Propability current
Posted: Tue Feb 17, 2009 11:52 am
Hello,
I am trying to compute the propability current through a slab by using vasp. Vasp computes the full wavefunction internally, which I wrote into a file with its fourier coefficients and G-vectors at every kpoint and band for a slab with and without efield in z-direction. The bloch-function is as far as I know not written.
I have used a 3x3x3 Monkhorst and Pack k-point file and vasp reduced this from 27 to at least 6 kpoints, because of symmetrie.
As known from literature the propability current through a plane in xy direction can be calculated as the:
sum(G, G') over Cjk(G)*Cjk_conj(G')*exp(i*(G-G')*r)*i(Gz+k_z)
for each band and kpoint.
Vasp gives me the coefficients of the full wavefunction at the 6 irreducible kpoints. Because the propability current is mainly dependent on the k-vectors in z-direction, those k-vectors (k_z) are important with their weight (+/-) because of reflecting and transmitting tunneling currents.
When I now want to calculate the total propability current in one xy-plane I calculate the sum in xy-direction (included in r) in a special band and kpoint.
But the question is, which k-points do I have to take into account for the total current? Are it just the weighted kpoints of the ruduced brillouin zone, or of the complete brillouin zone? How can I get the other 27-6=21 kpoints from vasp and how are they then related to the fourier coefficients of the WAVECAR file? Is it somekind of linear combination?
Is it also possible to use just 3 kpoints, for example (0,0,0); (0,0,-0.5) and (0,0,+0.5)?
Can somebody help me?
Thank you!
Regards,
kristian
I am trying to compute the propability current through a slab by using vasp. Vasp computes the full wavefunction internally, which I wrote into a file with its fourier coefficients and G-vectors at every kpoint and band for a slab with and without efield in z-direction. The bloch-function is as far as I know not written.
I have used a 3x3x3 Monkhorst and Pack k-point file and vasp reduced this from 27 to at least 6 kpoints, because of symmetrie.
As known from literature the propability current through a plane in xy direction can be calculated as the:
sum(G, G') over Cjk(G)*Cjk_conj(G')*exp(i*(G-G')*r)*i(Gz+k_z)
for each band and kpoint.
Vasp gives me the coefficients of the full wavefunction at the 6 irreducible kpoints. Because the propability current is mainly dependent on the k-vectors in z-direction, those k-vectors (k_z) are important with their weight (+/-) because of reflecting and transmitting tunneling currents.
When I now want to calculate the total propability current in one xy-plane I calculate the sum in xy-direction (included in r) in a special band and kpoint.
But the question is, which k-points do I have to take into account for the total current? Are it just the weighted kpoints of the ruduced brillouin zone, or of the complete brillouin zone? How can I get the other 27-6=21 kpoints from vasp and how are they then related to the fourier coefficients of the WAVECAR file? Is it somekind of linear combination?
Is it also possible to use just 3 kpoints, for example (0,0,0); (0,0,-0.5) and (0,0,+0.5)?
Can somebody help me?
Thank you!
Regards,
kristian