In Quantum ESPRESSO, which is an open-source software package for electronic structure calculations, the band structure diagram represents the electronic band structure of a crystalline material. It provides information about the allowed energy levels (bands) and their corresponding wave vectors (k-points) in the material's Brillouin zone.
To generate a band structure diagram in Quantum ESPRESSO, you typically follow these steps:
Perform a self-consistent field (SCF) calculation: First, you need to run a SCF calculation to obtain the electronic ground state of the material. This calculation determines the electron density and potential energy for the system.
Generate a k-point mesh: The Brillouin zone of a crystal is divided into a mesh of k-points. The choice of k-point mesh affects the resolution of the band structure. Generally, a denser mesh provides more accurate results. You can define the k-point mesh in the input file.
Perform a non-self-consistent field (NSCF) calculation: Using the obtained ground state, perform a NSCF calculation with the desired k-point mesh. This calculation computes the eigenvalues and eigenvectors for each k-point in the mesh. The eigenvalues correspond to the energy levels, and the eigenvectors describe the electronic wave functions.
Analyze the results: Once the NSCF calculation is complete, you can analyze the output files to obtain the band structure. The most common output file is the "bands.dat" file, which contains the eigenvalues and k-points for each band. These data can be visualized using external tools such as gnuplot or Matplotlib to create the band structure diagram.
The band structure diagram typically shows the energy levels (bands) along high-symmetry paths in the Brillouin zone. These paths connect high-symmetry points such as the Gamma point (Γ), X, Y, Z, and so on. The vertical axis represents the energy, while the horizontal axis represents the position in reciprocal space (k-vector).
By analyzing the band structure diagram, you can gain insights into the material's electronic properties, such as the energy bandgap, dispersion relations, and the presence of energy bands with high or low electron densities.