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 a sisl.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 and eN)

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 argument atoms

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 or spin=unpolarized or the corresponding sisl.physics.Spin object

  • atoms (sisl.Atom or sisl.Atoms, optional) – Atoms for the geometry containing orbital information. It can be a sisl.Atoms instance containing different sisl.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:

sisl.physics.Hamiltonian