym) def lead_shape(pos): x, y = pos return -5*d<y<5*d lead[latt.shape(lead_shape, (1,1))]=0 def delet_lead(pos): x, y = pos z=x**2+y**2 return z<(2*a1)**2 del lead[latt.shape(delet_lead, (1,1))] lead[[kwant.builder.HoppingKind((0,0),a,b)]]=t lead[[kwant.builder.HoppingKind((0,1),a,b)]]=t lead[[kwant.builder.HoppingKind((-1,1),a,b)]]=t syst.attach_lead(lead,add_cells=0) syst.attach_lead(lead.reversed(),add_cells=0) ax=kwant.plot(syst); Joseph Weston [image: Attachments]Sun, Nov 3, 1:10 PM (1 day ago) to me Hi, Please post Kwant usage questions to the Kwant mailing list, not my personal email address. Thanks, Joe On Sun, Nov 3, 2019 at 1:10 PM Joseph Weston <joseph.weston08(a)gmail.com> wrote: > Hi, > > Please post Kwant usage questions to the Kwant mailing list, not my > personal email address. > > Thanks, > > Joe > > On 11/3/19 9:29 AM, Nafise Nouri wrote: > > Dear Joseph > > > > At first thank you for your previous help. My problem for zigzag > > nanoribbon with defect (hole) was solved with your help. Now I have a > > bit problem with armchair nanoribbon. I have changed zigzag nanoribbon > > according to making the armchair nanoribbon. It is OK when we have no > > defect on the system but when I try to make hole on the scattering > > region and leads I have a problem. The shape of holes on the > > scattering region and leads are not same. My code is as the following. > > That is very king of you if you help me where is the problem. > > > > Thanks In advance for your help. > > > > Beat wishes, > > Nafise > > > > import kwant > > from math import sqrt > > import matplotlib.pyplot as plt > > import tinyarray > > import numpy as np > > import math > > import cmath > > #import scipy.linalg as la > > import matplotlib > > d=1.42; > > a1=d*math.sqrt(3); > > > > #on-site energy................................................... > > t=-2.7; > > > > latt = kwant.lattice.general([(0,a1),(a1*math.sqrt(3)/2,a1*0.5)], > > [(-d/2,a1/2),(d/2,a1/2)]) > > a,b = latt.sublattices > > syst= kwant.Builder() > > > > def rectangle(pos): > > x, y = pos > > z=x**2+y**2 > > return -2.4*a1<x<2.4*a1 and -5*d<y<5*d > > > > syst[latt.shape(rectangle,(1,1))]=0 > > > > def delet(pos): > > x, y = pos > > z=x**2+y**2 > > return z<(2*a1)**2 > > > > del syst[latt.shape(delet, (1,1))] > > > > #nearest > > neighbors............................................................. > > syst[[kwant.builder.HoppingKind((0,0),a,b)]] =t > > syst[[kwant.builder.HoppingKind((0,1),a,b)]] =t > > syst[[kwant.builder.HoppingKind((-1,1),a,b)]] =t > > > > ax=kwant.plot(syst); > > > > sym = kwant.TranslationalSymmetry(latt.vec((-2,4))) > > > > lead = kwant.Builder(sym) > > > > def lead_shape(pos): > > x, y = pos > > return -5*d<y<5*d > > > > lead[latt.shape(lead_shape, (1,1))]=0 > > > > def delet_lead(pos): > > x, y = pos > > z=x**2+y**2 > > return z<(2*a1)**2 > > > > del lead[latt.shape(delet_lead, (1,1))] > > > > lead[[kwant.builder.HoppingKind((0,0),a,b)]]=t > > lead[[kwant.builder.HoppingKind((0,1),a,b)]]=t > > lead[[kwant.builder.HoppingKind((-1,1),a,b)]]=t > > > > syst.attach_lead(lead,add_cells=0) > > syst.attach_lead(lead.reversed(),add_cells=0) > > ax=kwant.plot(syst); > > > > > >

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Kwant-discuss November 2019