What the heck is a Dirac electron?By Noel A. GarcÃa ( INL)
We hear everywhere that electrons in graphene (and some other materials) are "Dirac electrons"... but what is a Dirac electron?
It is an electron that follows the Dirac equation. Easy, right?
This statement is true, but probably not very useful, like the cartoon...
To introduce the Dirac equation, we need to talk about a couple of things first, namely quantum mechanics and special relativity.
Quantum Mechanics is a set of laws that describes the behaviour of really tiny things, tiny like atoms, or a bunch of atoms. A complex molecule such a protein is already too big to see any quantum effect.
Special Relativity is a set of laws that describes the behaviour of things moving at velocities close to that of the light.
When you try to merge these two theories you find the problem (one of many) that Schroedinger equation, the one that describes quantum particles, treats time and space asymmetrically, like they were different things, but the main point of special relativity is precisely that there is not such a difference.
Dirac's equation was the solution to this problem. It describes the behaviour of electrons while respecting the symmetry between space and time that is observed in nature.
Or to put it in other way, Dirac's equation describes quantum particles in the relativistic regime.
According to this equation the energy of a particle has two terms, and one is dominant over the other depending on the limit you are working at.
The two limits I will refer here are the limit when the particle has no mass (and hence, it moves at the speed of light), and when the particle moves very very slowly (compared to c, the speed of light). In physics it is useful to define a quantity called "momentum", p that is just the mass times the velocity, so the less momentum a particle has, the slower it is moving.
More:
http://www.spinograph.org/blog/what-heck-dirac-electron
