# What actually is the Dirac Point ?

#### JTPF

What actually is the "Dirac Point"?

I'm trying to find out what actually is the "Dirac Point"?!

I've Googled it and searched around on the internet, looked through books, but haven't actually been able to find a definitive definition and explanation, just general references to it within the context.

:grumpy:

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#### DarkScareCrow

Re: What actually is the "Dirac Point"?

All I know is that it has to do with Graphene. I don't have the exact definition. :uhh:

#### Drakkith

Staff Emeritus
Science Advisor
2018 Award
Re: What actually is the "Dirac Point"?

From wikipedia's article: http://en.wikipedia.org/wiki/Graphene#Electronic_properties

Graphene differs from most conventional three-dimensional materials. Intrinsic graphene is a semi-metal or zero-gap semiconductor. Understanding the electronic structure of graphene is the starting point for finding the band structure of graphite. It was realized as early as 1947 by P. R. Wallace[72] that the E-k relation is linear for low energies near the six corners of the two-dimensional hexagonal Brillouin zone, leading to zero effective mass for electrons and holes. [73] Due to this linear (or “conical") dispersion relation at low energies, electrons and holes near these six points, two of which are inequivalent, behave like relativistic particles described by the Dirac equation for spin 1/2 particles.[74][75] Hence, the electrons and holes are called Dirac fermions, and the six corners of the Brillouin zone are called the Dirac points.

#### lww

Re: What actually is the "Dirac Point"?

i think it's better to refer to the RMP paper writtern by M.O. Goerbig (2011), who says:

Although they (Dirac points) are situated at the same position in the ﬁrst BZ, it is useful to make a clear conceptual distinction between the Dirac points D and D', which are deﬁned as the contact points between the two bands, andthe crystallographic points K and K', which are deﬁned as the corners of the ﬁrst BZ. There are indeed situations where the Dirac points move away from the points K and K'.

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