Mailman 3 November 2022 - Kwant-discuss

To to separate spins, electron and hole
by Khani Hosein Oct. 11, 2024

Oct. 11, 2024

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

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Realistic values of hopping parameters
by Yu Li Oct. 19, 2023

Oct. 19, 2023

Dear all, Now I’m studying some transport property based on multilayered system, with nonmagnetic layer/ferromagnetic layer (NM/FM) stack. May I ask when creating a tight binding system, and setting hoppings by the following function: syst[(lat(1, 0), lat(1, 1))] = t, how to associate the hopping with a realistic system? Such as hoppings between FM and FM atoms, or between FM and NM atoms? I found in many literatures people just simply put t=1, but I assume the value should depend on the type of atoms. My another question is, is it possible to define more than one type of hopping between two sites? For the tight-binding approximation of p electrons, there are two types of hopping integrals: Vppσ, and Vppπ, so I’m wondering if it’s possible to simulate the effect of both hoppings? Thanks a lot for reading my questions! Cheers, Yu Li

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Defining uniaxial strain in specified region of graphene
by shrushti.tapar07＠gmail.com Jan. 20, 2023

Jan. 20, 2023

I want to create the graphene strained superlattice-like structure, having uniaxial strain defined at the specified region. Please, someone can suggest to me how to define the strained region and interface between unstrained and strained graphene regions. Thanks in Advance Shrushti

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Resolution of Tkwant
by Clarke, Isobel Dec. 5, 2022

Dec. 5, 2022

Dear Kwant developers, I was wondering if there is a limit on the resolution of Kwant and Tkwant when calculating the density of an evolved wavefunction. I am currently working on a code to simulate the response of a carbon nanotube spin qubit to an electric dipole spin resonance drive. I am using Kwant to define the carbon nanotube as a scattering region and then apply a Hamiltonian to the system. The lowest eigenvector of the Hamiltonian at t=0 is determined and associated with a tkwant.onebody.WaveFunction. This wavefunction is evolved over time and the density of the wavefunction calculated using kwant.operator.Density. The relevant part of my code is given below: class System: def __init__(self, hamiltonian, pertubation_type, number_of_lattices, potential_type): self.potential_type = potential_type self.hamiltonian = hamiltonian self.number_of_lattices = number_of_lattices self.pertubation_type = pertubation_type self.evolve_state = False def potential(self, z, time): if self.potential_type == 0: #infinite square well total_potential = 0 elif self.potential_type == 1: #parabolic potential total_potential = .5 * (z * self.omega_0_au) ** 2 if self.pertubation_type == "cos": self.pertubation = self.cosine_v_ac else: self.pertubation = self.sine_v_ac total_potential += self.pertubation(time, z, self.eV_0_au, self.pulse_frequency_au, self.total_length_au) return total_potential def kwant_shape(self, site): (z,) = site.pos return (-self.total_length_au / 2 <= z < self.total_length_au / 2) def make_system(self): self.template = kwant.continuum.discretize(self.hamiltonian, grid=self.lattice_size_au) self.syst = kwant.Builder() # add the nanotube to the system self.syst.fill(self.template, self.kwant_shape, (0,)) self.syst = self.syst.finalized() def B_constant(z): return -self.g * self.mu_B_au * self.B_z_au * self.hbar_au / 2 def C_constant(z): return -self.g * self.mu_B_au * self.b_sl_au * z * self.hbar_au / 2 def D_constant(z): return -self.g * self.mu_B_au * self.B_y_au * self.hbar_au / 2 # coefficient for the kinetic energy term A_constant = self.hbar_au ** 2 / (2 * self.m_au) # parameters of hamiltonian self.params = dict(A=A_constant, V=self.potential, B=B_constant, C=C_constant, D=D_constant) self.tparams = self.params.copy() # copy the params array self.tparams['time'] = 0 # initial time = 0 # compute the Hamiltonian matrix hamiltonian = self.syst.hamiltonian_submatrix(params=self.tparams) # compute the eigenvalues (energies) and eigenvectors (wavefunctions). eigenValues, eigenVectors = np.linalg.eig(hamiltonian) # sort the eigenvectors and eigenvalues according the ascending eigenvalues. idx = eigenValues.argsort() self.initial_eigenvalues = eigenValues[idx] eigenVectors = eigenVectors[:, idx] # initial wave functions unperturbed by time dependent part of hamiltonian self.psi_1_init = eigenVectors[:, 0] self.psi_2_init = eigenVectors[:, 1] # an object representing the spin-up state self.spin_up_state = tkwant.onebody.WaveFunction.from_kwant(syst=self.syst, psi_init=self.psi_1_init, energy=eigenValues[0], params=self.params) return self.syst def evolve(self, time_steps): self.evolve_state = True total_osc_time = self.second_to_au(0.5e-8) times_au = np.linspace(0, total_osc_time, num=time_steps) times_SI = np.linspace(0, self.au_to_second(total_osc_time), num=time_steps) density_operator = kwant.operator.Density(self.syst) psi = self.spin_up_state data = {'states': []} for time in times_au: psi.evolve(time) # evolve the wavefunction density = psi.evaluate(density_operator) # compute density data['states'].append({'pdf': density.tolist()}) json_string = json.dumps(data) with open(r'\{}.json'.format(timestr), 'w') as outfile: outfile.write(json_string) self.evolve_state = False return True def main(): lattices = 100 potential = 0 system = System("((A * k_z**2) + V(z, time)) * identity(2) + B(z) * sigma_z + C(z) * sigma_x + D(z) * sigma_y", pertubation_type="sin", number_of_lattices=lattices, potential_type=potential) system.make_system() system.evolve(10) if __name__ == '__main__': main() Please note that I haven't included some conversion functions in the above code. Using this code, I obtain the results shown in the animation attached. The first subplot shows the density of the wavefunction across the carbon nanotube evolving with time. The animation shows an expected smooth Gaussian response for the first few time steps, however the graph then becomes very noisy. I was wondering why this occurs and if it could be due to a limit on the resolution of Tkwant? The second subplot shows the energy of the time-dependent perturbation over time, displaying a sin wave perturbation as a simple 'see-sawing' potential. In addition, I was wondering if you had any advice for making the code run faster? I ran the simulation for 10 time steps over a very short time period to obtain the attached animation and it took around 4 hours on my desktop. Thank you for any help with this. Best wishes, Isobel

