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Twisted_Bilayer_butterfly_plot.py
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Twisted_Bilayer_butterfly_plot.py
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#construct the Twisted graphene Bilayer model without magnetic field
#(REf: PHYSICAL REVIEW B 88, 125426 (2013):Periodic Landau gauge and quantum Hall effect in twisted bilayer graphene)
#3D model(with hoppings and magnetic field, Finite system, without kx,ky,etc)
from math import pi, sqrt, tanh, exp,acos,cos,sin
import csv
import sys
import tinyarray
import time
import os
import kwant
import cmath
# For computing eigenvalues
import scipy.sparse.linalg as sla
from numpy import linalg as LA
import numpy as np
# import matlab.engine
# For plotting
from matplotlib import pyplot as plt
from datetime import datetime
#lattice parameters:
t=2.7; #eV
t12=-0.48; #eV
delta_a=0.142; #nm: all intraplane distance are in unit of sqrt(3)*delta_a
d_0=0.335; #nm: all interplane distance are in unit of (delta_0)
delta_12=0.0453; #nm: interplane decay length
#delta_12=0.026128;
delta=delta_12; #nm: inplane decay length
#lattice of the supercells
(m1,m2)=(3,2);
# Define the graphene lattice
sin_30, cos_30 = (1 / 2, sqrt(3) / 2)
Base_a1=(cos_30, -sin_30,0); Base_a2=(cos_30,sin_30,0);
A_position=(0, 0,0)
B_position=(1 / sqrt(3),0,0)
L1=m1*np.matrix(Base_a1)+m2*np.matrix(Base_a2);
L1_prime=m2*np.matrix(Base_a1)+m1*np.matrix(Base_a2);
alpha=acos((m1**2+4*m1*m2+m2**2)/(2*(m1**2+m1*m2+m2**2)));
M_Rotation=[[cos(pi/3-alpha),-sin(pi/3-alpha),0],[sin(pi/3-alpha),cos(pi/3-alpha),0],[0,0,1]];
#M_Rotation=[[cos(-alpha),-sin(-alpha),0],[sin(-alpha),cos(-alpha),0],[0,0,1]];
M_Rotation3=[[cos(pi/3),-sin(pi/3),0],[sin(pi/3),cos(pi/3),0],[0,0,1]];
a1p=np.transpose(np.matrix(M_Rotation)*np.transpose(np.matrix(Base_a1)));
a1p=a1p.tolist();a1p[0][2]=0;
a1p=tuple(a1p[0]);
a2p=np.transpose(np.matrix(M_Rotation)*np.transpose(np.matrix(Base_a2)));
a2p=a2p.tolist();a2p[0][2]=0;
a2p=tuple(a2p[0]);
L2=np.transpose(np.matrix(M_Rotation3)*np.transpose(L1));
L2=L2.tolist();L2=tuple(L2[0]);
L2_prime=np.transpose(np.matrix(M_Rotation3)*np.transpose(L1_prime));
L2_prime=L2_prime.tolist();L2_prime=tuple(L2_prime[0]);
L1=L1.tolist();L1=tuple(L1[0]);
L1_prime=L1_prime.tolist();L1_prime=tuple(L1_prime[0]);
A_Prime_position=np.transpose(np.matrix(M_Rotation)*np.transpose(np.matrix(A_position)));
A_Prime_position=A_Prime_position.tolist();A_Prime_position[0][2]=1;
#print(A_Prime_position)
A_Prime_position=tuple(A_Prime_position[0]);
B_Prime_position=np.transpose(np.matrix(M_Rotation)*np.transpose(np.matrix(B_position)));
B_Prime_position=B_Prime_position.tolist();B_Prime_position[0][2]=1;
B_Prime_position=tuple(B_Prime_position[0]);
graphene = kwant.lattice.general([Base_a1, Base_a2],
[A_position, B_position])
a, b = graphene.sublattices
graphene1 = kwant.lattice.general([a1p, a2p],
[A_Prime_position, B_Prime_position])
a1, b1 = graphene1.sublattices
supercell=kwant.lattice.general([L1, L2],[A_position])
c=supercell.sublattices[0]
eta=10**-12;
s1x=(np.sqrt(3)*m1+2*np.sqrt(3)*m2)/(3*(m1**2 + m1* m2 + m2**2));
s1y=(- 3*m1)/(3*(m1**2 + m1* m2 + m2**2));
s2x=(np.sqrt(3)*m1- np.sqrt(3)* m2)/(3* (m1**2 + m1*m2 + m2**2));
s2y=(3*m1+3*m2)/(3* (m1**2 + m1*m2 + m2**2));
f1=sqrt(3)*delta_a;
f2=d_0;
SC1=1;
SC2=1;
def make_system_step1(q=3):
#def pause():
