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DOS_graphen_kpm1.py
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# Tutorial 2.5. Beyond square lattices: graphene
# ==============================================
#
# Physics background
# ------------------
# Transport through a graphene quantum dot with a pn-junction
#
# Kwant features highlighted
# --------------------------
# - Application of all the aspects of tutorials 1-3 to a more complicated
# lattice, namely graphene
import numpy as np
from math import pi, sqrt, tanh, exp, tan,acos,sin,cos
import csv
from kpmMethod import *
import numpy as np
from scipy.signal import find_peaks_cwt
from scipy.sparse import identity
from numpy import linalg as LA
import sys
import kwant
import tinyarray
import cmath
# For computing eigenvalues
import scipy.sparse.linalg as sla
# For plotting
from matplotlib import pyplot
from datetime import datetime
sq3=sqrt(3);
# Define the graphene lattice
sin_30, cos_30 = (1 / 2, sqrt(3) / 2)
graphene = kwant.lattice.general([(cos_30, -sin_30), (cos_30,sin_30)],
[(0, 0), (1 / sqrt(3),0)])
Base_a1=(cos_30, -sin_30); Base_a2=(cos_30,sin_30);
a, b = graphene.sublattices
Nx=1;
Ny=1;
def make_system_step1(q):
L1=tinyarray.array((3/sqrt(3),0));SC1=L1;
L2=tinyarray.array((0,q)); SC2=L2;
syst = kwant.Builder()
##primitive graphene,dispersion without B:
# for i in range(1):
# #for i in range(q):
# for j in range(1):
# # On-site Hamiltonian
# syst[a(i, j)] =0
# syst[b(i, j)] =0
# syst[a(0,0),b(0,0)]=-1-np.exp(1j*k1)-np.exp(1j*k2)
#
def rectangle(pos):
xR, yR = pos
#print(pos)
#sys.exit()
# xR,yR=list(x*v1+y*v2)
#return (xR <=Lx2)&(yR<=Ly2)&(xR >= Lx1)&(yR>=Ly1)
return (-cos_30/3-0.00001<=xR<3/sqrt(3)*Nx-1/sqrt(3))&(0-0.0001<=yR<=Ny*q-0.0001)
syst[graphene.shape(rectangle, (0, 0))] = 0
syst0=syst.finalized()
N_ToT=syst0.graph.num_nodes;
print(N_ToT);
def neighbors():
nns=[[] for i in range(N_ToT)];
for ni in range(N_ToT):
#print(ni)
ri=syst0.sites[ni].pos;
for nj in range(N_ToT):
rj=syst0.sites[nj].pos;
for n1 in range(-1,2):
for n2 in range(-1,2):
rjn=rj+(n1*SC1+n2*SC2);
ss=ri-rjn;
dis=sqrt(np.dot(ss,ss))
if (abs(dis-1/sqrt(3))<10**-5):
if not((n1==0)&(n2==0)&(nj==ni)):
nns[ni].append((nj,n1,n2))
return nns
nns=neighbors();
return nns,syst,syst0
def make_system_step2(k1,k2,syst,syst0,nns,p,q):
L1=tinyarray.array((3/sqrt(3),0));SC1=L1;
L2=tinyarray.array((0,q)); SC2=L2;
N_ToT=syst0.graph.num_nodes
start=datetime.now()
def amp(ri,rj):
hop_t=0;
ss=ri-rj;
dis=sqrt(np.dot(ss,ss))
if (abs(dis-1/sqrt(3))<10**-5):
hop_t=-1;
return hop_t
def hoppping(site1,site2):
r1=site1.pos;
r2=site2.pos;
return -1*phase(r1,r2)
def set_hoppings(ri,rj,n1n2_is):
