This section describes the input files as necessary for the tight-binding part of the code.

Hamiltonian setup

The main property of the tight-binding part is the electronic Hamiltonian which is described in this section

Prerequisites

In order to correctly input the Hamiltonian first one has to set up the geometry correctly as described here.

What is of particular importance is the number of orbitals and whether a state has a magnetic moment or not. The input number of orbital is independent of whether magnetism or superconductivity is considered. In case that any atom has both a non-vanishing magnetic moment and non-zero number of orbitals the final number of orbitals is automatically doubled to account for the spin degeneracy. If superconductivity is included, then the total number of states again doubles to include the holes for the BdG-transformation. All hole terms are automatically defined from the electron terms.

Hamiltonian input

This section describes the different Hamiltonian terms implemented for tight-binding. Most terms are defined by a keyword followed by several lines of input where each line describes on particular term. No empty lines or comments should be put in-between as this stops the reading at the previous line.

Hopping Hamiltonian

The keyword TB_hopping allows to define a Hopping Hamiltonian in the space of the atom types.

Each input line following the keyword consists of 7 integers, followed by a real number. These numbers encode the connected atom types (1,2), the orbitals the connected atoms (3,4), the spins (5,6) (0: spin up and down, 1: spin up, 2:spin down), the distance (7) (0: onsite, 1: first neighbor, ...), and finally the real magnitude of the Hopping amplitude.

For example:

TB_hopping
1 2  3 4  0 0  1  5.6

defines a hopping amplitude of magnitude of 5.6 between atom type 1 orbital 3 and atoms type 2 orbital 4 for both spin up and spin down for all atoms where the considered atoms types have minimal distance compared to the entire lattice.

Jsd-coupling

The keyword TB_Jsd allows to define a Jsd coupling for the atom types that both have tight-binding orbitals and non-vanishing magnetic moment.

It requires 2 integers and one real number which are the atom type (1), the orbital (2), and the real magnitude.

For example:

TB_Jsd
1 2 3.4

adds a Jsd-coupling for atom-type 1, orbital 2 with magnitude 3.4.

S-type superconductivity

The keyword TB_delta allows to define an s-type superconducting delta-term.

While the input format would allow for more general input, so far only onsite terms are implemented, hence the atom types always have to be the same and the distance has to be 0. The input line requires 5 integers and one complex vlue, the atom types (1,2), the orbitals (3:4), the distance (5) (should always be 0), and the complex value of delta.

For example:

TB_delta
1 1 2 2 0 0.3 0.4

would define a delta of 0.3+0.4i on the second orbital of the first atom type.

Further information on the definition of delta can be found here

Self-consistent s-type superconductivity

Additionally the attractive potential causing a s-type on-site superconducting delta can be defined by the keyword TB_scfdelta.

The required input is 3 integers and a real value, which are the atom type (1), the connected orbitals (2,3), and the value of the attractive potential. To yield meaningful deltas several iteration have to be done controlled by further input variables, which will be described elsewhere.

Defects

The keyword TB_defect allows to insert magnetic or non-magnetic defects as a potential on certain sites within the supercell.

The input line consists of 5 integers and 2 reals which are the atom index (1, not atom-type), the orbital (2), the nonmagnetic (3) and magnetic (4) potential, and the position in the supercell (5,6,7), and . The positions indices should be within [1,Nx],[1,Ny],[1,Nz] where Nx, Ny, Nz are the supercell repetitions of the lattice defined though Nsize. The non-magnetic potential adds a simple onsite term on the spin-up and the spin-down part, while the magnetic part acts as an S.sigma term where S is the magnetic moment direction and sigma is the spin-operator in the tight-binding base.

For example

TB_defect
1 2 6.0d0 0.0d0 3 4 5

adds a single, non-magnetic potential of 6.0eV on the second orbital of the first atom in the super-cell at site 3,4,5.

Fermi-level adjustment

The keyword TB_Efermi allows to add a diagonal term on all orbitals with the negative of its input which effectively shifts the Fermi level from zero to the specified entry. For example

 TB_Efermi 1.0d0

moves all energies down by 1eV. This is particularly convenient to quickly change the Fermi level in case of superconducting calculations.

Wannier-based Hamiltonian

The keywords wann_ham, wann_up_ham, and wann_dn_ham allow to specify wannier90 *_tb.dat files whose Hamiltonian are read in for the entire system, the up-spins, or the down-spins, respectively.

After the keyword a string with a full name of the respective file has to be defined. For example:

 wann_ham WF1_tb.dat

If wann_ham is set, the alternatives are not checked. The basis of the wannier Hamiltonian is expected to be sorted the same as the Matjes orbitals and localized at the Matjes atom positions, hence the number of orbitals per atom-type and the order of the atoms has to be equivalent.

Tight-binding functionalities

The tight-binding functionalities are divided into 2 parts, the real-space and the reciprocal-space part. Each part has to be activated with the respective keyword do_TB_r or do_TB_k.

The real-space part allows to write the spectrum do_spec_r, calculate the Fermi energy do_fermi_r, obtains the density of states do_dos_r, calculate the occupation distribution (localization of occupied eigenstates in TB-basis) for a single energy do_occ_r or for several with do_occ_mult_r.

The reciprocal-space part consists of the density of states do_dos_k, calculation of projections at the fermi energy do_fermi_dos_k, and calculation of the band-structure do_highs_k.

All Fermi energy terms are only implemented without superconductivity.