[Pw_forum] [OT] How to identify NFE states ?

[Stefano de Gironcoli]

Dear  Hai-Ping Lan,
 
I think that the idea of NFE is that there are situations in which the 
effective (pseudo)-potential resulting from
e-ion, e-e, and orthogonality to core electrons results to be weak and 
hence the eigenvalue problem  to be solved
is close to the free-electron one.
Obviously at very high energies  the kinetic energy dominates  and  the 
potential can be thought to be weak.
But early empirical pseudopotential calculations (such 
Cohen-Bergstressen PhysRev 141, 789 (1966) or similar)
show that silicon  band structures is also close to FE in a certain 
sense... especially away from the regions
of the BZ where the free electron bands would cross (where the 
pseudopotential opens gaps there and the dispersion
is strongly modified)...
But the true potential in silicon IS NOT smooth and valence 
wave-functions ARE NOT simple plane waves since
they are orthogonal to core states and only when things are recast in a 
way that the effective  hamiltonian, acting on
some properly defined pseudo-wfc, is weak then the FE features of the 
dispersion relation can be understood...

here come my question:

WHY do you want to know which states are NFE-like ? what is the physical 
property you are interested in and
what are the peculiar features of NFE for that property?

This would help a great deal in understanding what a NFE should mean for 
your problem...

  best regards,

         Stefano de Gironcoli - SISSA and DEMOCRITOS


lan haiping wrote:
> Thank you ,Stefano!
> I have misinterpreted the meaning of effective mass.
> When we talk about NFE states, does it mean that such
> E-K dispersion should be held between 2 symmetry points, like from X-> 
> Gamma ?
>
> On Mon, Apr 28, 2008 at 1:40 AM, Stefano Baroni <baroni at sissa.it 
> <mailto:baroni at sissa.it>> wrote:
>
>     The higher the energy, the lower the effect of the
>     pseudopotential, so high-energy states are expected to be more
>     free-electron like than low-lying ones. I am afraid that the very
>     ocncept of "effective mass" is not very meaningful for these
>     states. However, I would expect (although I have never verified)
>     that for high-lying states the derivative of the band energy with
>     respect to the wavenumber be linear with respect to the
>     wavenumber, with the coefficient given by the inverse of the
>     free-electron mass. SB
>
>     On Apr 27, 2008, at 8:27 AM, lan haiping wrote:
>
>>     Dear All,
>>
>>      I am wondering about the nearly free electron states . To
>>     identify such states,
>>     does it mean that its effective mass is very close to free
>>     electron ,And we can identify
>>     it from bands' dispersion ?      
>>
>>      Bests
>>     H.P
>>
>>     -- 
>>     Hai-Ping Lan
>>     Department of Electronics ,
>>     Peking University , Bejing, 100871
>>     lanhaiping at gmail.com <mailto:lanhaiping at gmail.com>,
>>     hplan at pku.edu.cn <mailto:hplan at pku.edu.cn>
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>
>
>     ---
>     Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center -
>     Trieste
>     [+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)
>
>     La morale est une logique de l'action comme la logique est une
>     morale de la pensée - Jean Piaget
>
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> -- 
> Hai-Ping Lan
> Department of Electronics ,
> Peking University , Bejing, 100871
> lanhaiping at gmail.com <mailto:lanhaiping at gmail.com>, hplan at pku.edu.cn 
> <mailto:hplan at pku.edu.cn>
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