# programPause = raw_input("Press the <ENTER> key to continue...")
print(Base_a1)
print(Base_a2)
print(a1p)
print(a2p)
print(L1)
print(L2)
print(A_Prime_position)
print(B_Prime_position)
#sys.exit()
#soa1=np.array([list((0,0)+Base_a1[0:2]),list((0,0)+Base_a2[0:2])])
soa1=np.array([list((0,0)+a1p[0:2]),list((0,0)+a2p[0:2])])
#soa1=np.array([list((0,0)+L1[0:2]),list((0,0)+L2[0:2])])
#soa1=np.array([list((0,0)+L1[0:2]),list((0,0)+L2[0:2]),list((0,0)+L1_prime[0:2]),list((0,0)+L2_prime[0:2])])
#X, Y, U, V = zip(*soa1)
#plt.figure()
#ax = plt.gca()
#ax.quiver(X, Y, U, V, angles='xy', scale_units='xy', scale=1)
#ax.set_xlim([-2, 4])
#ax.set_ylim([-2, 4])
#plt.draw()
#plt.show()
#print(a)
#print(c)
syst = kwant.Builder()
#eta=10**-12;
sc1L=0-eta;sc1R=1-eta; #boundaries along L1 direction
sc2L=0-eta;sc2R=q-eta; #boundaries along L2 direction
SC1=(sc1R+eta)*tinyarray.array(L1);
SC2=(sc2R+eta)*tinyarray.array(L2); #the magnetic unite cell
start=datetime.now()
s1x=(np.sqrt(3)*m1+2*np.sqrt(3)*m2)/(3*(m1**2 + m1* m2 + m2**2));
s1y=(- 3*m1)/(3*(m1**2 + m1* m2 + m2**2));
s2x=(np.sqrt(3)*m1- np.sqrt(3)* m2)/(3* (m1**2 + m1*m2 + m2**2));
s2y=(3*m1+3*m2)/(3* (m1**2 + m1*m2 + m2**2));
for n1 in range(-200,200):
for n2 in range(-200,200):
xR,yR,zR=a(n1,n2).pos;
ss1=s1x*xR+s1y*yR;
ss2=s2x*xR+s2y*yR;
if ((sc1L<=ss1<sc1R)&(sc2L<=ss2<sc2R)):
syst[a(n1,n2)]=0
xR,yR,zR=b(n1,n2).pos
ss1=s1x*xR+s1y*yR;
ss2=s2x*xR+s2y*yR;
if ((sc1L<=ss1<sc1R)&(sc2L<=ss2<sc2R)):
syst[b(n1,n2)]=0
xR,yR,zR=a1(n1,n2).pos
ss1=s1x*xR+s1y*yR;
ss2=s2x*xR+s2y*yR;
if ((sc1L<=ss1<sc1R)&(sc2L<=ss2<sc2R)):
syst[a1(n1,n2)]=0
xR,yR,zR=b1(n1,n2).pos
ss1=s1x*xR+s1y*yR;
ss2=s2x*xR+s2y*yR;
if ((sc1L<=ss1<sc1R)&(sc2L<=ss2<sc2R)):
syst[b1(n1,n2)]=0
#xR,yR,zR=c(n1,n2).pos
#if ((sc1L<=(sqrt(3)*m1*xR+2*sqrt(3)*m2*xR - 3*m1*yR)/(3*(m1**2 + m1* m2 + m2**2))<sc1R)&(sc2L<=(sqrt(3)*m1*xR - sqrt(3)* m2*xR + 3* m1* yR +3* m2* yR)/(3* (m1**2 + m1*m2 + m2**2))<sc2R)):
# syst[c(n1,n2)]=0
print('onsite construction finish:')
start=datetime.now()
# print (datetime.now()-start)
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;
xi,yi,zi=ri; ri=np.array([xi*f1,yi*f1,zi*f2]);
for nj in range(N_ToT):
rj=syst0.sites[nj].pos;
xj,yj,zj=rj; rj=np.array([xj*f1,yj*f1,zj*f2]);
for n1 in range(-2,3):
for n2 in range(-2,3):
rjn=rj+(n1*SC1+n2*SC2)*f1;
ss=ri-rjn;
dis=sqrt(np.dot(ss,ss))
if (dis<5*delta_a):
if not((n1==0)&(n2==0)&(nj==ni)):
nns[ni].append((nj,n1,n2))
return nns
nns=neighbors();
return nns,syst,syst0,SC1,SC2
def make_system_step2(p,k1,k2,syst,syst0,nns,SC1,SC2,q):
N_ToT=syst0.graph.num_nodes
start=datetime.now()
def amp(ri,rj):
xi,yi,zi=ri; ri=[xi*f1,yi*f1,zi*f2];
xj,yj,zj=rj; rj=[xj*f1,yj*f1,zj*f2];
ss=np.array(ri)-np.array(rj);
