Why is the valence band maxima at k = 0?

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Discussion Overview

The discussion revolves around the positioning of the valence band maxima in different materials, specifically whether it is always located at k = 0. Participants explore the definitions and characteristics of direct and indirect materials in the context of band structure.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants assert that in direct materials, both the valence band maxima and conduction band minima are at k = 0, while in indirect materials, the valence band maxima is at k = 0 and the conduction band minima is at a non-zero k.
  • Others suggest that the assumption of the valence band maxima being at k = 0 is a common convention found in literature.
  • A participant challenges the notion that the valence band maxima is always at k = 0, providing lead sulfide as an example where it occurs at the L point.
  • Another participant mentions graphene and graphite, implying that these materials may also have different characteristics regarding the valence band maxima.

Areas of Agreement / Disagreement

Participants do not reach a consensus; there are multiple competing views regarding the positioning of the valence band maxima in different materials.

Contextual Notes

Some claims depend on specific definitions of direct and indirect materials, and the discussion highlights the need for clarity regarding the conditions under which the valence band maxima is considered to be at k = 0.

nmbr28albert
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In general, materials are either direct or indirect materials. For direct materials, both the valence band maxima and the conduction band minima are at k = 0. For indirect materials, only the valence band maxima is at k = 0 and the conduction band minima is at some other non-zero value of k. In all the books I've read, it seems to always be assumed that the valence band maxima is at k = 0. Is this true, and if so why?
 
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I have always seen the same, I think it's arbitrary defined like this.
 
After some digging, I found that it actually isn't true that the valence band maxima is always at k = 0. In lead sulfide for example, the valence band maximum is at the L point.
 
Graphene and gaphite also come to my mind.
 

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