Mailman 3 November 2021 - Kwant-discuss

How to get higher plateaus in quantum Hall conductivity?
by Jerry xhm Nov. 27, 2021

Nov. 27, 2021

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()

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Kwant code discussion
by ruhao Liu Nov. 15, 2021

Nov. 15, 2021

Dear author： I am a PHD student and my research is using pizeoelectric potential regulate spin and valley transport. I am quite intristed about Kwant and I have published an article on Nona Energy using Kwant I wonder could you please help me to solve the folowing two questions, the first one is how to calculate a one-dimensional quantum transport system, can you give a case? The second one is how to use Kwant to caculate heat transport system like electric current, heat current, temperature-dependent electrical conductance , the thermal conductivity, the Seebeck thermopower, and the thermoelectric efficiency. Could you give me an example? Thank you. Best wishes Ruhao Liu

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Creating virtual self-energy leads to extract Green's function between arbitrary sites:
by Sayandip Dhara Nov. 10, 2021

Nov. 10, 2021

Hello, I am trying to extract Green's function between two arbitrary sites in a system. I have noticed from one of the previous threads that one way to do it is to attach virtual leads with zero self-energy on those specific sites. However, I am having trouble with the suggested function. It is telling me that whichever site I want to attach is not in the scattering region. The following is the code: import kwant from types import SimpleNamespace from copy import copy import tinyarray import numpy as np import csv import ipywidgets #import holoviews as hv #hv.extension('bokeh') from scipy import sparse from matplotlib import pyplot from scipy.optimize import minimize sigma_x = tinyarray.array([[0, 1], [1, 0]]) sigma_y = tinyarray.array([[0, -1j], [1j, 0]]) sigma_z = tinyarray.array([[1, 0], [0, -1]]) sigma_0 = tinyarray.array([[1, 0], [0, 1]]) 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]]) # mu=0.5, # t=-1.,delta=0.5,V_N=1.25, phi=0, L=3 def make_system_ex3(L=10): lat = kwant.lattice.chain(norbs=2) syst = kwant.Builder() #### Define the scattering region. #### def onsite_sc(site,t,mu,delta): return (2.*t-mu )*tau_z + delta*tau_x def onsite_N(site,t,mu,V_N): return (2.*t-mu + V_N)*tau_z syst[(lat(x) for x in range(1, L))] = onsite_sc #superconducting onsite hamiltonian syst[lat(L)] = onsite_N #normal onsite hamiltonian syst[(lat(x) for x in range(L+1,2*L+1))] = onsite_sc #superconducting onsite hamiltonian def hop(site1,site2,t,phi): return -t*np.matmul(np.exp(1j*phi*tau_z),tau_z) syst[(lat(L-1), lat(L))] = hop for i in range(1,L-1): syst[(lat(i), lat(i+1))] = -t*tau_z for i in range(L,2*L): syst[(lat(i), lat(i+1))] = -t*tau_z #### Define the leads. #### sym_left = kwant.TranslationalSymmetry([-1]) lead0 = kwant.Builder(sym_left) lead0[(lat(0))] = (2.*t-mu)*tau_z + delta*tau_x lead0[lat.neighbors()] = -t*tau_z sym_right = kwant.TranslationalSymmetry([1]) lead1 = kwant.Builder(sym_right) lead1[(lat(2*L+1))] = (2.*t-mu)*tau_z + delta*tau_x lead1[lat.neighbors()] = -t*tau_z # #### Attach the leads and return the system. #### syst.attach_lead(lead0) syst.attach_lead(lead1) return syst,lat ---------------------------------------------------------------------------------------------------------------------------- mu=1 t=1.0 delta=0.5 V_N=1 phi=0 L=10 par = dict(t=t,mu=mu,delta=delta,phi=phi,V_N=V_N) # syst,lat = make_system_ex3(L=10) def mount_vlead(sys, vlead_interface, norb): dim = norb zero_array = np.zeros((dim, dim), dtype=float) def selfenergy_func(energy, args=()): return zero_array vlead = kwant.builder.SelfEnergyLead(selfenergy_func, vlead_interface,()) sys.leads.append(vlead) mount_vlead(syst,[L-1], 2) # number of orbitals =4. Here we mount lead number 2 mount_vlead(syst,[L], 2) # number of orbitals =4. Here we mount lead number 3 syst =syst.finalized() G12=kwant.greens_function(syst, energy=-1.8*1j, in_leads=[L-1],out_leads=[L],\ check_hermiticity=False,params=par).data G21=kwant.greens_function(syst, energy=-1.8*1j, in_leads=[L],out_leads=[L-1],\ check_hermiticity=False,params=par).data ---------------------------------------------------------------------------------------------------------------------------------- The error message I am getting is " ValueError: Lead 2 is attached to a site that does not belong to the scattering region: 9" It would be great if you can suggest to me where I am going wrong. Thanks, Sayandip

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Spin Hall conductance in a four terminal device
by mondal18＠iitg.ac.in Nov. 2, 2021

Nov. 2, 2021

Dear developer, I am looking for the calculation of spin Hall conductance in a four-terminal device. I am searching the mailing archives for a few days, but couldn't get anything useful. But, I found a thread where Mr Joseph Weston (https://mail.python.org/archives/list/kwant-discuss@python.org/message/MHYO…) had given some links for this calculation and unfortunately those links are not working. It would be very useful if you provide one example of calculating spin Hall conductance of a four-terminal device. I shall look forward to your kind reply. Thanking you. Sincerely yours, Sayan Mondal, IIT Guwahati,

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