dis=sqrt(np.dot(ss,ss))
#print('dis=',dis,'delta_a=',delta_a,'delta=',delta)
if abs(zi-zj)<10**-8:
dis1=dis-delta_a;
dis1=dis1/delta;
hop_t=t*np.exp(-dis1);
else:
dis2=dis-d_0;
dis2=dis2/delta;
hop_t=t12*np.exp(-dis2);
#print('hop_t=',hop_t)
#monolayer: the usual nearest hopping model:#
#hop_t=0;
if abs(zi-zj)<10**-8:
hop_t=0;
if abs(dis-delta_a)<=10**-6:
hop_t=t;
return -hop_t
def phase(ri,rj):
ss=abs(ri-rj);
if (ss[0]+ss[1])<=10**-8:
return 1
xR,yR,zi=ri;
#ss1_i=s1x*xR+s1y*yR+2*eta;
#ss2_i=s2x*xR+s2y*yR
ss1_i=(sqrt(3)*m1*xR+2*sqrt(3)*m2*xR - 3*m1*yR)/(3*(m1**2 + m1* m2 + m2**2)) +0.33*eta;
ss2_i=(sqrt(3)*m1*xR - sqrt(3)* m2*xR + 3* m1* yR +3* m2* yR)/(3* (m1**2 + m1*m2 + m2**2));
xR,yR,zj=rj;
ss1_j=(sqrt(3)*m1*xR+2*sqrt(3)*m2*xR - 3*m1*yR)/(3*(m1**2 + m1* m2 + m2**2)) +0.3003*eta ;
ss2_j=(sqrt(3)*m1*xR - sqrt(3)* m2*xR + 3* m1* yR +3* m2* yR)/(3* (m1**2 + m1*m2 + m2**2));
#ss1_j=s1x*xR+s1y*yR+2*eta;
#ss2_j=s2x*xR+s2y*yR;
#ss=(ss1_i+ ss1_j )/2;
#phase1=(ss- np.floor(ss))*(ss2_j - ss2_i);
#theta integrated from j to i:
phase2=0;
#print('ssi=',ss1_i,ss2_i)
#print('ssi=',ss1_j,ss2_j)
#print('np.floor(ss1_i)=',np.floor(ss1_i))
#print('np.floor(ss1_j)=',np.floor(ss1_j))
mn1=0;
if abs(np.floor(ss1_i)-np.floor(ss1_j))==1:
mn1=max(np.floor(ss1_i),np.floor(ss1_j))
ss = (mn1-ss1_j)/(ss1_i - ss1_j); #r(ss)=ss*r_i+(1-ss)*r_j;
phase2 = -(ss*ss2_i + (1 - ss)*ss2_j)*np.sign(ss1_i-ss1_j);
phase1= -(ss2_i-ss2_j)*(np.floor(ss1_j)*(mn1-ss1_j)/(ss1_i-ss1_j) +np.floor(ss1_i)*(ss1_i-mn1)/(ss1_i-ss1_j)) + (ss1_i+ss1_j)/2*(ss2_i-ss2_j);
#print('mn1=',mn1,'ss=',ss,'ss2_i=',ss2_i,'ss2_j=',ss2_j,'phase2=',phase2)
phase1=np.exp(2*pi*1j*phase1*p/q )
phase2=np.exp(2*pi*1j*phase2*p/q )
return phase2*phase1
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([0,0,0]);
r0=(2*aa2-aa1)/3;
r=np.zeros((6,3))
# 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+SC1,rj+SC1))
print(phase(ri+6*tinyarray.array(L2),rj+6*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+SC1,rj+SC1))
print(phase(ri+6*tinyarray.array(L2),rj+6*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,:]))**q)
return '1111here'
# ss=phase_check()
# print('herehere')
# sys.exit()
#
# def Given_link_ijs(family_i,tag_i,family_j,tag_j):
# print(family_i,family_j)
# print(tag_i,tag_j)
# for ni in range(N_ToT):
# if (syst0.sites[ni].family==family_i)&(syst0.sites[ni].tag==tag_i):
# n_i=ni;
#
# break
# for nj in range(N_ToT):
# if (syst0.sites[nj].family==family_j)&(syst0.sites[nj].tag==tag_j):
# n_j=nj;
# break
# return n_i,n_j
#
#
#
# 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;
#
#
# # ri=tinyarray.array([0,0,1]); rj=tinyarray.array([3.1,0.1,1]);
# p=1;
# print('q=',q)
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;
