def berry(self):
# Calculate Berry phase around Dirac cones
K = -(4 * np.pi) / (3 * np.sqrt(3))
if self.Haldane.value() != 0:
Lat = lattice('Sheet', 'Haldane')
else:
Lat = lattice('Sheet', 'Monolayer')
H = Hamiltonian(Lat, self.Hoppingt2.value(), 0, 0, self.Haldane.value())
if self.Magneticfield2.value() != 0:
H.add_magnetic_field(self.Magneticfield2.value(), 'Perpendicular')
if self.OnsiteV2.value() != 0:
H.add_lattice_imbalance(self.OnsiteV2.value())
i = topology(H)
k1 = i.berry_curvature(np.array([-(4 * np.pi) / (3 * np.sqrt(3)), 0]))
k2 = i.berry_curvature(np.array([(4 * np.pi) / (6 * np.sqrt(3)), (4 * np.pi) / (3 * 2)]))
k3 = i.berry_curvature(np.array([(4 * np.pi) / (6 * np.sqrt(3)), -(4 * np.pi) / (3 * 2)]))
k4 = i.berry_curvature(np.array([(4 * np.pi) / (3 * np.sqrt(3)), 0]))
k5 = i.berry_curvature(np.array([-(4 * np.pi) / (6 * np.sqrt(3)), (4 * np.pi) / (3 * 2)]))
k6 = i.berry_curvature(np.array([-(4 * np.pi) / (6 * np.sqrt(3)), -(4 * np.pi) / (3 * 2)]))
G = i.berry_curvature(np.array([0, 0]))
msgBox = QtWidgets.QMessageBox()
s = "K-point: {:.4f} \n K'-point: {:.4f} \n Gamma-point: {:.4f}".format(k1, k4, G)
msgBox.setText("Berry phase")
msgBox.setInformativeText(s)
msgBox.exec_()
def locchernKprime(self):
# Calculate local chern number at K' valley from chosen lattice and Hamiltonian
K = -(4 * np.pi) / (3 * np.sqrt(3))
if self.Haldane.value() != 0:
Lat = lattice('Sheet', 'Haldane')
else:
Lat = lattice('Sheet', 'Monolayer')
H = Hamiltonian(Lat, self.Hoppingt2.value(), 0, 0, self.Haldane.value())
if self.Magneticfield2.value() != 0:
H.add_magnetic_field(self.Magneticfield2.value(), 'Perpendicular')
if self.OnsiteV2.value() != 0:
H.add_lattice_imbalance(self.OnsiteV2.value())
i = topology(H)
ch = i.chern_valley("K'", 0.01) # calculate chern number
s = "{:.4f}".format(ch)
msgBox = QtWidgets.QMessageBox()
msgBox.setText("Local Chern number:")
msgBox.setInformativeText(s)
msgBox.exec_()
def dos(self):
# Calculate density of states from chosen lattice and Hamiltonian
K = -(4 * np.pi) / (3 * np.sqrt(3))
if self.Haldane.value() != 0 or self.AntiHaldane.value() != 0:
Lat = lattice('Sheet', 'Haldane')
else:
Lat = lattice('Sheet', 'Monolayer')
if self.AntiHaldane.value() != 0:
H = Hamiltonian(Lat, self.Hoppingt2.value(), 0, 0, self.AntiHaldane.value())
H.add_antiHaldane()
else:
H = Hamiltonian(Lat, self.Hoppingt2.value(), 0, 0, self.Haldane.value())
if self.Magneticfield2.value() != 0:
H.add_magnetic_field(self.Magneticfield2.value(), 'Perpendicular')
if self.OnsiteV2.value() != 0:
H.add_lattice_imbalance(self.OnsiteV2.value())
H.build_Hamiltonian()
dos, ev = H.dos(self.numberofKop.value(), emin = -self.energy.value(), emax = self.energy.value(), kxmin=-np.pi, kxmax=np.pi, kymin=-np.pi, kymax=np.pi)
plt.plot(dos[1][:-1], dos[0])
plt.ylabel('Density of states')
plt.xlabel('Energy')
plt.show()
def plot_summary(self):
# Generate summary plot from chosen lattice and Hamiltonian
K = -(4 * np.pi) / (3 * np.sqrt(3))
if self.Haldane.value() != 0 or self.AntiHaldane.value() != 0:
Lat = lattice('Sheet', 'Haldane') # Get correct lattice
else:
Lat = lattice('Sheet', 'Monolayer')
if self.AntiHaldane.value() != 0:
H = Hamiltonian(Lat, self.Hoppingt2.value(), 0, 0, self.AntiHaldane.value())
H.add_antiHaldane() # If selected, add complex hopping
else:
H = Hamiltonian(Lat, self.Hoppingt2.value(), 0, 0, self.Haldane.value()) # If selected, add complex hopping
if self.Magneticfield2.value() != 0: # Add magnetic field
