[Pw_forum] K Points and Band structures

[dev sharma]

Dear Shaptrishi Sharma,
 I am also a student like you and what i have understood, what is K points,
is as follows.

We know that charge density is given by

ῤ(r) =  Σi=1 Ne/2 |Ψi(r)|2

 with the Bloch theorem we can write as

ῤ= Σn=1 Ne/cell ʃ d3k|Ψkn(r)|2

 but since the integration is a continuous quantity, we choose the K point
mesh in the Brillouin Zone  and we have

ῤ= Σn=1 Nb (2Π)3/V Σ (k ε mesh in BZ)  d3k|Ψkn(r)|2

Where  Ψkn(r)= eik.r Σ(G=reciprocal Lattice vector) Ckn[eiG.r/V(1/2)]
 And the term in bracket is the plane wave basis

and for visualization, what u can do, make any structure, open with Xcrysden
,and go to tools --> K-path selection, there the BZ of your structure will
be displayed, with some high symmetry K points (dots).

Dear Shaptrishi Sharma, also a lot of times they have asked you to provide
your full affilation. Please Do it.

To all my guides, in the forum, I may be wrong at any point above, if so
please correct me as my group is totally experimental and its my own
understanding.

Dev Sharma,

University of Delhi


On Fri, Sep 11, 2009 at 5:29 PM, Stefano de Gironcoli <degironc at sissa.it>wrote:

> Shaptrishi Sharma wrote:
> > Hi QEs users,
> >
> > Can anybody please help me in understanding what are the k points ?? I
> > have read books a lot but its difficult to understand.
> Please ask to any solid state physicist nearby.
>
> > And also  how do we choose k points while performing a band structure
> > calculation in quantum espresso when we are having 330 atoms.
> If you still have QE specific doubts after you have understood Bloch
> theorem, Real and Reciprocal Space lattices, Brilloun Zone and the like
> please  formulate them again, trying to be specific.
> > Thanks
> > S
> Please provide your affilaition.
>
> Best regards,
>
> Stefano de Gironcoli - SISSA and DEMOCRITOS
>
> > ------------------------------------------------------------------------
> >
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