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 set_hoppings1(ri,rj):
# 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 n1 in range(-2,3):
for n2 in range(-2,3):
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(-5,6):
# for n2 in range(-5,6):
# 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,p);
return non_diag_term
def on_site_term(ri):
# k1,k2,p=k_and_p
#print('on_site k1=',k1)
#ri=site.pos;
diag_term=0;
for n1 in range(-1,2):
for n2 in range(-1,2):
rjn=ri+n1*SC1+n2*SC2;
if not((n1==0)and(n2==0)):
diag_term=diag_term+np.exp(1j*(n1*k1+n2*k2))*amp(ri,rjn) *phase(ri,rjn);
#sys.exit()
return diag_term
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()
#
# for ni in range(1,N_ToT):
# #print('ni=',ni);
# ri=syst0.sites[ni].pos;
# for nj in range(ni):
# rj=syst0.sites[nj].pos;
# syst[syst0.sites[ni],syst0.sites[nj]]=set_hoppings(ri,rj);
# #syst[syst0.sites[ni],syst0.sites[nn_i[nj]]]=t*(1+np.exp(-1j*k2)+np.exp(-1j*k1))
# #sys.exit()
for ni in range(0,N_ToT):
ri=syst0.sites[ni].pos;
syst[syst0.sites[ni]]=on_site_term(ri);
def amp1(ri,rj):
xi,yi,zi=ri; ri=[xi*f1,yi*f1,zi*f2];
xj,yj,zj=rj; rj=[xj*f1,yj*f1,zj*f2];
ss=np.array(ri)-np.array(rj);
dis=sqrt(np.dot(ss,ss))
dis1=dis-delta_a;
dis1=dis1/delta;
Vpp_pi=t*np.exp(-dis1);
dis2=dis-d_0;
dis2=dis2/delta;
Vpp_sigma=t12*np.exp(-dis2);
hop_t=Vpp_pi*(1-(ss[2]/dis)**2)+Vpp_sigma*(ss[2]/dis)**2
# hop_t=0;
# if (abs(dis-delta_a)<10**-5):
# hop_t=t;
# if (abs(dis-d_0)<10**-5):
# hop_t=t12
return -hop_t
#print('system finish::')
#print (datetime.now()-start)
# syst0=syst.finalized()
#N_ToT=syst0.graph.num_nodes;
# def Given_link_ijs(family_i,tag_i,family_j,tag_j):
# print(family_i,family_j)
# print(tag_i,tag_j)
# for ni in range(N_ToT):
# if (syst0.sites[ni].family==family_i)&(syst0.sites[ni].tag==tag_i):
# n_i=ni;
#
# break
# for nj in range(N_ToT):
# if (syst0.sites[nj].family==family_j)&(syst0.sites[nj].tag==tag_j):
# n_j=nj;
# break
# return n_i,n_j
#
#
#n_i,n_j=Given_link_ijs(a,tinyarray.array([0,0]),b,tinyarray.array([0,0]))
# print('k1=',k1,'k2=',k2)
#print('n_i=,n_j=',n_i,n_j)
#sys.exit()
#sys.exit()
#print('ddddd1111111')
return syst
def main():
start=datetime.now()
q=17; #if no manetic field, set q=1;
print(alpha/pi*180)
#syst, hoppings = make_system(q)
nns,syst1,syst0,SC1,SC2 = 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 'g' if site.family in (a,b) else 'm'
k1=0.1;k2=0.1;p=5;
Bfields=range(0,q*(m1*m2+m1**2+m2**2),10);
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 = [];
energies_kpm = [];
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)
# Obtain the Hamiltonian as a dense matrix
# ham_mat = syst.hamiltonian_submatrix(args=[p], sparse=True)
k_and_p=(k1,k2,p)
