sp2
- hubbard.sp2(ext_geom, t1=2.7, t2=0.2, t3=0.18, eB=3.0, eN=-3.0, s1=0, s2=0, s3=0, dq=0, spin=<sisl.physics.Spin object>, atoms=None)[source]
Function to create a Tight Binding Hamiltoninan for sp2 Carbon systems
It takes advantage of the
sisl
class for building sparse Hamiltonian matrices,sisl.physics.Hamiltonian
It obtains the Hamiltonian for
ext_geom
(which must be asisl.Geometry
instance) with the parameters for first, second and third nearest neighbors (t1
,t2
,t3
).One can also use a non-orthogonal basis of atomic orbitals by passing the parameters for the overlap matrix between first, second and third nearest neighbors (
s1
,s2
,s3
).The function will also take into account the possible presence of Boron or Nitrogen atoms, for which one would need to specify the on-site energy for those atoms (
eB
andeN
)If no atoms are passed it will assign to each sp2 atom a pz hydrogen-like orbital (i.e.,
sisl.HydrogenicOrbital
with effective nuclear charge Zeff=3.2). This can be modified by the user with the argumentatoms
- Parameters
ext_geom (sisl.Geometry) – geometry of the sp2 carbon system
t1 (float, optional) – 1NN hopping defaults to 2.7 eV
t2 (float, optional) – 2NN hopping defaults to 0.2 eV
t3 (float, optional) – 3NN hopping defaults to 0.18 eV
eB (float, optional) – on-site energy for Boron atoms
eN (float, optional) – on-site energy for Nitrogen atoms
s1 (float, optional) – overlap between 1NN, default to zero (orthogonal basis)
s2 (float, optional) – overlap between 2NN, default to zero
s3 (float, optional) – overlap between 3NN, default to zero
dq (float, optional) – additional atomic charge, defaults to zero
spin (str or sisl.physics.Spin, optional) – to define a polarized or unpolarized system pass
spin=polarized
orspin=unpolarized
or the correspondingsisl.physics.Spin
objectatoms (sisl.Atom or sisl.Atoms, optional) – Atoms for the geometry containing orbital information. It can be a
sisl.Atoms
instance containing differentsisl.Atom
objects. In this case it should contain all atoms of the sp2 geometry (i.e. Z in [5,6,7])
- Returns
H – tight-binding Hamiltonian for the sp2 structure
- Return type