19

Topological materials form a broad family including insulators, semimetals, and superconductors, of which perhaps the best known are topological insulators. For concreteness, I will focus on topological insulators as these are the ones specifically mentioned in the question. Topological insulator. A topological insulator is an insulator whose Hamiltonian ...


18

Here is an excellent answer by Andrew on pre/post processing tools available for VASP. I will introduce another tool I have used for plotting bandstructure and DOS. PyProcar is an open-source Python library providing a set of functions that manage data from the PROCAR file obtained with VASP calculations. It supports VASP, Elk, Quantum ESPRESSO and ABINIT. ...


17

I have seen all the methods you mentioned but have only done one myself; I'll explain here how to use Wannier90 in conjunction with Quantum Espresso to get band structures for hybrid functional calculations. It does take a bit of time to learn, but not very long! You can learn the basics and do some first calculations in an afternoon. There are subtleties of ...


17

Short answer: Modern implementations of these two methods lead to similar accuracies. Longer answer: The calculation of phonons requires the calculation of the Hessian of the potential energy surface $V(\mathbf{R})$, also known as the matrix of force constants: $$ \frac{\partial^2 V(\mathbf{R})}{\partial \mathbf{R}_i\partial\mathbf{R}_j}=-\frac{\partial \...


16

Background theory. In the harmonic approximation, the potential energy surface (PES) is expanded about an equilibrium point to second order, to obtain the Hamiltonian: $$ \hat{H}=\sum_{p,\alpha}-\frac{1}{2m_{\alpha}}\nabla_{p\alpha}^2+\frac{1}{2}\sum_{p,\alpha,i}\sum_{p^{\prime},\alpha^{\prime},i^{\prime}}D_{i\alpha;i^{\prime}\alpha^{\prime}}(\mathbf{R}_p,\...


16

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{...


14

The reason why graphene has Dirac points at K and $-$K is because of a combination of time reversal and inversion symmetries. Therefore, if you impose these symmetries in your VASP calculation, there is no reason why there should be a gap at K. Even if you do not impose these symmetries explicitly, you should be able to get the degeneracy to very high ...


14

The y-axis corresponds to the direct eigenvalues from your DFT calculation. You need to set the valence band maximum to '0' manually. The DFT output of your calculation will give the highest occupied state energy (or the Fermi energy, if you use occupations smearing). So whatever that energy is, subtract that from the energies in your band plot. A note on ...


13

Here I provide an example with my own python scripts to realize your purpose rather than using Pymatgen (You can save data firstly with Pymatgen and plot with python). I assume that you can perform correctly the band and dos calculations with the VASP code. The example I pick up is the monolayer FM NiBr$_2$ and the final result is the following: Example ...


13

The density of states reads: $$ \tag{1} g(E)=\sum_{n}\int\frac{d\mathbf{k}}{(2\pi)^3}\delta(E-E_{n\mathbf{k}}), $$ where $E_{n\mathbf{k}}$ are the electronic energies and the integral is over the Brillouin zone (BZ). If you calculate $g(E)$ in the primitive cell, then you will integrate over the primitive cell BZ. If you calculate $g(E)$ in a supercell, then ...


13

Band structure is a concept for periodic system only. As proteins are not periodic structures, they don't have electronic bands. The fact that you can download a PDB file (or a CIF file) with information about the crystal, it is just due to one of the ways we found to determine the protein structure that is crystalizing the protein and then using single ...


12

Theory. The Rashba effect can be described with a 2-band model: $$ \hat{H}=\frac{\hbar^2}{2m}(k_x^2+k_y^2)\mathbb{1}_2+\alpha_{\mathrm{R}}(\sigma_1 k_y-\sigma_2 k_x), $$ where $\alpha_{\mathrm{R}}$ is the Rashba parameter and all other terms have their usual meanings. Diagonalizing this Hamiltonian gives the energy dispersion: $$ E_{\pm}=\frac{\hbar^2}{2m}(...


12

The answer of @ProfM is already very complete, but I wanted to tackle your question from a more practical point of view. The presence of imaginary frequencies indicate that there are atomic positions which are more energetically favorable at the ground state. So, the concept of "following" a mode means condensing it onto the reference structure, ...


12

Another option is Sumo, which is a Python toolkit for plotting and analysis of ab initio solid-state calculation data. It supports VASP, CASTEP and Questaal. Plotting is mostly done through a command-line interface. It can also generate the band paths in the first place. There is also support for plotting phonon bands generate with phononpy.


