"""Here we define some models, that can be used to test the code, or just to play around"""
import numpy as np
[docs]def Haldane_tbm(delta=0.2, hop1=-1.0, hop2=0.15, phi=np.pi / 2):
"""
Defines a Haldane model within `TBmodels <https://tbmodels.greschd.ch>`__
Parameters
-----------
delta : float
difference between the on-site potentials of the two atoms
t : float
nearest-neighbour hopping
hop2 : float
magnitude of next nearest-neighbour hopping
phi : float
phase of next nearest-neighbour hopping
Note:
--------
TBmodels should be installed to use this (`pip install tbmodels`)
"""
import tbmodels
t2 = hop2 * np.exp(1.j * phi)
t2c = t2.conjugate()
my_model = tbmodels.Model(
on_site=[delta, -delta],
uc=[[1.0, 0.0], [0.5, np.sqrt(3.0) / 2.0]],
dim=2,
occ=1,
pos=[[1. / 3., 1. / 3.], [2. / 3., 2. / 3.]])
my_model.add_hop(hop1, 0, 1, [0, 0])
my_model.add_hop(hop1, 1, 0, [1, 0])
my_model.add_hop(hop1, 1, 0, [0, 1])
my_model.add_hop(t2, 0, 0, [1, 0])
my_model.add_hop(t2, 1, 1, [1, -1])
my_model.add_hop(t2, 1, 1, [0, 1])
my_model.add_hop(t2c, 1, 1, [1, 0])
my_model.add_hop(t2c, 0, 0, [1, -1])
my_model.add_hop(t2c, 0, 0, [0, 1])
return my_model
[docs]def Haldane_ptb(delta=0.2, hop1=-1.0, hop2=0.15, phi=np.pi / 2):
"""same as :func:`~wannierberri.models.Haldane_tbm`, but uses `PythTB <http://www.physics.rutgers.edu/pythtb/>`__
Note:
--------
PythTB should be installed to use this (`pip install pythtb`)
"""
import pythtb
lat = [[1.0, 0.0], [0.5, np.sqrt(3.0) / 2.0]]
orb = [[1. / 3., 1. / 3.], [2. / 3., 2. / 3.]]
my_model = pythtb.tb_model(2, 2, lat, orb)
delta = 0.2
t2 = hop2 * np.exp(1.j * phi)
t2c = t2.conjugate()
my_model.set_onsite([-delta, delta])
my_model.set_hop(hop1, 0, 1, [0, 0])
my_model.set_hop(hop1, 1, 0, [1, 0])
my_model.set_hop(hop1, 1, 0, [0, 1])
my_model.set_hop(t2, 0, 0, [1, 0])
my_model.set_hop(t2, 1, 1, [1, -1])
my_model.set_hop(t2, 1, 1, [0, 1])
my_model.set_hop(t2c, 1, 1, [1, 0])
my_model.set_hop(t2c, 0, 0, [1, -1])
my_model.set_hop(t2c, 0, 0, [0, 1])
return my_model
[docs]def Chiral(delta=2, hop1=1, hop2=1 / 3, phi=np.pi / 10, hopz_right=0.0, hopz_left=0.2, hopz_vert=0.0):
"""Create a chiral model - a chirally stacked haldane model -
using `PythTB <http://www.physics.rutgers.edu/pythtb/>`__
Following the article by
`Yoda,Yokoyama & Murakami 2018 <https://doi.org/10.1021/acs.nanolett.7b04300>`__
this model breaks time-reversal and inversion, so it
can be used to test almost any quantity.
Has a symmetry C3z
Parameters
-----------
delta : float
difference between the on-site potentials of the two atoms
hop1 : float
nearest-neighbour in-plane hopping
hop2 : float
magnitude of next nearest-neighbour in-plane hopping
phi : float
phase of next nearest-neighbour in-plane hopping
hopz_vert : float or complex
interlayer vertical hopping
hopz_right : float or complex
chiral right-handed hopping in the z direction
hopz_left : float or complex
chiral left-handed hopping in the z direction
Note:
--------
PythTB should be installed to use this (`pip install pythtb`)
"""
import pythtb
lat = [[1.0, 0.0, 0.0], [0.5, np.sqrt(3.0) / 2.0, 0.0], [0.0, 0.0, 1.0]]
# define coordinates of orbitals
orb = [[1. / 3., 1. / 3., 0.0], [2. / 3., 2. / 3., 0.0]]
# make tree dimensional (stacked) tight-binding Haldene model
my_model = pythtb.tb_model(3, 3, lat, orb)
# set model parameters
t2 = hop2 * np.exp(1.j * phi)
# set on-site energies
my_model.set_onsite([-delta, delta])
# set hoppings (one for each connected pair of orbitals)
# from j in R to i in 0
# (amplitude, i, j, [lattice vector to cell containing j])
my_model.set_hop(hop1, 0, 1, [0, 0, 0])
my_model.set_hop(hop1, 1, 0, [1, 0, 0])
my_model.set_hop(hop1, 1, 0, [0, 1, 0])
# add second neighbour complex hoppings
my_model.set_hop(t2, 0, 0, [0, -1, 0])
my_model.set_hop(t2, 0, 0, [1, 0, 0])
my_model.set_hop(t2, 0, 0, [-1, 1, 0])
my_model.set_hop(t2, 1, 1, [-1, 0, 0])
my_model.set_hop(t2, 1, 1, [1, -1, 0])
my_model.set_hop(t2, 1, 1, [0, 1, 0])
# add vertical hoppings
my_model.set_hop(hopz_vert, 0, 0, [0, 0, 1])
my_model.set_hop(hopz_vert, 1, 1, [0, 0, 1])
# add chiral hoppings (left-handed)
my_model.set_hop(hopz_left, 0, 0, [0, -1, 1])
my_model.set_hop(hopz_left, 0, 0, [1, 0, 1])
my_model.set_hop(hopz_left, 0, 0, [-1, 1, 1])
my_model.set_hop(hopz_left, 1, 1, [-1, 0, 1])
my_model.set_hop(hopz_left, 1, 1, [1, -1, 1])
my_model.set_hop(hopz_left, 1, 1, [0, 1, 1])
# add chiral hoppings (right-handed)
my_model.set_hop(hopz_right, 0, 0, [0, -1, -1])
my_model.set_hop(hopz_right, 0, 0, [1, 0, -1])
my_model.set_hop(hopz_right, 0, 0, [-1, 1, -1])
my_model.set_hop(hopz_right, 1, 1, [-1, 0, -1])
my_model.set_hop(hopz_right, 1, 1, [1, -1, -1])
my_model.set_hop(hopz_right, 1, 1, [0, 1, -1])
return my_model
def CuMnAs_2d(
nx=0,
ny=1,
nz=0,
hop1=1,
hop2=0.08,
l=0.8,
J=0.6,
dt=0.0,
):
"""Create a 2D model of antiferromagnetic CuMnAs
using `PythTB <http://www.physics.rutgers.edu/pythtb/>`__
Following the article by
`Šmejkal, Železný, Sinova & Jungwirth 2017 <https://doi.org/10.1103/PhysRevLett.118.106402>`__
this model breaks time-reversal and inversion, but it
preserves the combination of both (P*T).