H.add_magnetic_field(self.Magneticfield2.value(), 'Perpendicular')
if self.OnsiteV2.value() != 0: # Add sublattice imbalance
H.add_lattice_imbalance(self.OnsiteV2.value())
# Generate summary plot
P = Plot(H)
P.summary(self.Nk.value(), K, 0, self.xIndex.value(), self.yIndex.value(), self.dxIndex.value(),
self.dyIndex.value())
plt.show()
def locchernKprime(self):
# Calculate local chern number in K' valley
K = -(4 * np.pi) / (3 * np.sqrt(3))
Lat = lattice('Sheet', self.SelectStack.currentText())
H = Hamiltonian(Lat, self.Hoppingt2.value(), self.Hoppingtprime2.value())
if self.Magneticfield2.value() != 0:
H.add_magnetic_field(self.Magneticfield2.value(), self.SelectBBil.currentText(), self.BAngle.value())
if self.OnsiteV_2.value() != 0:
H.add_sublattice_imbalance(self.OnsiteV_2.value())
i = topology(H)
ch = i.chern_valley("K'", 0.01)
s = "{:.4f}".format(ch)
#print("Local Chern number:", i.chern_valley("K'", 0.01))
msgBox = QtWidgets.QMessageBox()
msgBox.setText("Local Chern number:")
msgBox.setInformativeText(s)
msgBox.exec_()
def locchernKprime(self):
# Calculate local chern number at K' valley from chosen lattice and Hamiltonian
K = -(4 * np.pi) / (3 * np.sqrt(3))
Lat = lattice('Sheet', self.SelectStack.currentText()) # Create lattice
H = Hamiltonian(Lat, self.Hoppingt2.value(), self.Hoppingtprime2.value()) # Create Hamiltonian
if self.Magneticfield2.value() != 0: # Add magnetic field
H.add_magnetic_field(self.Magneticfield2.value(), self.SelectBBil.currentText(), self.BAngle.value())
if self.OnsiteV.value() != 0: # Add layer potentials
H.add_lattice_imbalance(self.OnsiteV.value())
if self.OnsiteV_2.value() != 0: # Add sublattice potentials
H.add_sublattice_imbalance(self.OnsiteV_2.value())
i = topology(H) # Create invariants object
ch = i.chern_valley("K'", 0.01) # Calculate chern number
s = "{:.4f}".format(ch)
msgBox = QtWidgets.QMessageBox()
msgBox.setText("Local Chern number:")
msgBox.setInformativeText(s)
msgBox.exec_()
def ldos(self):
# Calculate local density of states from chosen lattice and Hamiltonian
Lat = lattice(
'Ribbon',
self.SelectEdge.currentText() + ' ' +
self.SelectStack.currentText(), self.NUnit.value())
H = Hamiltonian(Lat, self.Hoppingt.value(), self.Hoppingtprime.value())
if self.Magneticfield.value() != 0:
H.add_magnetic_field(self.Magneticfield.value(),
self.SelectBBil.currentText())
if self.OnsiteV.value() != 0:
H.add_lattice_imbalance(self.OnsiteV.value())
H.build_Hamiltonian()
# calculate ldos
ldos = H.expec_operators(es=np.linspace(-self.energy.value(),
self.energy.value(), 100),
delta=self.delta.value(),
nk=self.numberofKop.value(),
op=None)
X, E = np.meshgrid(
np.arange(0, len(Lat.orb[:, 1]), 1),
np.linspace(-self.energy.value(), self.energy.value(), 100))
plt.contourf(X, E, ldos)
cbar = plt.colorbar()
cbar.set_label('Local density of states')
plt.ylabel('Energy')
plt.xlabel('Lattice sites')
plt.show()
def dos(self):
# Calculate density of states from chosen lattice and Hamiltonian
Lat = lattice('Ribbon',
self.SelectEdge.currentText() + ' ' +
self.SelectStack.currentText(),
self.NUnit.value()) # Generate lattice
H = Hamiltonian(Lat, self.Hoppingt.value(),
self.Hoppingtprime.value()) # Generate Hamiltonian
if self.Magneticfield.value() != 0: # Add magnetic field
H.add_magnetic_field(self.Magneticfield.value(),
self.SelectBBil.currentText())
if self.OnsiteV.value() != 0: # Add layer polarization
H.add_lattice_imbalance(self.OnsiteV.value())
H.build_Hamiltonian()
