If you have done some post-processing of the electronic or phonon band structure you get from Quantum Espresso then hopefully you can correctly understand and answer my question:
For both electronic and phonon band structure, what is the unit of x-axis? I know it is a cumulative distance from the starting symmetry point (usually Gamma) to other given symmetry points. But, I need to extract only a portion of the band structure for further calculations, for e.g. acoustic phonon velocity by fitting linear portion near gamma point in the phonon band structure, what are the constants that I have to multiply or divide from the x- data to get the values correct in say SI unit? To be much specific, should I divide it by (pi/a) or (2*pi/a) or something else? If I have to use 'a' what unit will it have when I am multiplying or dividing? y-axis is very straight forward, it is cm-1 for phonon and eV for electron band structure. Cheers!
Dear Bharat Thapa,
You know that Band Structure is plotted in Reciprocal Lattice Space.
That means , the X-Axis is propagation Vector ( k = 2π/λ) . As λ is the wavelength, it has the dimension of length.
So, the propagation Vector has the dimension of inverse of Length. [L^(-1)].
I think I can understand your question.
If not, please tell me.
Thanks
N Das
Dear Nityananda,
Thank you for your response. It is true that x-axis or the k vector has the unit of the inverse of length. But when you are computing it in Quantum Espresso, the reciprocal vectors are normalised with (2*pi/a), which now I am quite sure of. So, it is definitely not 2*pi/lambda like you said in this particular case. So, I think if I want to get some constants from the band structure (from Quantum Espresso), I must divide the x-axis values with (2*-pi/a). The important thing is 'a' is in 'atomic unit' or 'bohr' unit, so it must be converted accordingly. If you have some comment on this, please go ahead.
Regards,
Bharat.
Dear Bharat Thapa,
You are absolutely right.
But the reciprocal lattice unit vectors are defined as
a*= ( b×c)/a.(b×c) and so on.
So, a* has the dimension of length inverse.
In this basis the value of x axis is a number.
As the basis is not mentioned, the x axis seems be a number.
But, it is to be remembered that this number is interns of those basis system which is length inverse.
Please tell me, if there is still doubt or If I am wrong.
Thanks
N Das
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