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Resolution of Tkwant
by zcapicc＠ucl.ac.uk Nov. 30, 2022

Nov. 30, 2022

Dear Kwant developers, I was wondering if there is a limit on the resolution of Kwant and Tkwant when calculating the density of an evolved wavefunction. I am currently working on a code to simulate the response of a carbon nanotube spin qubit to an electric dipole spin resonance drive. I am using Kwant to define the carbon nanotube as a scattering region and then apply a Hamiltonian to the system. The lowest eigenvector of the Hamiltonian at t=0 is determined and associated with a tkwant.onebody.WaveFunction. This wavefunction is evolved over time and the density of the wavefunction calculated using kwant.operator.Density. The relevant part of my code is given below: class System: def __init__(self, hamiltonian, pertubation_type, number_of_lattices, potential_type): self.potential_type = potential_type self.hamiltonian = hamiltonian self.number_of_lattices = number_of_lattices self.pertubation_type = pertubation_type self.evolve_state = False def potential(self, z, time): if self.potential_type == 0: #infinite square well total_potential = 0 elif self.potential_type == 1: #parabolic potential total_potential = .5 * (z * self.omega_0_au) ** 2 if self.pertubation_type == "cos": self.pertubation = self.cosine_v_ac else: self.pertubation = self.sine_v_ac total_potential += self.pertubation(time, z, self.eV_0_au, self.pulse_frequency_au, self.total_length_au) return total_potential def kwant_shape(self, site): (z,) = site.pos return (-self.total_length_au / 2 <= z < self.total_length_au / 2) def make_system(self): self.template = kwant.continuum.discretize(self.hamiltonian, grid=self.lattice_size_au) self.syst = kwant.Builder() # add the nanotube to the system self.syst.fill(self.template, self.kwant_shape, (0,)) self.syst = self.syst.finalized() def B_constant(z): return -self.g * self.mu_B_au * self.B_z_au * self.hbar_au / 2 def C_constant(z): return -self.g * self.mu_B_au * self.b_sl_au * z * self.hbar_au / 2 def D_constant(z): return -self.g * self.mu_B_au * self.B_y_au * self.hbar_au / 2 # coefficient for the kinetic energy term A_constant = self.hbar_au ** 2 / (2 * self.m_au) # parameters of hamiltonian self.params = dict(A=A_constant, V=self.potential, B=B_constant, C=C_constant, D=D_constant) self.tparams = self.params.copy() # copy the params array self.tparams['time'] = 0 # initial time = 0 # compute the Hamiltonian matrix hamiltonian = self.syst.hamiltonian_submatrix(params=self.tparams) # compute the eigenvalues (energies) and eigenvectors (wavefunctions). eigenValues, eigenVectors = np.linalg.eig(hamiltonian) # sort the eigenvectors and eigenvalues according the ascending eigenvalues. idx = eigenValues.argsort() self.initial_eigenvalues = eigenValues[idx] eigenVectors = eigenVectors[:, idx] # initial wave functions unperturbed by time dependent part of hamiltonian self.psi_1_init = eigenVectors[:, 0] self.psi_2_init = eigenVectors[:, 1] # an object representing the spin-up state self.spin_up_state = tkwant.onebody.WaveFunction.from_kwant(syst=self.syst, psi_init=self.psi_1_init, energy=eigenValues[0], params=self.params) return self.syst def evolve(self, time_steps): self.evolve_state = True total_osc_time = self.second_to_au(0.5e-8) times_au = np.linspace(0, total_osc_time, num=time_steps) times_SI = np.linspace(0, self.au_to_second(total_osc_time), num=time_steps) density_operator = kwant.operator.Density(self.syst) psi = self.spin_up_state data = {'states': []} for time in times_au: psi.evolve(time) # evolve the wavefunction density = psi.evaluate(density_operator) # compute density data['states'].append({'pdf': density.tolist()}) json_string = json.dumps(data) with open(r'\{}.json'.format(timestr), 'w') as outfile: outfile.write(json_string) self.evolve_state = False return True def main(): lattices = 100 potential = 0 system = System("((A * k_z**2) + V(z, time)) * identity(2) + B(z) * sigma_z + C(z) * sigma_x + D(z) * sigma_y", pertubation_type="sin", number_of_lattices=lattices, potential_type=potential) system.make_system() system.evolve(10) if __name__ == '__main__': main() Please note that I haven't included some conversion functions in the above code. Using the results from this code, I can obtain a graph of density of the wavefunction across the carbon nanotube evolving with time. The graph shows an expected smooth Gaussian response for the first few time steps, however the graph then becomes very noisy and spiky. I was wondering why this occurs and if it could be due to a limit on the resolution of Tkwant? In addition, I was wondering if you had any advice for making the code run faster? I ran the simulation for 10 time steps over a very short time period to obtain the attached animation and it took around 4 hours on my desktop. Thank you for any help with this. Best wishes, Isobel

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About calculating local observables using Green function
by Hari Gautam Nov. 25, 2022

Nov. 25, 2022

Dear kwant users, I find the wavefunction methods with sufficient example for calculation of local observables using operators in kwant. I would also like to calculate the local observables using Green functions. As far as I know, I understood that the green_function method only provides the surface Green function at the interface of the lead and the scattering system which is helpful to calculate the total conductance. How can we define local observables using Green functions in kwant? Is there any methods like operators included in the kwant? Thank you Hari

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Attaching lead to a system
by Shashank Kumar Nov. 3, 2022

Nov. 3, 2022

Hi all, I have made a one dimensional system with 3 sub-lattices. However, in order to attach leads I have to make a lead and manually attach it to sublattice A. But, apparently this code below is not working. Any suggestion will be help full. def make_system(nlattice): lat = kwant.lattice.Polyatomic([(1, 0), (0, 1)], [(0, 0), (1/3.0, 0), (2/3.0, 0)]) sub_a, sub_b, sub_c = lat.sublattices # central scattering region syst = kwant.Builder() syst[(sub_a(x,0) for x in range(nlattice))] = 4 syst[(sub_b(x,0) for x in range(nlattice))] = 4 syst[(sub_c(x,0) for x in range(nlattice))] = 4 syst[lat.neighbors()] = -1 # add leads lat_lead = kwant.lattice.square() sym_lead1 = kwant.TranslationalSymmetry((-1, 0)) lead1 = kwant.Builder(sym_lead1) lead1[lat_lead(-1, 0)] = 4 lead1[lat_lead.neighbors()] = -1 syst[lat_lead(-1,0)] = 4 syst[lat_lead(-1,0), sub_a(0,0)] = -1 syst.attach_lead(lead1) syst.attach_lead(lead1.reversed()) kwant.plot(lead1) return syst fsyst = make_system(nlattice=10).finalized() kwant.plot(sys, fig_size=[10,8], site_size=0.2) Shashank Kumar

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