[Pw_forum] Calculation for determining Band Inversion due to Spin Orbit Coupling.

[Marrazzo Antimo]

Dear Mohammed,

once you compute the projected k-resolved DOS (projwfc.x, Wannier90, you name it...) the “procedure” has very little to do with Quantum Espresso  and much more with theory of topological insulators.
Hence, I suggest you to give a look at some review papers on the subject and spend some time on them. A good recent one is https://doi.org/10.1103/RevModPhys.88.021004 (have a look at Fig.1 for instance, it is quite clear) but there are many others.
The band inversion is literally an inversion of the character of bands (e.g. an s-band and a p-band, or a p-band and a d-band, ...), that happens in a small region in k-space. So you have two bands crossing each other with well defined orbital character and in a small region of k-space (for instance around the Gamma point) one of the two band (for instance an s-band) gets the character of the other band (e.g. p-band) and viceversa (Fig. 1 is quite perspicuous). Actually, you can have band inversion even without spin-orbit coupling; however SOC is quite fundamental to open a gap.

HTH


Antimo Marrazzo
Doctoral Assistant
EPFL STI IMX THEOS
ME-D2 1019 (Bâtiment ME)
Station 9
CH-1015 Lausanne (Switzerland)

Il giorno 21 gen 2017, alle ore 11:27, Mohammed Ghadiyali <m786g at live.co.uk<mailto:m786g at live.co.uk>> ha scritto:

Hi All,

I 'm working on band structure of stanene - with and with spin orbit coupling (SOC). I have been able to replicate the

results but I 'm not getting how should I detect the band inversion due to SOC. I have performed the k resolved DOS

for the same, but I am not to determine any thing conclusive.

In short, can some one inform me procedure of finding if there is a band inversion in the band structure due to SOC or not.

Regards,
Ghadiyali Mohammed Kader
University of Mumbai.
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