def single_honeycomb(self, initbond=array([1., 0])):
a = initbond
r = rotate(pi / 3)
b = zeros([6, 2])
b[0] = a
for i in xrange(1, 6):
b[i] = r.dot(b[i - 1])
# b = b - a
return b
def plot_lattice(self, magic_angle, color='black'):
scalex, scaley = 10, 10
a, b = self.alpha[:2], self.betha[:2]
bond0 = self.single_honeycomb()
r = rotate(magic_angle)
for i in xrange(-scalex, scalex + 1):
opointx = i * a
for j in xrange(-scaley, scaley + 1):
opointy = j * b
opoint = opointx + opointy
# bond = opoint + bond0
bond = (opoint + bond0).T
bond = (r.dot(bond)).T
self.plot_single_honeycomb(bond, color)
def get_tba(self, k):
alpha = self.alpha
betha = self.betha
mu, t1 = self.mu, self.t1
angle = 2 * pi / 3
alpha = alpha[:-1]
betha = betha[:-1]
delta1 = (alpha + betha) / 3
delta2 = rotate(angle).dot(delta1)
delta3 = -delta1 - delta2
#print delta1,delta2,delta3
phi1 = k.dot(delta1)
phi2 = k.dot(delta2)
phi3 = k.dot(delta3)
xk = -t1 * (cos(phi1) + cos(phi2) + cos(phi3))
yk = -t1 * (sin(phi1) + sin(phi2) + sin(phi3))
#pdb.set_trace()
hk = general_kron(xk, sigma1)
hk = hk - general_kron(yk, sigma2)
hk += -mu * sigma0
return hk
def get_TBG_model(self, kmesh, t2, tt1, tt2):
hk = self.get_tba(kmesh)
bondnnn = zeros([6, 2])
bondnnn[0] = array([0, sqrt(3)])
r_nnn = rotate(pi / 3)
for i in xrange(1, 6):
bondnnn[i] = r_nnn.dot(bondnnn[i - 1])
bondnn = zeros([3, 2])
bondnn[0] = (self.alpha + self.betha)[:-1] / 3
r_nn = rotate(2 * pi / 3)
for i in xrange(1, 3):
bondnn[i] = r_nn.dot(bondnn[i - 1])
isigma2 = 1j * sigma2
sigmap = (sigma1 + isigma2) / 2.
sigmam = sigmap.T.conj()
warp_nnn = 0.
fsign = array([1, -1, 1, -1, 1, -1.])
for i in xrange(6):
phi = kmesh.dot(bondnnn[i])
warp_nnn = warp_nnn + general_kron(exp(1j * phi),
sigma0) * fsign[i]
warp_nnn = warp_nnn * tt2
# fsign = fsign*1j; hop_nnn = 0.
# for i in xrange(6):
# phi = kmesh.dot(bondnnn[i])
# hop_nnn = hop_nnn + general_kron(exp(1j*phi),sigma0)*fsign[i]
# hop_nnn *= tt1
bondnnn = zeros([6, 2])
bondnnn[0] = array([1., 0])
for i in xrange(1, 6):
bondnnn[i] = r_nnn.dot(bondnnn[i - 1])
hop = 0.
for i in xrange(6):
phi = kmesh.dot(bondnnn[i])
hop = hop + general_kron(exp(1j * phi), sigma0)
hop *= t2
hop_nn = 0.
for i in xrange(3):
bond = bondnn[i] * sqrt(3)
xx = bond[0]**2
yy = bond[1]**2
xy = bond[0] * bond[1]
sigma_orbital = array([[xx - yy, 2 * xy], [2 * xy, yy - xx]])
phi = kmesh.dot(bondnn[i])
hop_xy = general_kron(cos(phi), sigma1) - general_kron(
sin(phi), sigma2)
hop_nn = hop_nn + kron(sigma_orbital, hop_xy)
hop_nn *= tt1
Hk = 0.
Hk = Hk + kron(sigma0, hk)
Hk = Hk + kron(isigma2, warp_nnn)
Hk = Hk + kron(sigma0, hop)
# Hk = Hk + kron(sigma0,hop_nnn)
Hk = Hk + hop_nn
# pdb.set_trace()
return Hk
mu = -0
t2 = 0.15
tt1 = 0.
tt2 = -0.02
gph = graphen(mu, Nx, Ny)
# plt.subplot(122)
# plt.subplot(122)
# gph.get_dos(t2,tt1,tt2)
alpha = gph.alpha
betha = gph.betha
kalpha, kbetha = gph.get_kvector(alpha, betha, Nx, Ny)
kalpha *= Nx
kbetha *= Ny
Kpoint = gph.get_Kpoint(kalpha, kbetha)
Mpoint = gph.get_Mpoint(kalpha, kbetha)
Kp_point = rotate(pi / 3).dot(Kpoint)
GKMG = gph.generate_loop(Kpoint, Mpoint, Kp_point)
Hk = gph.get_TBG_model(GKMG, t2, tt1, tt2)
Ek, Uk = linalg.eigh(Hk)
plt.subplot(121)
plt.plot([0, Ek.shape[0]], [-1.29, -1.29], linestyle='--', color='black')
# plt.plot([0,Ek.shape[0]],[-1.8,-1.8],linestyle = '--',color = 'black')
# plt.plot([0,Ek.shape[0]],[-1.65,-1.65],linestyle = '--',color = 'black')
# plt.plot([0,Ek.shape[0]],[1.4,1.4],linestyle = '--',color = 'black')
# plt.plot([0,Ek.shape[0]],[1.6,1.6],linestyle = '--',color = 'black')
plt.plot(arange(Ek.shape[0]), Ek, linewidth=1.5)
plt.yticks(size=16)
plt.xticks([0, 500, 750, 750 + 250 * sqrt(3)],
['$\Gamma$', 'K', 'M', '$\Gamma$'],
size=16)
plt.ylabel('$\epsilon_k$', size=32)