# A 'Massless' Electrons in Graphene

#### sanman

So I've read that electrons traveling inside a sheet of graphene are said to travel "masslessly". I'm interpreting this as meaning "zero apparent mass" and not zero actual mass. Presumably, the graphene doesn't somehow weigh less than the sum of its constituent electrons and nuclei.

But given this extraordinary massless behavior by the electrons in the graphene, can it be said that work has been done on the electrons to make them behave this way? If so, then what is doing the work? Where is the energy coming from to cause this unusual behavior of the electrons?

• tech99
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#### PRB147

So I've read that electrons traveling inside a sheet of graphene are said to travel "masslessly". I'm interpreting this as meaning "zero apparent mass" and not zero actual mass. Presumably, the graphene doesn't somehow weigh less than the sum of its constituent electrons and nuclei.

But given this extraordinary massless behavior by the electrons in the graphene, can it be said that work has been done on the electrons to make them behave this way? If so, then what is doing the work? Where is the energy coming from to cause this unusual behavior of the electrons?
The electron in Graphene at the corners of the irreducible brillioun zone where Fermi surface lies behaves like massless Dirac particle. It does not refer to the massless of the electron but the quasiparticle.

#### sanman

So the quasi-particle exists inside the crystal(graphene), and can move masslessly.
But if I apply an electric field while it's moving, then it will move non-masslessly (ie. move in a way that exihibits mass)
In each of these cases, will the surrounding crystal(graphene) feel some action-reaction type of force in relation to the motion of the quasi-particle? Is there a Newtonian type of force that occurs in either of these cases?

Now suppose I arrange to have the quasi-particle move back and forth in the graphene, then it will do so masslessly.
But suppose I allow the quasi-particle to move masslessly in one direction, and then when it is returning back I apply the electric field so that it now moves in a way that exhibits mass.

Due to the asymmetry in this cycle (ie. moving masslessly in one direction, and then moving non-masslessly in the other direction) then is the surrounding crystal (graphene) feeling any net directional force on it?

#### Lord Jestocost

So I've read that electrons traveling inside a sheet of graphene are said to travel "masslessly". I'm interpreting this as meaning "zero apparent mass" and not zero actual mass. Presumably, the graphene doesn't somehow weigh less than the sum of its constituent electrons and nuclei.

But given this extraordinary massless behavior by the electrons in the graphene, can it be said that work has been done on the electrons to make them behave this way? If so, then what is doing the work? Where is the energy coming from to cause this unusual behavior of the electrons?
Maybe, this could be of help: [PDF]The effective mass in graphene - Philip Hofmann

#### DrDu

The absolute value $v$ of a (quasi-)electron in graphene near the Dirac point is constant (this velocity is not equal to the velocity of light c).
If an electric field acts on such an electron, its (quasi-)momentum will increase $\dot{p} = -e E$. Hence it's energy $E=pv$ will increase, too.
Compare this to the increase of a photon which enters a gravitational field. It's momentum and energy will also increase, but it's speed $c$ will remain constant, so that $E=\hbar \nu =pc=\hbar k c$.

• PRB147

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