Parameters
-----------
nx : float
x-component of the Néel vector
ny : float
y-component of the Néel vector
nz : float
z-component of the Néel vector
hop1 : float
magnitude of nearest-neighbour hopping (A-A)
hop2 : float
magnitude of next nearest-neighbour hopping (A-B)
l : float
second nearest-neighbor spin-orbit coupling
J : float
magnitude of the Néel vector
dt : float
PT-breaking term making the A-A and B-B hoppings different
Note:
--------
PythTB should be installed to use this (`pip install pythtb`)
"""
import pythtb
# initialize the CuMnAs model
lat = [[1.0, 0.0], [0.0, 1.0]]
orb = [[0., 0.], [0., 0.], [0.5, 0.5], [0.5, 0.5]]
# Neel vector orientation
nabs = np.sqrt(nx**2 + ny**2 + nz**2)
nx = nx / nabs
ny = ny / nabs
nz = nz / nabs
my_model = pythtb.tb_model(2, 2, lat, orb)
# set hoppings (one for each connected pair of orbitals)
# (amplitude, i, j, [lattice vector to cell containing j])
# nearest-neighbor (A-B hopping)
my_model.set_hop(-0.5 * hop1, 0, 2, [0, 0])
my_model.set_hop(-0.5 * hop1, 0, 2, [-1, 0])
my_model.set_hop(-0.5 * hop1, 0, 2, [0, -1])
my_model.set_hop(-0.5 * hop1, 0, 2, [-1, -1])
my_model.set_hop(-0.5 * hop1, 1, 3, [0, 0])
my_model.set_hop(-0.5 * hop1, 1, 3, [-1, 0])
my_model.set_hop(-0.5 * hop1, 1, 3, [0, -1])
my_model.set_hop(-0.5 * hop1, 1, 3, [-1, -1])
# second nearest-neighbor (A-A hopping)
my_model.set_hop(-0.5 * hop2, 0, 0, [1, 0])
my_model.set_hop(-0.5 * hop2, 0, 0, [0, 1])
my_model.set_hop(-0.5 * hop2, 1, 1, [1, 0])
my_model.set_hop(-0.5 * hop2, 1, 1, [0, 1])
my_model.set_hop(-0.5 * hop2, 2, 2, [1, 0])
my_model.set_hop(-0.5 * hop2, 2, 2, [0, 1])
my_model.set_hop(-0.5 * hop2, 3, 3, [1, 0])
my_model.set_hop(-0.5 * hop2, 3, 3, [0, 1])
# second neighbor SOC
my_model.set_hop(-0.5 * l, 0, 1, [1, 0])
my_model.set_hop(0.5 * l, 0, 1, [-1, 0])
my_model.set_hop(0.5 * l * 1j, 0, 1, [0, 1])
my_model.set_hop(-0.5 * l * 1j, 0, 1, [0, -1])
my_model.set_hop(0.5 * l, 2, 3, [1, 0])
my_model.set_hop(-0.5 * l, 2, 3, [-1, 0])
my_model.set_hop(-0.5 * l * 1j, 2, 3, [0, 1])
my_model.set_hop(0.5 * l * 1j, 2, 3, [0, -1])
# AF exchange coupling
my_model.set_hop(J * (nx - 1j * ny), 0, 1, [0, 0])
my_model.set_hop(J * (-nx + 1j * ny), 2, 3, [0, 0])
# set on-site energies
my_model.set_onsite([J * nz, -J * nz, -J * nz, J * nz])
# break PT by making sublattices different
my_model.set_hop(-0.5 * dt, 0, 0, [1, 0], mode='add')
my_model.set_hop(-0.5 * dt, 0, 0, [0, 1], mode='add')
my_model.set_hop(-0.5 * dt, 1, 1, [1, 0], mode='add')
my_model.set_hop(-0.5 * dt, 1, 1, [0, 1], mode='add')
my_model.set_hop(0.5 * dt, 2, 2, [1, 0], mode='add')
my_model.set_hop(0.5 * dt, 2, 2, [0, 1], mode='add')
my_model.set_hop(0.5 * dt, 3, 3, [1, 0], mode='add')
my_model.set_hop(0.5 * dt, 3, 3, [0, 1], mode='add')
return my_model