# k1,k2,p=k_and_p
# ri=site1.pos;
# rj=site2.pos;
#if (site1.pos==tinyarray.array([0,0]))&(site2.pos==tinyarray.array([0,0]))&(site1.family=='a')&(site2.family=='b'):
# print('k_and_p=',k1,k2,p)
#print(site1.tag,site2.tag,syst0.sites[0].tag)
#print(site1.family,site2.family,syst0.sites[0].family)
non_diag_term=0;
#print('Again, n1n2_is=',n1n2_is)
#print('hopping k1=',k1)
#if (ri==syst0.sites[0].pos):
# print('insethoppings_n1n2_is=',n1n2_is)
#time.sleep(10)
# (for i in range(len(n1n2_is)):
# n1,n2=n1n2_is[i]
# rjn=rj+n1*SC1+n2*SC2
# non_diag_term=non_diag_term+np.exp(1j*(n1*k1+n2*k2))*amp(ri,rjn) *phase(ri,rjn);)
#if not((n1==0)&(n2==0)):
#print('n1=',n1,'n2=',n2,'Hamiltonian_elements=',np.exp(1j*(n1*k1+n2*k2))*amp(ri,rjn))
for n1 in range(-1,2):
for n2 in range(-1,2):
rjn=rj+n1*SC1+n2*SC2;
#print(rj,rjn);
#print(amp(ri,rjn));
non_diag_term=non_diag_term + np.exp(1j*(n1*k1+n2*k2)) *amp(ri,rjn)*phase(ri,rjn);
#rj1=rj-SC1
#rj2=rj-SC2;
#non_diag_term=t*(1*phase(ri,rj)+np.exp(-1j*k2)*phase(ri,rj1)+np.exp(-1j*k1)*phase(ri,rj2))
#if abs(ri[2]-rj[2])>10**-3:
# non_diag_term=0
return non_diag_term
def phase(rj,ri):
xi,yi=ri;
xj,yj=rj;
phase=(yi+yj)/2* (xj-xi);
phase=np.exp(2*pi*1j*phase*p/q*2*sqrt(3)) #p/q
return phase
def rearrange(nn_i0,n1n2_i0):
n1n2_is=[[] for i in range(len(nn_i0))];
nn_is=[[] for i in range(len(nn_i0))];
ns=0;
n1n2_is[ns]=[n1n2_i0[0]];
nn_is[ns]=nn_i0[0];
for i in range(1,len(nn_i0)):
if nn_i0[i]==nn_is[ns]:
n1n2_is[ns].append(n1n2_i0[i]);
else:
ns=ns+1;
nn_is[ns]=nn_i0[i];
n1n2_is[ns]=[n1n2_i0[i]]
return n1n2_is, ns, nn_is
for ni in range(0,N_ToT):
#print('ni=',ni);
ri=syst0.sites[ni].pos;
nnn_sites=nns[ni];lennn_i=len(nnn_sites);
nn_i=[nnn_sites[i][0] for i in range(lennn_i)];
#print('nn_i=',nn_i)
n1n2_i=[nnn_sites[i][1:3] for i in range(lennn_i)];
#print('lennn_i=',lennn_i,'n1n2_i=',n1n2_i)
n1n2_i, ns, nn_i=rearrange(nn_i,n1n2_i); #压缩近邻
#print('After rearrangement:n1n2_i=',n1n2_i,'ns=,',ns+1)
#print('ni=',ni)
#print('nn_i=',nn_i)
#sys.exit()
#set hopping
for nj in range(ns+1):
n1n2_is=n1n2_i[nj];
#print('n1n2_is=',n1n2_is)
if (nn_i[nj]>ni):
rj=syst0.sites[nn_i[nj]].pos;
syst[syst0.sites[ni],syst0.sites[nn_i[nj]]]=set_hoppings(ri,rj,n1n2_is);
#syst[syst0.sites[ni],syst0.sites[nn_i[nj]]]=t*(1+np.exp(-1j*k2)+np.exp(-1j*k1))
#sys.exit()
# syst[graphene.neighbors()] = hoppping;
#
# hopping = ((1*Nx, 1*Nx), a, b);
# r1=(0,0);r2=(0,1/sqrt(3)); #from r2 to r1
# syst[kwant.builder.HoppingKind(hopping[0],hopping[1],hopping[2])] =-phase(r1,r2)*np.exp(1j*k1) #kx shold be changed to kx
# hopping = ((-q*Ny, q*Ny-1), b, a)
# r1=(0,0);r2=(1/2/sqrt(3),1/2);
# syst[kwant.builder.HoppingKind(hopping[0],hopping[1],hopping[2])] =-phase(r1,r2)* np.exp(1j*k2) #k2 shold be changed to ky
# hopping = ((1-q*Ny, q*Ny), a, b)
# r1=(0,0);r2=(-1/2/sqrt(3),1/2);
# syst[kwant.builder.HoppingKind(hopping[0],hopping[1],hopping[2])] =-phase(r1,r2)* np.exp(1j*k2) #k2 shold be changed to ky
def family_colors(site):
