Electronic velocities of degenerate states
Posted: Wed Nov 23, 2016 2:38 pm
Dear EPW Users,
With a view to extract RTA thermoelectric properties, I used the diamond test case with fine grids of 10x10x10 to extracted the electronic velocities using the following expression:
Looking at k-point 2 (0.0,0.0,0.1), the energies and velocities for the 4 valence bands are:
The velocities of the degenerate bands 3 and 4 are different. The same trend is observed in all k points that have degenerate bands. In addition, symmetry-equivalent points disagree in the velocities of bands 3 and 4. For example for k-point 10 (0.0,0.0,0.9) I get:
The velocities for the first two bands for k-points 2 and 10 are consistent and differ by +/- sign as expected. However, bands 3 and 4 are inconsistent.
I tested other equivalent k-points with no degeneracies and they are fine. For example for equivalent k-points 37 (0.0,0.3,0.6) and 48 (0.0,0.4,0.7), we have:
I would appreciate any thoughts on how these inconsistencies in electronic velocities for degenerate states may be resolved.
Best,
Vahid
Vahid Askarpour
Department of Physics and Atmospheric Science
Dalhousie University
Halifax, NS Canada
With a view to extract RTA thermoelectric properties, I used the diamond test case with fine grids of 10x10x10 to extracted the electronic velocities using the following expression:
Code: Select all
vkk(:,ibnd) = 2.0 * REAL (dmef(:,ibndmin-1+ibnd,ibndmin-1+ibnd, ikk))
Looking at k-point 2 (0.0,0.0,0.1), the energies and velocities for the 4 valence bands are:
Code: Select all
ENERGIES
2 1 -0.566406269532078
2 2 0.896037640310406
2 3 0.980593932883515
2 4 0.980593934077102
VELOCITIES
2 1 -0.1750304088 0.1750304046 -0.1750304033
2 2 0.7796141206 -0.7796141151 0.7796140748
2 3 0.0961879298 -0.1261303222 0.2925564189
2 4 0.2470620776 -0.2171194495 0.0506931518
The velocities of the degenerate bands 3 and 4 are different. The same trend is observed in all k points that have degenerate bands. In addition, symmetry-equivalent points disagree in the velocities of bands 3 and 4. For example for k-point 10 (0.0,0.0,0.9) I get:
Code: Select all
ENERGIES
10 1 -0.566406268602839
10 2 0.896037639699794
10 3 0.980593932623874
10 4 0.980593934017855
VELOCITIES
10 1 0.1750304539 -0.1750304667 0.1750305038
10 2 -0.7796141798 0.7796142709 -0.7796141136
10 3 -0.1994467913 0.2396866194 -0.0757409008
10 4 -0.1438025082 0.1035625485 -0.2675091844
The velocities for the first two bands for k-points 2 and 10 are consistent and differ by +/- sign as expected. However, bands 3 and 4 are inconsistent.
I tested other equivalent k-points with no degeneracies and they are fine. For example for equivalent k-points 37 (0.0,0.3,0.6) and 48 (0.0,0.4,0.7), we have:
Code: Select all
ENERGIES (same for both k-points)
37 1 4.187508120565024E-003
37 2 0.143849038349193
37 3 0.360023104630337
37 4 0.640827982129482
VELOCITIES
37 1 0.3805651532 0.6128871404 0.3805651419
37 2 0.1168264368 0.3803884837 0.1168264280
37 3 -0.3425894618 -1.3808010707 -0.3425895230
37 4 -0.3285271749 -0.1390662617 -0.3285265241
48 1 0.3805650766 -0.6128868454 0.3805650628
48 2 0.1168262835 -0.3803885162 0.1168262721
48 3 -0.3425895170 1.3808018967 -0.3425894063
48 4 -0.3285268578 0.1390662045 -0.3285267317
I would appreciate any thoughts on how these inconsistencies in electronic velocities for degenerate states may be resolved.
Best,
Vahid
Vahid Askarpour
Department of Physics and Atmospheric Science
Dalhousie University
Halifax, NS Canada