Thank you very much,Stefano.<br><br>In fact, I just noticed some discussions on n-type doping on carbon nanotubes systems and graphite intercalated compounds. On these systems, NFE states have particular importance or some particular behaviors, for instance, the occupied NFE states were thought to account for superconducting transition behavior in some GICs. <br>
With regard to NFE, there seems no clear definition. <br>I noticed that some discussion denoted band that is not <br>a parabola along two high symmetry points but just a part .<br><br>Best<br><br><br>Best<br><br><br><div class="gmail_quote">
On Wed, Apr 30, 2008 at 6:52 PM, Stefano de Gironcoli <<a href="mailto:degironc@sissa.it">degironc@sissa.it</a>> wrote:<br><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
Dear Hai-Ping Lan,<br>
<br>
I think that the idea of NFE is that there are situations in which the<br>
effective (pseudo)-potential resulting from<br>
e-ion, e-e, and orthogonality to core electrons results to be weak and<br>
hence the eigenvalue problem to be solved<br>
is close to the free-electron one.<br>
Obviously at very high energies the kinetic energy dominates and the<br>
potential can be thought to be weak.<br>
But early empirical pseudopotential calculations (such<br>
Cohen-Bergstressen PhysRev 141, 789 (1966) or similar)<br>
show that silicon band structures is also close to FE in a certain<br>
sense... especially away from the regions<br>
of the BZ where the free electron bands would cross (where the<br>
pseudopotential opens gaps there and the dispersion<br>
is strongly modified)...<br>
But the true potential in silicon IS NOT smooth and valence<br>
wave-functions ARE NOT simple plane waves since<br>
they are orthogonal to core states and only when things are recast in a<br>
way that the effective hamiltonian, acting on<br>
some properly defined pseudo-wfc, is weak then the FE features of the<br>
dispersion relation can be understood...<br>
<br>
here come my question:<br>
<br>
WHY do you want to know which states are NFE-like ? what is the physical<br>
property you are interested in and<br>
what are the peculiar features of NFE for that property?<br>
<br>
This would help a great deal in understanding what a NFE should mean for<br>
your problem...<br>
<br>
best regards,<br>
<br>
Stefano de Gironcoli - SISSA and DEMOCRITOS<br>
<div class="Ih2E3d"><br>
<br>
lan haiping wrote:<br>
> Thank you ,Stefano!<br>
> I have misinterpreted the meaning of effective mass.<br>
> When we talk about NFE states, does it mean that such<br>
> E-K dispersion should be held between 2 symmetry points, like from X-><br>
> Gamma ?<br>
><br>
> On Mon, Apr 28, 2008 at 1:40 AM, Stefano Baroni <<a href="mailto:baroni@sissa.it">baroni@sissa.it</a><br>
</div><div class="Ih2E3d">> <mailto:<a href="mailto:baroni@sissa.it">baroni@sissa.it</a>>> wrote:<br>
><br>
> The higher the energy, the lower the effect of the<br>
> pseudopotential, so high-energy states are expected to be more<br>
> free-electron like than low-lying ones. I am afraid that the very<br>
> ocncept of "effective mass" is not very meaningful for these<br>
> states. However, I would expect (although I have never verified)<br>
> that for high-lying states the derivative of the band energy with<br>
> respect to the wavenumber be linear with respect to the<br>
> wavenumber, with the coefficient given by the inverse of the<br>
> free-electron mass. SB<br>
><br>
> On Apr 27, 2008, at 8:27 AM, lan haiping wrote:<br>
><br>
>> Dear All,<br>
>><br>
>> I am wondering about the nearly free electron states . To<br>
>> identify such states,<br>
>> does it mean that its effective mass is very close to free<br>
>> electron ,And we can identify<br>
>> it from bands' dispersion ?<br>
>><br>
>> Bests<br>
>> H.P<br>
>><br>
>> --<br>
>> Hai-Ping Lan<br>
>> Department of Electronics ,<br>
>> Peking University , Bejing, 100871<br>
</div>>> <a href="mailto:lanhaiping@gmail.com">lanhaiping@gmail.com</a> <mailto:<a href="mailto:lanhaiping@gmail.com">lanhaiping@gmail.com</a>>,<br>
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> ---<br>
> Stefano Baroni - SISSA & DEMOCRITOS National Simulation Center -<br>
> Trieste<br>
> [+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)<br>
><br>
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> --<br>
> Hai-Ping Lan<br>
> Department of Electronics ,<br>
> Peking University , Bejing, 100871<br>
</div>> <a href="mailto:lanhaiping@gmail.com">lanhaiping@gmail.com</a> <mailto:<a href="mailto:lanhaiping@gmail.com">lanhaiping@gmail.com</a>>, <a href="mailto:hplan@pku.edu.cn">hplan@pku.edu.cn</a><br>
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</div></div></blockquote></div><br><br clear="all"><br>-- <br>Hai-Ping Lan <br>Department of Electronics ,<br>Peking University , Bejing, 100871<br><a href="mailto:lanhaiping@gmail.com">lanhaiping@gmail.com</a>, <a href="mailto:hplan@pku.edu.cn">hplan@pku.edu.cn</a>