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Two-band model for graphene. To simplify the discussion of Dirac points, it is sufficient to consider a nearest-neighbor tight-binding 2-band model for graphene. This is a spinless model because spin-orbit is negligible in graphene. The Bloch Hamiltonian is:  \hat{H}(\mathbf{k})= \begin{pmatrix} 0 & h(\mathbf{k}) \\ h^{\dagger}(\mathbf{k}) & 0 \end{...

10

One way of determining this is using the projected density of states (P-DOS) This resolves the DOS into specific orbitals thereby allowing you to discretize each orbitals weight for a specific energy. $\mathrm{PDOS}_\nu(E) = \sum_i \psi^*_{i,\nu} [\mathbf S | \psi_{i}\rangle]_\nu D(E-\epsilon_i)$ Note here that $|\psi_i\rangle$ is the $i$th eigenvector and ...

10

Spherical harmonics are not themselves full atomic orbitals. Consider the Hydrogen wave function, which separates into a radial part and an angular part. The latter is a spherical harmonic, but the former is some other function (in the case of Hydrogen it's a Laguerre polynomial). In general, we can approximate the angular part for other atoms with the same ...

9

Oh! I found the answer already. Since I'm doing the calculation along the High symmetry point. Im doing the calculation along G -> K -> M -> G, that's why the right hand sides show such phenomena. In tight binding I plot the band along G -> K -> G. I try to reproduce the band along this direction, it matched with the tight binding solution. Thanks guys. It's ...

8

Yes! It is definitely possible and it is useful for calculating other things like electronic transport and first-principles values of Hubbard U (i.e. the ACBN0 method, which I have used a bit). Some good papers to read are from Prof. Marco Buongiorno Nardelli's group at UNT: L. A. Agapito, A. Ferretti, A. Calzolari, S. Curtarolo, and M. Buongiorno Nardelli, ...

7

Not really sure about benchmarks for solid state TS geometries. A couple of scattered piece of references are: (i) This paper by Ceder's group has several related TS barriers: aip.scitation.org/doi/pdf/10.1063/1.4960790 (ii) Then there is Henkelman's paper for bulk unit cell TS calculations: aip.scitation.org/doi/abs/10.1063/1.3684549. Maybe you are already ...

7

The following code is a python function to read the wannier90_hr.dat, from which you should figure out its data structure. def read_hamiltonian(path): """ Read hopping matrix element from the wannier90 output file:wannier90_hr.dat wan_num: number of wannier functions wsc_num: number of wigner-sitez cells wsc_count: ...

6

You can read the wanniertools code. In wanniertools, to calculate surface state, they write a surfstate subroutine in surfstate.f90 file. The slab Hamiltonian is restructured from a bulk Hamiltonian in ham_qlayer2qlayer.f90 file. enter code here ! This is a fortran code. ! H00 Hamiltonian between nearest neighbour-quintuple-layers ! the factor 2 is ...

5

The answer by Anyon does not address how to calculate the form of the Slater-Koster two-center integrals (2CI) but rather how to determine the direction cosines that appear in the 2CI's (the $l$,$m$,$n$'s in things like $\sqrt{3}lm*(sd\sigma)$, but not the $\sqrt{3}$). I am currently trying to explicitly perform the same calculation to include in my comps so ...

5

Consider the energy eigenstate $|\psi_{n\mathbf{k}}\rangle$, where $n$ is the band you are interested in and $\mathbf{k}$ is wave vector of the TRIM point. Then, if the system has inversion symmetry, these energy eigenstates are also eigenstates of the parity operator $\hat{\pi}$. This means that to determine the parity of that state, you can calculate the ...

4

Wannier90 might not be good at preserving the symmetry. But they probably include a few new methods to enforce symmetry in Wannier90.v.3.1.0. Maybe you can check this. http://www.wannier.org/features/ Also, WannierTools can symmetrize the hr.dat, but from my personal experience it sometimes gives you worse results than the original hr.dat. http://www....

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