#syst = make_system(k1,k2,q)
syst=make_system_step2(p,k1,k2,syst1,syst0,nns,SC1,SC2,q);
#print('ddddddddddd')
#print(syst[a(0,0),b(0,0)])
syst=syst.finalized()
# print('eeeeeeeeeee')
# print(syst.sites[0].tag,syst.sites[1].tag,syst.sites[2].tag,syst.sites[3].tag)
# print(syst.sites[0].family,syst.sites[1].family,syst.sites[2].family,syst.sites[3].family)
# print(syst.sites[0].pos,syst.sites[1].pos,syst.sites[2].pos,syst.sites[3].pos)
#
ham_mat= syst.hamiltonian_submatrix(args=[], sparse=False)
# print(ham_mat)
# print('----------------------')
# print(syst.hamiltonian_submatrix(args=[],to_sites=(0,2),from_sites=(0,2)))
# print('----------------------')
# print(syst.hamiltonian_submatrix(args=[],to_sites=(1,3),from_sites=(1,3)))
# sys.exit()
#
# we only calculate the 15 lowest eigenvalues
#ev = sla.eigsh(ham_mat, k=4*q*(m1*m2+m1**2+m2**2)-10, which='SM', return_eigenvectors=False)
#print(ham_mat.shape)
ev=LA.eigvalsh(ham_mat)
ev=sorted(ev)
energies.append(ev)
#print(ev)
# rho = kwant.kpm.SpectralDensity(ham_mat,num_vectors=10,num_moments=800)
# rho.add_moments(energy_resolution=0.0001)
# energies_rho,densities = rho()
#
# d_max=max(densities);
# def peak_position():
# index=[]
# for id in range(1,len(densities)-1):
# if (densities[id]>densities[id+1])&(densities[id]>densities[id-1])&(densities[id]>d_max/50):
# index.append(id)
# return index
#
# indexes=peak_position()
# energies_kpm.append([energies_rho[i1] for i1 in indexes]);
# print('nk_kpm=',nk)
#print(np.array(energies).reshape(Num_kpoints,4*q*(m1*m2+m1**2+m2**2)))
filename='Butterfly_Bilayer_with_B_q={0}-m1={1}-m2={2}AB.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)
# filename1='Butterfly_Bilayer_no_B_q={0}-m1={1}-m2={2}_kpm.dat'.format(q,m1,m2);
# csvfile1 = "/Users/jyj/Dropbox/A-Ningbo/graphene_Hafstder_butterfly/code/"+filename1
# with open(csvfile1, "w") as output:
# writer = csv.writer(output, lineterminator='\n')
# writer.writerows(energies_kpm)
plt.figure()
plt.plot(Bfields, energies,'-');plt.xlabel("magnetic field [arbitrary units]")
# plt.plot(k1_list, energies,'*')
#plt.plot(range(len(k2_list)), np.array(energies),'-');plt.xlabel("from K to Gamma to M to K")
#plt.plot(range(Num_p), np.array(energies),'-')
plt.ylabel("energy ")
plt.show()
sys.exit()
# fsyst = syst.finalized()
print (datetime.now()-start)
start=datetime.now()
rho = kwant.kpm.SpectralDensity(fsyst)
energies, densities = rho()
print (datetime.now()-start)
energies, densities = rho.energies, rho.densities
plt.figure()
plt.plot(energies,densities )
#pyplot.ylim(-1.6,1.6)
plt.xlabel("energy")
plt.ylabel("DOS[eV]")
# pyplot.title('band structure along z with'+' Wx=' + str(Width));
plt.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()