[Pw_forum] band symmetry analysis for Pt (example04 in PP directory)

[Miao Gao]

Dear Paolo,

Thanks again for your reply.

> There is no difference between the two sets of results, apart from 
> the presence of two additional states. Notice that when these two
> states are found, the upper manifold of states (fourfold degenerate)
> is "cut into half" because the number of calculated states is fixed. 
> Of course the code gets confused and doesn't find a suitable symmetry
> label for the "half manifold", for a good reason: there isn't one.

As you know, one popular subfield in condensed matter physics is
topological insulator, which can be characterized by product of parities
at eight time reversal invariant points in the Brillouin zone, so these
little difference may affect the result of product.

> 
> > X point,           energy bands,     reference results, PRB 2, 883 (1970) 
> > e(  1 -  2) =     10.44178  eV     2   --> G_6+  M_6+ | G_6+
> > e(  3 -  4) =     10.87347  eV     2   --> G_7+  M_7+ | G_7+
> > e(  5 -  6) =     17.37445  eV     2   --> G_7+  M_7+ | G_7+
> > e(  7 -  8) =     17.67776  eV     2   --> G_6+  M_6+ | G_6+
> > e(  9 - 10) =     18.65959  eV     2   --> G_7+  M_7+ | G_7+
> > e( 11 - 12) =     19.10266  eV     2   --> G_6-  M_6- | G_6+ Inconsistent
> > e( 13 - 14) =     26.26903  eV     2   --> G_6+  M_6+ |
> 
> Maybe the last G6+ state of PRB 2, 883 (1970) corresponds to states
> 13-14 of today's calculation? While it is quite possible that bands.x
> incorrectly labels some irreps, it is exceedingly unlikely that it
> confuses an odd-parity irrep with an even-parity one

But 13-14 is about 7 eV higher than 11-12.

> 
> > L point,           energy bands,     reference results, PRB 2, 883 (1970)
> > e(  1 -  2) =     10.17424  eV     2   --> G_4+  L_6+ | L_6+
> > e(  3 -  4) =     13.14245  eV     2   --> G_5+  L_4+ | L_4+
> > e(  3 -  4) =     13.14245  eV     2   --> G_6+  L_5+ | L_5+
> > e(  5 -  6) =     14.15869  eV     2   --> G_4+  L_6+ | L_6+
> > e(  7 -  8) =     16.90324  eV     2   --> G_4-  L_6- | L_6+ Inconsistent
> > e(  9 - 10) =     17.29982  eV     2   --> G_4+  L_6+ | L_6- Inconsistent
> 
> as above: most likely in the old calculation the ordering of the 
> two doubly degenerate bands is reversed wrt today's calculations


Considering the similarity between these two band structures, no obvious
cross connection of energy band is found between 7-8 and 9-10 near L point.

Best

Miao Gao

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Ph.D. student of Department of Physics, 
Renmin University of China.
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