def test_attach():
"""Attach 2 leads to a square lattice system"""
w, h = 2, 3
model = square_model(w, h)
model.attach_lead(-1, pb.line([0, -h / 2], [0, h / 2]))
model.attach_lead(+1, pb.line([0, -h / 2], [0, h / 2]))
assert len(model.leads) == 2
assert np.all(model.leads[0].indices == [0, 2, 4])
assert np.all(model.leads[1].indices == [1, 3, 5])
# Linear hopping grows from lead 0 to system to lead 1
model.add(linear_hopping())
assert model.leads[0].h1.data.max() < model.hamiltonian.data.min()
assert model.hamiltonian.data.max() < model.leads[1].h1.data.min()
# With the linear hopping modifier, the h1 hoppings should be equal to the
# x position between the lead and main system
x_mid_0 = (model.system.x.min() + model.leads[0].system.x.max()) / 2
assert np.allclose(model.leads[0].h1.data, x_mid_0)
x_mid_1 = (model.system.x.max() + model.leads[1].system.x.min()) / 2
assert np.allclose(model.leads[1].h1.data, x_mid_1)
# Linear onsite potential grows from lead 0 to system to lead 1
model.add(linear_onsite())
assert model.leads[0].h0.diagonal().max() < model.hamiltonian.diagonal(
).min()
assert model.hamiltonian.diagonal().max() < model.leads[1].h0.diagonal(
).min()
def test_line():
"""1D shape with 1D lattice"""
model = pb.Model(examples.chain_lattice(a=1), pb.line(0, 4.5))
assert model.system.num_sites == 4
model = pb.Model(examples.chain_lattice(a=1), pb.line([0, -0.5], [5, 0.5]))
assert model.system.num_sites == 6
def make_model(v0=0):
model = pb.Model(
graphene.monolayer().with_min_neighbors(1),
pb.rectangle(length, width),
potential_barrier(v0),
)
model.attach_lead(
-1, pb.line([-length / 2, -width / 2], [-length / 2, width / 2]))
model.attach_lead(
+1, pb.line([length / 2, -width / 2], [length / 2, width / 2]))
return model
def test_api(ring_model):
with pytest.raises(RuntimeError) as excinfo:
ring_model.attach_lead(0, pb.line(0, 0))
assert "Lead direction must be one of" in str(excinfo.value)
for direction in [3, -3]:
with pytest.raises(RuntimeError) as excinfo:
ring_model.attach_lead(direction, pb.line(0, 0))
assert "not valid for a 2D lattice" in str(excinfo.value)
with pytest.raises(RuntimeError) as excinfo:
pb.Model(examples.chain_lattice()).attach_lead(2, pb.line(0, 0))
assert "Attaching leads to 1D lattices is not supported" in str(
excinfo.value)
def pb_model(v=0, length=2, width=10):
def square_lattice(d, t):
lat = pb.Lattice(a1=[d, 0], a2=[0, d])
lat.add_sublattices(("A", [0, 0], 4 * t))
lat.add_hoppings(([0, 1], "A", "A", -t), ([1, 0], "A", "A", -t))
return lat
@pb.onsite_energy_modifier
def potential_well(energy, x):
energy[np.logical_and(x >= 0, x <= 1)] -= v
return energy
model = pb.Model(square_lattice(d=1, t=1), pb.rectangle(length, width),
potential_well)
model.attach_lead(-1, pb.line([0, -width / 2 - 0.1], [0, width / 2]))
model.attach_lead(+1, pb.line([0, -width / 2 - 0.1], [0, width / 2]))
return model
def test_empty(ring_model):
with pytest.raises(RuntimeError) as excinfo:
ring_model.attach_lead(2, pb.line(0, 0))
assert ring_model.system
assert "no sites in lead junction" in str(excinfo.value)
def test_complete_miss(ring_model):
with pytest.raises(RuntimeError) as excinfo:
ring_model.attach_lead(2, pb.line([4, -5], [5, -5]))
assert ring_model.system
assert "completely misses main structure" in str(excinfo.value)
def pb_model(v=0, length=2, width=10):
model = pb.Model(square_lattice(d=1, t=1),
pb.rectangle(x=length, y=width), potential_well(v))
model.attach_lead(-1, pb.line([0, -width / 2 - 0.1], [0, width / 2]))
model.attach_lead(+1, pb.line([0, -width / 2 - 0.1], [0, width / 2]))
return model
import matplotlib.pyplot as plt
pb.pltutils.use_style()
def simple_chain_lattice(a=1, t=-1):
"""Very simple 1D lattice"""
lat = pb.Lattice(a)
lat.add_one_sublattice('A', [0, 0])
lat.add_one_hopping(1, 'A', 'A', t)
return lat
model = pb.Model(
simple_chain_lattice(),
pb.line(-3.5, 3.5) # line start/end in nanometers
)
model.plot()
plt.show()
def trestle(a=0.2, t1=0.8 + 0.6j, t2=2):
"""A more complicated 1D lattice with 2 sublattices"""
lat = pb.Lattice(1.3 * a)
lat.add_sublattices(('A', [0, 0], 0), ('B', [a / 2, a], 0))
lat.add_hoppings((0, 'A', 'B', t1), (1, 'A', 'B', t1), (1, 'A', 'A', t2),
(1, 'B', 'B', t2))
lat.min_neighbors = 2
return lat