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:

 

[DarkScareCrow]

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

 

[Drakkith]

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]

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

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'.

 

[pmacias]

The Dirac point, also known as the Dirac cone, is a concept in physics that was first proposed by the British physicist Paul Dirac in the 1920s. It refers to a point in the energy-momentum space of a material where the energy of electrons or other particles is zero and their momentum is also zero. This point is typically found in materials with a linear energy-momentum relationship, such as graphene, where the energy of electrons is directly proportional to their momentum. The Dirac point is significant because it represents a unique state of matter and has important implications for the behavior of particles in the material. It has been extensively studied in the field of condensed matter physics and has led to many important discoveries and applications. In summary, the Dirac point is a fundamental concept in physics that describes a special state of matter and plays a crucial role in understanding the behavior of particles in certain materials.