# calculate dos
dos, ev = H.dos(self.numberofKop.value(),
emin=-self.energy.value(),
emax=self.energy.value(),
kxmin=-np.pi,
kxmax=np.pi,
kymin=-np.pi,
kymax=np.pi)
plt.plot(dos[1][:-1], dos[0])
plt.ylabel('Density of states')
plt.xlabel('Energy')
plt.show()
def berry(self):
# calculate Berry phases
K = -(4 * np.pi) / (3 * np.sqrt(3))
Lat = lattice('Sheet', self.SelectStack.currentText())
H = Hamiltonian(Lat, self.Hoppingt2.value(), self.Hoppingtprime2.value())
if self.Magneticfield2.value() != 0:
H.add_magnetic_field(self.Magneticfield2.value(), self.SelectBBil.currentText(), self.BAngle.value())
if self.OnsiteV_2.value() != 0:
H.add_sublattice_imbalance(self.OnsiteV_2.value())
i = topology(H)
k1 = i.berry_curvature(np.array([-(4 * np.pi) / (3 * np.sqrt(3)), 0]))
k2 = i.berry_curvature(np.array([(4 * np.pi) / (6 * np.sqrt(3)), (4 * np.pi) / (3 * 2)]))
k3 = i.berry_curvature(np.array([(4 * np.pi) / (6 * np.sqrt(3)), -(4 * np.pi) / (3 * 2)]))
k4 = i.berry_curvature(np.array([(4 * np.pi) / (3 * np.sqrt(3)), 0]))
k5 = i.berry_curvature(np.array([-(4 * np.pi) / (6 * np.sqrt(3)), (4 * np.pi) / (3 * 2)]))
k6 = i.berry_curvature(np.array([-(4 * np.pi) / (6 * np.sqrt(3)), -(4 * np.pi) / (3 * 2)]))
G = i.berry_curvature(np.array([0, 0]))
msgBox = QtWidgets.QMessageBox()
s = "K-point: {:.4f} \n K'-point: {:.4f} \n Gamma-point: {:.4f}".format(k1, k4, G)
msgBox.setText("Berry phase")
msgBox.setInformativeText(s)
msgBox.exec_()
def upper_edge(self):
# Calculate bandstructure and highlight edge states
Lat = lattice('Ribbon', self.SelectEdge.currentText()+' '+self.SelectStack.currentText(), self.NUnit.value()) # Create lattice
H = Hamiltonian(Lat, self.Hoppingt.value(), self.Hoppingtprime.value())# Create Hamiltonian
if self.Magneticfield.value() != 0:# Add magnetic field
H.add_magnetic_field(self.Magneticfield.value(), self.SelectBBil.currentText())
if self.OnsiteV.value() != 0:# Add lattice imbalance
H.add_lattice_imbalance(self.OnsiteV.value())
P = Plot(H)
P.upper_edge()
def calc_bands(self):
# Calculate bandstructure of finite system
Lat = lattice('Ribbon', self.SelectEdge.currentText()+' '+self.SelectStack.currentText(), self.NUnit.value()) # Create lattice
H = Hamiltonian(Lat, self.Hoppingt.value(), self.Hoppingtprime.value())# Create Hamiltonian
if self.Magneticfield.value() != 0:# Add magnetic field
H.add_magnetic_field(self.Magneticfield.value(), self.SelectBBil.currentText())
if self.OnsiteV.value() != 0:# Add lattice imbalance
H.add_lattice_imbalance(self.OnsiteV.value())
P = Plot(H)
P.show_rib()
def plot_summary(self):
# Generate summary plot from chosen lattice and Hamiltonian
K = -(4 * np.pi) / (3 * np.sqrt(3))
Lat = lattice('Sheet', self.SelectStack.currentText()) # Create lattice
H = Hamiltonian(Lat, self.Hoppingt2.value(), self.Hoppingtprime2.value()) # Create Hamiltonian
if self.Magneticfield2.value() != 0: # Add magnetic field
H.add_magnetic_field(self.Magneticfield2.value(), self.SelectBBil.currentText(), self.BAngle.value())
if self.OnsiteV_2.value() != 0: # Add layer polarization
H.add_sublattice_imbalance(self.OnsiteV_2.value())
P = Plot(H)
P.summary(self.Nk.value(), K, 0, self.xIndex.value(), self.yIndex.value(), self.dxIndex.value(), self.dyIndex.value())
def calc_edge(self):
# Calculate bandstructure from chosen lattice and Hamiltonian with colormap highlighting edge states
Lat = lattice(
'Ribbon',
self.SelectEdge.currentText() + ' ' +
self.SelectStack.currentText(), self.NUnit.value())