return 1 if site.family == a else 0
#kwant.plot(syst, site_color=family_colors, site_lw=0.1,colorbar=False)
# n_i,n_j=Given_link_ijs(a,tinyarray.array([0,1]),b,tinyarray.array([-1,1]))
# ri=syst0.sites[n_i].pos; rj=syst0.sites[n_j].pos;
#
# sys.exit()
#
#print([syst0.sites[i].tag for i in range(N_ToT)])
#print(N_ToT);
def phase_check():
aa1=np.array(Base_a1);aa2=np.array(Base_a2);
r1=(aa1+aa2)/3;
r2=aa2;
r3=(4*aa2-2*aa1)/3;
r4=aa2-aa1;
r5=(aa2-2*aa1)/3;
r6=np.array([0,0]);
r0=(2*aa2-aa1)/3;
r=np.zeros((6,2))
# print(phase(r3,r2))
# print(phase(r3+SC1,r2+SC1))
# print(phase(r5,r6))
# print(phase(r5+SC1,r6+SC1))
# print(phase(r6,r1))
# print(phase(r6+SC1,r1+SC1))
# sys.exit()
r[0,:]=r1;r[1,:]=r2;r[2,:]=r3;r[3,:]=r4;
r[4,:]=r5;r[5,:]=r6;
rr=r;
print(r1+r2+r3+r4+r5-6*r0)
print('sum=',r.sum(0)-6*r0)
print('total phase1=',phase(r1,r6) *phase(r2,r1) *phase(r3,r2) *phase(r4,r3) *phase(r5,r4) *phase(r6,r5))
for n1 in range(-5,5):
for n2 in range(-5,5):
r=rr+n1*aa1+n2*aa2*0.1
print('total phase=',phase(r[0,:],r[5,:])*phase(r[1,:],r[0,:])*phase(r[2,:],r[1,:])*phase(r[3,:],r[2,:])*phase(r[4,:],r[3,:])*phase(r[5,:],r[4,:]))
#
print('the periocity of phase efactor:')
for i in range(5):
ri=r[i,:];rj=r[i+1,:];
#the periocity of phase factor:
print(str(i+1)+'---'+str(i+2)+':')
print(phase(ri,rj))
print(phase(ri+tinyarray.array(L1),rj+tinyarray.array(L1)))
print(phase(ri+(q-1)*tinyarray.array(L2),rj+(q-1)*tinyarray.array(L2)))
print(phase(ri+q*tinyarray.array(L2),rj+q*tinyarray.array(L2)))
ri=r[5,:];rj=r[0,:];
#the periocity of phase factor:
print(str(6)+'---'+str(1)+':')
print(phase(ri,rj))
print(phase(ri+tinyarray.array(L1),rj+tinyarray.array(L1)))
print(phase(ri+(q-1)*tinyarray.array(L2),rj+(q-1)*tinyarray.array(L2)))
print(phase(ri+q*tinyarray.array(L2),rj+q*tinyarray.array(L2)))
print('q=',q,'p=',p)
print('total phase=',(phase(r[0,:],r[5,:])*phase(r[1,:],r[0,:])*phase(r[2,:],r[1,:])*phase(r[3,:],r[2,:])*phase(r[4,:],r[3,:])*phase(r[5,:],r[4,:]))**(2*q))
return '1111here'
#ss=phase_check()
#print('herehere')
#sys.exit()
return syst
def main():
start=datetime.now()
q=89;
nns,syst1,syst0 = make_system_step1(q)
# To highlight the two sublattices of graphene, we plot one with
# a filled, and the other one with an open circle:
def family_colors(site):
return 1 if site.family == a else 0
def hopping_colors(site1,site2):
