Graphene¶
Lattices¶
-
monolayer
(nearest_neighbors=1, onsite=(0, 0), **kwargs)¶ Monolayer graphene lattice up to
nearest_neighbors
hoppingsParameters: nearest_neighbors : int
Number of nearest neighbors to consider.
onsite : Tuple[float, float]
Onsite energy for sublattices A and B.
**kwargs
Specify the hopping parameters
t
,t_nn
andt_nnn
. If not given, the default values fromgraphene.constants
will be used.
-
monolayer_4atom
(onsite=(0, 0))¶ Nearest-neighbor with 4 atoms per unit cell: square lattice instead of oblique
Parameters: onsite : Tuple[float, float]
Onsite energy for sublattices A and B.
-
bilayer
(gamma3=False, gamma4=False, onsite=(0, 0, 0, 0))¶ Bilayer lattice in the AB-stacked form (Bernal-stacked)
- \(\gamma_0\) is the single-layer hopping within the top layer (A1/B1) and bottom layer (A2/B2)
- \(\gamma_1\) is the inter-layer hopping between B1 and A2 (where atom B1 lies directly over A2)
- Hoppings \(\gamma_3\) and \(\gamma_4\) are optional (see parameters)
Parameters: gamma3, gamma4 : bool
Enable \(\gamma_3\) and/or \(\gamma_4\) hoppings. By default, only \(\gamma_0\) and \(\gamma_1\) are active.
onsite : Tuple[float, float, float, float]
Onsite energy for A1, B1, A2, B2
Constants¶
-
a
= 0.24595¶ [nm] unit cell length
-
a_cc
= 0.142¶ [nm] carbon-carbon distance
-
beta
= 3.37¶ strain hopping modulation
-
t
= -2.8¶ [eV] nearest neighbor hopping
-
t_nn
= 0.1¶ [eV] next-nearest neighbor hopping
-
vf
= 906091185689731.9¶ [nm/s] Fermi velocity
Shapes¶
-
hexagon_ac
(side_width, lattice_offset=(-0.122975, 0))¶ A graphene-specific shape which guaranties armchair edges on all sides
Parameters: side_width : float
Hexagon side width. It may be adjusted slightly to ensure armchair edges.
lattice_offset : array_like
Offset the lattice so a carbon hexagon is at the center of the shape. The default value is specific for
monolayer()
andbilayer()
lattices from this material repository.
Modifiers¶
-
mass_term
(delta)¶ Break sublattice symmetry, make massive Dirac electrons, open a band gap
Only for monolayer graphene.
Parameters: delta : float
Onsite energy +delta is added to sublattice ‘A’ and -delta to ‘B’.
-
coulomb_potential
(beta, cutoff_radius=0.0, offset=(0, 0, 0))¶ A Coulomb potential created by an impurity in graphene
Parameters: beta : float
Charge of the impurity [unitless].
cutoff_radius : float
Cut off the potential below this radius [nm].
offset: array_like
Position of the charge.
-
constant_magnetic_field
(magnitude)¶ Constant magnetic field in the z-direction, perpendicular to the graphene plane
Parameters: magnitude : float
In units of Tesla.
-
triaxial_strain
(magnetic_field)¶ Triaxial strain corresponding to a homogeneous pseudo-magnetic field
Parameters: magnetic_field : float
Intensity of the pseudo-magnetic field to induce.
-
gaussian_bump
(height, sigma, center=(0, 0))¶ Gaussian bump deformation
Parameters: height : float
Height of the bump [nm].
sigma : float
Gaussian sigma parameter: controls the width of the bump [nm].
center : array_like
Position of the center of the bump.