12

Here I will take Mg3Sb2 from Materials Project as an example to demonstrate the bandstructure calculation flow with the MBJ method. (I) structure relaxation (II) PBE band calculation based on the relaxed structure (a) self-consistent (SCF) calculation [10_scf_cal]. (b) band calculation based on converged charge density at (II-a) [11_band_cal]. (c) read ...


12

If the crystal unit cell is in a format readable by ASE, then you can use code that looks approximately like so: from ase.io import read atoms = read("myfilename.xyz") bandpath = atoms.cell.bandpath() This bandpath object will have the relevant attributes to play with (kpoint coordinates, special point labels, special point coordinates, etc). ...


11

Model potentials for exchange: Exchange-correlation potentials like mBJ and GLLBSC have model orbital-dependent corrections included in the form of the functional. I'll first try to get the fundamental motivation across using GLLBSC as an example, and then attempt to go into how mBJ does this. GLLB/SC: In the case of the GLLB work, the authors used a ...


11

I will try to outline this in simple terms. There are certainly more rigorous explanations. The high-symmetry points in the Brillouin zone are those that remain physically identical when certain symmetry operations of the point-group are applied. Therefore, we notice that the first and higher derivatives of the dispersion relation have the same magnitude in ...


11

First of all, I assume that you are taking VASP to perform your calculation. Secondly, I assume that your structural defect is taking a Hf atom from your structure. (You can deal with substitutional doping with similar logic.) Thirdly, for the HfS2 monolayer, there are two phases, namely T-phase and H-phase. The T-phase monolayer was fabricated in the ...


11

Is this calculated indirect bandgap at room temp. or at 0K? QE is based on the density functional theory (DFT). DFT is a ground-state (0K) theory and hence the calculated bandstructure is 0K. If it is at room temperature the indirect bandgap should be around 1.1 eV as from the literature. So is there any energy correction factor that has to be performed to ...


11

If you are really interested in learning how to generate the path, I strongly advice you to avoid using any automatic tool like suggested in previous answers. In the Wiki page entitle Brillouin zone you can find the first Brillouin zone for each one of the Bravais lattice. This Wiki is based on the following paper: Setyawan, Wahyu; Curtarolo, Stefano (2010)....


10

Like many other parameters in QE one of the best methods is to simply test yourself and weight your options. You may start with 1x1x1 and go to 3x3x3 for example and check the following. Do you get convergence? What is final energy? What is dE in the final step? (plot the above parameters to see the diminishing returns) Then determine computation time ...


10

As already specified in the previous answers, the choice of K-Grid mesh should be taken upon verifying the convergence of the desired quantity. We usually start with the convergence of the total energy, but for other properties like optical spectra, for example, the converged grid with respect to the energy should not be enough, and a denser grid is usually ...


10

I would like to add a few clarifications to Jack's answer: Standard DFT calculations with fixed ionic positions are actually not even 0 K. A better way to describe them is that they are static lattice calculations. The difference between static lattice and 0 K is the contribution from quantum zero-point fluctuations. This contribution is generally small, ...


10

Consider a graphene Hamiltonian, whose dispersion looks a lot like the one in your figure. Per these notes, its k-space Hamiltonian may be written as: $$ H(k)=-t \sum_{\delta} [\cos(k\cdot\delta)\sigma_x-\sin(k\cdot\delta)\sigma_y], $$ where $k=(k_x,k_y)$, $\delta$ are nearest-neighbor vectors, $\sigma_i$ are Pauli matrices and $t$ is a hopping parameter. ...


10

Yes, broken symmetry solutions do break time-reversal symmetry, and that's one of the reasons why they are unphysical when the total magnetic moment of the system is 0 (although they are physical when the total magnetic moment is not 0, due to spin polarization). The reason is that, suppose you have a spin polarized $M_S=0$ state, then if you flip the spin ...


10

1. Is it possible that the energy gap of the material is direct in the bulk but indirect in the slab? Yes, this is possible (as is the reverse). The 2D slab does not have the same symmetry as the full 3D slab, and there is no requirement for the conduction band minima and valence band minima to be at the same points in reciprocal-space. As you make the slab ...


9

Quantum confinement can occur when the exciton (electron-hole quasiparticle) radius is larger than the size of the semiconductor. Due to this confinement, the energy levels which can be occupied by the exciton are quantized into discrete energy levels. This will spread the band gap due to missing states that would exist in the bulk material. This ...


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 ...


9

If you give the explicit points in the KPOINTS file in VASP for a band structure calculation, for example as required for hybrid functionals, the bands will only be calculated at the explicit $\mathbf{k}$-points you list. For example, if you have a cubic cell and want the path between $\Gamma$ at $(0,0,0)$ and X at $(0.5,0,0)$, then simply writing: $$ 0.0 \,\...


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