return 1 if site1.tag-site2.tag==hoppings[1][0] else 0
# Plot the closed system without leads.
#kwant.plot(syst, site_color=family_colors, site_lw=0.1, hop_color=hopping_colors,colorbar=False)
#kwant.plot(syst, site_color=family_colors, site_lw=0.1,colorbar=False)
#fsyst = syst.finalized()
k1=0.1;k2=0.1;p=1;
#Num_p=len(Bfields);
Num_kpoints=50;
#from Gamma to K to Gamma
k1_list=list(np.linspace(0, 2/3*(2*pi), Num_kpoints))+list(np.linspace(2/3*(2*pi),(2*pi), Num_kpoints));
k1_list=list(reversed(k1_list));
k2_list=list(np.linspace(0, 1/3*(2*pi), Num_kpoints))+list(np.linspace(1/3*(2*pi),(2*pi), Num_kpoints));
k2_list=list(reversed(k2_list));
#from K to Gamma to M to K':
k1_list=list(np.linspace( -2/3*(2*pi),(2*pi), Num_kpoints))+list(np.linspace((2*pi),0, Num_kpoints))+list(np.linspace(0, 2/3*(2*pi), Num_kpoints));
k1_list=list(reversed(k1_list));
k2_list=list(np.linspace(-1/3*(2*pi),(2*pi), Num_kpoints))+list(np.linspace((2*pi),0, Num_kpoints))+list(np.linspace(0, 1/3*(2*pi), Num_kpoints));
k2_list=list(reversed(k2_list));
Num_kpoints=len(k1_list);
energies = []
Bfields=range(q)
for p in Bfields:
print(p);
#for nk in range(len(k2_list)):
# print(nk);k1=k1_list[nk];k2=k2_list[nk];
# print('k1=',k1,'k2=',k2,'p=',p,'q=',q)
syst=make_system_step2(k1,k2,syst1,syst0,nns,p,q)
fsyst = syst.finalized()
ham_mat = fsyst.hamiltonian_submatrix(args=[], sparse=False)
# energies_rho1,densities1 = kpm(ham_mat) #我的程序
# we only calculate the 15 lowest eigenvalues
#ev = sla.eigsh(ham_mat, k=2*q-2, which='SM', return_eigenvectors=False)
ev=LA.eigvalsh(ham_mat)
ev=sorted(ev)
energies.append(ev)
#以下三行，算 DOS， 不是 LDOS：
#rho = kwant.kpm.SpectralDensity(ham_mat,num_vectors=10,num_moments=800)
#rho.add_moments(energy_resolution=0.0001)
#energies_rho,densities = rho()
#break
m1=200;m2=100;
#np.savetxt(f,energies)
filename='Butterfly_q={0}-m1={1}-m2={2}.dat'.format(q,m1,m2);
#res = [x, y, z, ....]
csvfile = "/Users/jyj/Dropbox/A-Ningbo/graphene_Hafstder_butterfly/code/"+filename
with open(csvfile, "w") as output:
writer = csv.writer(output, lineterminator='\n')
writer.writerows(energies)
# pyplot.figure()
# pyplot.plot(energies_rho, densities,'*'); pyplot.xlabel("DOS from KPM]")
# pyplot.figure()
# pyplot.plot(energies_rho1, densities1.real,'*'); pyplot.xlabel("DOS from my KPM]")
# pyplot.show()
# sys.exit()
# file('data2','w').write('\n'.join(' '.join(repr(item)for item in
#row)for row in rows)+'\n')
#np.save(f,energies)
pyplot.figure()
pyplot.plot(Bfields, energies,'*'); pyplot.xlabel("magnetic field [arbitrary units]");pyplot.ylabel("energy [t]")
#
# pyplot.figure()
# pyplot.plot(energies_rho, densities,'*'); pyplot.xlabel("DOS from KPM]")
# pyplot.plot(kregion, energies,'*')
# pyplot.plot(range(len(k2_list)), np.array(energies),'-');pyplot.xlabel("from K to Gamma to M to K")
pyplot.show()
sys.exit()
#sys.exit()
# fsyst = syst.finalized()
print (datetime.now()-start)
start=datetime.now()
ham_mat = fsyst.hamiltonian_submatrix(args=[(k1,k2,p)], sparse=True)
rho = kwant.kpm.SpectralDensity(ham_mat,num_vectors=15,num_moments=8000)
#energies, densities = rho()
print (datetime.now()-start)
energies1, densities = rho.energies, rho.densities
energies= list(np.linspace(min(energies1),max(energies1),6*10**4))
rho.add_moments(energy_resolution=0.0001)
energies,densities = rho()
print('len_energy=',len(energies))
#indexes = detect_peaks(densities, mph=0.04, mpd=100)
#indexes = find_peaks_cwt(densities, np.arange(1, 550))
d_e=(energies[1]-energies[0])*10**4; d_max=max(densities);
def peak_position():
index=[]
for id in range(1,len(densities)-1):
if (densities[id]-densities[id+1]> d_e)&(densities[id]-densities[id-1]> d_e)&(densities[id]>d_max/50):
index.append(id)
return index
indexes=peak_position()
print(len(indexes),2*q)
pyplot.figure()
pyplot.plot(energies,densities)
pyplot.plot([energies[i1] for i1 in indexes],[densities[i2] for i2 in indexes],'r*')
#pyplot.ylim(-1.6,1.6)
#pyplot.show()
pyplot.xlabel("energy")
pyplot.ylabel("DOS[eV]")
# pyplot.title('band structure along z with'+' Wx=' + str(Width));
pyplot.show()
sys.exit()
# Call the main function if the script gets executed (as opposed to imported).
# See <http://docs.python.org/library/__main__.html>.
if __name__ == '__main__':
main()