[Wien] Metal or semimetal

[Karel Vyborny]

A quick question to add my bit into this conversation: where does the 
definition of semimetal as "insulating (semiconducting) in one direction 
and conducting in another one" come from? I have never heard of this; it 
may the lack of my knowledge but I hold that it's the overlaping valence 
and conduction bands that define semimetals (and indeed, bismuth has 
always been the prime example for me). The strong anisotropy in 
conductivity may be a concomitant feature, however, it is not necessary.

Cheers,

Karel


--- x ---
dr. Karel Vyborny
Fyzikalni ustav AV CR, v.v.i.
Cukrovarnicka 10
Praha 6, CZ-16253
tel: +420220318459


On Tue, 29 Jan 2019, Fecher, Gerhard wrote:

> Thank you for the Link, but I don't understand your remarks
> Wikipedia tells:
> - Schematic
> C) a semimetal (like tin (Sn) or graphite and the alkaline earth metals).
> and further
> - Classic semimetals
> The classic semimetallic elements are arsenic, antimony, bismuth, ?-tin (gray tin) and graphite, an allotrope of carbon.
>
> on the page https://en.wikipedia.org/wiki/Graphite one finds
> Graphite has a layered, planar structure. The individual layers are called graphene. ...
> Atoms in the plane are bonded covalently, with only three of the four potential bonding sites satisfied. The fourth electron is free to migrate in the plane, making graphite electrically conductive. 
> However, it does not conduct in a direction at right angles to the plane.
>
> Maybe check the band structures of Graphite and Bi to find out what is common and what is different.
>
> You did not understand the remark on the integration of the density of states, please read it correctly.
> The initial question was on the Fermi energy beeing slightly below the top of the valence band 
> and this might be caused by a bad integration which depends on the number of k-points (indeed among others)
> and is used to find the Fermi energy.
>
> PS.: Please check the definition of the density of states and you see why flat (say better narrow) bands result in a high density of states and steep ones in a low density of states.
> (that a band is horizontal at a certain point of the Brillouin zone does not mean that the complete band is flat, this situation you have always at the bottom of a parabola) .
>
> Ciao
> Gerhard
>
> DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:
> "I think the problem, to be quite honest with you,
> is that you have never actually known what the question is."
>
> ====================================
> Dr. Gerhard H. Fecher
> Institut of Inorganic and Analytical Chemistry
> Johannes Gutenberg - University
> 55099 Mainz
> and
> Max Planck Institute for Chemical Physics of Solids
> 01187 Dresden
> ________________________________________
> Von: Wien [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von delamora [delamora at unam.mx]
> Gesendet: Dienstag, 29. Januar 2019 19:43
> An: A Mailing list for WIEN2k users
> Betreff: [Wien] Metal or semimetal
>
> I strongly disagree
>
> Wikipedia gives a very different definition
>
> https://en.wikipedia.org/wiki/Semimetal
>
> Bi would be a good example; it has a very low DOS at Ef (with the wikipedia definition of semimetal)
>
> Graphite is conductor in the ab plane and a poor conductor (not insulating) in the c direction
>
> As I said, the bands are flat near the band edge, so it would be a bad conductor (does this fall into the definition of semimetal???)
> Flat bands give high DOS? Not always, for example NaCl at the bottom of the conduction band, the band is flat and DOS is very low
> And I do not think I need a high density of k points
>
> On the other hand the f orbitals have flat bands and DO HAVE high DOS
>
> ________________________________
> De: Wien <wien-bounces at zeus.theochem.tuwien.ac.at> en nombre de Fecher, Gerhard <fecher at uni-mainz.de>
> Enviado: martes, 29 de enero de 2019 03:49 a. m.
> Para: A Mailing list for WIEN2k users
> Asunto: Re: [Wien] Metal or semimetal
>
> I strongly disagree,
> a semi-metal (not to be confused with a half-metall) is a material that is insulating (semiconducting) in one direction and conducting in another one, a typical example is graphite.
> (this has nothing to do whether the bands are flat or not;
> and just to mention, the density of states is HIGH when the bands are FLAT.)
>
> The question is: What is slightly below ?
>
> If you have one (or more) partially filled band(s) that is(are) crossing the Fermi energy, then you have a metal.
> (You find the occupation of the bands e.g.: in case.scf2)
>
> If you have not enough k-points (or some other bad conditions), then the integration of the density of states might be bad
> and the Fermi energy may fall into the valence or conduction band (probably few meV or less) even though the material is an insulator,
> this can be healed in most cases by increasing the number of k-points.
>
> In some cases you have to check whether there might be an overlapp of the valence and and conduction bands at different k-points, resulting in a semimetallic or zero-bandgap type behavior.
> For example you may have a large gap at Gamma with EF at the top of the valence band and a large gap at another k-point, say X, with EF at the bottom of the conduction band.
>
> PS.: To complete; in a half-metal one spin channel (e.g. minority) is insulating (semiconducting) and the other spin channel is metallic (e.g.: majority)
>
>
>
> Ciao
> Gerhard
>
> DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:
> "I think the problem, to be quite honest with you,
> is that you have never actually known what the question is."
>
> ====================================
> Dr. Gerhard H. Fecher
> Institut of Inorganic and Analytical Chemistry
> Johannes Gutenberg - University
> 55099 Mainz
> and
> Max Planck Institute for Chemical Physics of Solids
> 01187 Dresden
> ________________________________________
> Von: Wien [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von delamora [delamora at unam.mx]
> Gesendet: Freitag, 25. Januar 2019 01:53
> An: A Mailing list for WIEN2k users
> Betreff: Re: [Wien] Metal or semimetal
>
> If Ef is near the edge of a band, close to the bandgap then it would be a bad conductor, since the bands would be quite flat (and the velocity of the electrons is proportional to the slope of the band) and the DOS would be low, so I would call it a semimetal
>
>
> ________________________________
>
> Dear wien2k users:
>
> I have a question that does not have any relation with wien2k but I would be grateful if you can answer me or send me a document:
>
> When the fermi level passes slightly below the top of the valance band with the presence of a wide gap, this indicates a metal or semimetalic behavior.?
>
> Thank you in advance
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