H = Hamiltonian(Lat, self.Hoppingt.value(), self.Hoppingtprime.value())
if self.Magneticfield.value() != 0:
H.add_magnetic_field(self.Magneticfield.value(),
self.SelectBBil.currentText())
if self.OnsiteV.value() != 0:
H.add_lattice_imbalance(self.OnsiteV.value())
P = Plot(H)
P.calc_edge()
def berry(self):
# Calculate berry phase around valleys from chosen lattice and Hamiltonian
K = -(4 * np.pi) / (3 * np.sqrt(3))
Lat = lattice('Sheet', self.SelectStack.currentText()) # Create lattice
H = Hamiltonian(Lat, self.Hoppingt2.value(), self.Hoppingtprime2.value()) # Create Hamiltonian
if self.Magneticfield2.value() != 0: # Add magnetic field
H.add_magnetic_field(self.Magneticfield2.value(), self.SelectBBil.currentText(), self.BAngle.value())
if self.OnsiteV.value() != 0: # Add layer potentials
H.add_lattice_imbalance(self.OnsiteV.value())
if self.OnsiteV_2.value() != 0: # Add sublattice potentials
H.add_sublattice_imbalance(self.OnsiteV_2.value())
i = topology(H) # Create invariants object
def calc_edge(self):
# Calculate bandstructure from chosen lattice and Hamiltonian and highlight edge states
Lat = lattice('Ribbon', 'Twisted Bilayer', self.NUnit.value(),
self.TwistAngle.value())
H = Hamiltonian(Lat, self.Hoppingt.value())
if self.Magneticfield.value() != 0:
H.add_magnetic_field(self.Magneticfield.value(),
self.SelectBBil.currentText())
if self.OnsiteV.value() != 0:
H.add_lattice_imbalance(self.OnsiteV.value())
if self.OnsiteV_2.value() != 0:
H.add_sublattice_imbalance(self.OnsiteV_2.value())
P = Plot(H)
P.calc_edge()
def plot_summary(self):
# Generate summary plot of chosen lattice and Hamiltonian
K = -(4 * np.pi) / (3 * np.sqrt(3))
Lat = lattice('Sheet', 'Twisted Bilayer', 1, self.TwistAngle.value())
H = Hamiltonian(Lat, self.Hoppingt2.value())
if self.Magneticfield2.value() != 0:
H.add_magnetic_field(self.Magneticfield2.value(),
self.SelectBBil.currentText(),
self.BAngle.value())
if self.OnsiteV.value() != 0:
H.add_lattice_imbalance(self.OnsiteV.value())
if self.OnsiteV_2.value() != 0:
H.add_sublattice_imbalance(self.OnsiteV_2.value())
P = Plot(H)
P.summary(self.Nk.value(), K, 0, 17, 75, 75, 75)
def dos(self):
# Calculate density of states from chosen lattice and Hamiltonian
K = -(4 * np.pi) / (3 * np.sqrt(3))
Lat = lattice('Sheet', self.SelectStack.currentText()) # Create lattice
H = Hamiltonian(Lat, self.Hoppingt2.value(), self.Hoppingtprime2.value()) # Create Hamiltonian
if self.Magneticfield2.value() != 0: # Add magnetic field
H.add_magnetic_field(self.Magneticfield2.value(), self.SelectBBil.currentText(), self.BAngle.value())
if self.OnsiteV.value() != 0: # Add layer potentials
H.add_lattice_imbalance(self.OnsiteV.value())
if self.OnsiteV_2.value() != 0: # Add sublattice potentials
H.add_sublattice_imbalance(self.OnsiteV_2.value())
H.build_Hamiltonian()
dos, ev = H.dos(self.numberofKop.value(), emin=-self.energy.value(), emax=self.energy.value(), kxmin=-np.pi,
kxmax=np.pi, kymin=-np.pi, kymax=np.pi)
plt.plot(dos[1][:-1], dos[0])
plt.ylabel('Density of states')
plt.xlabel('Energy')
plt.show()
ax.plot(H.axis2[:, 0], E[x, :, 5])
ax.set_xlabel("$k_ya$")
ax.set_title('Plot along ky', fontsize=10)
ax.set_ylabel("$\epsilon_{k}$")
# List of parameters
alpha = 0
theta = 0
t7 = 1
# Get lattice
Lat = lattice('Sheet', 'Trilayer ABC')
# Get Hamiltonian
H = Hamiltonian(Lat, 3, 0.3)
H.build_Hamiltonian()
def run():
def update(ax1, ax2, ax3, ax4, val):
alpha = alpha_slider.val
theta = theta_slider.val
t7 = t7_slider.val
