'Massless' Electrons in Graphene

In summary: 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?
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sanman
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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?
 
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  • #2
sanman said:
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.
 
  • #3
Thank you for your reply.

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?
 
  • #4
sanman said:
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
 
  • #5
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##.
 
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1. What is graphene and how is it related to massless electrons?

Graphene is a two-dimensional material composed of a single layer of carbon atoms arranged in a hexagonal lattice. It is related to massless electrons because in graphene, the electrons behave as if they have no mass, resulting in unique electronic properties.

2. How can electrons in graphene be considered 'massless'?

In graphene, the electrons behave as if they have no mass because of the unique band structure of the material. The valence and conduction bands touch at specific points in the graphene lattice, known as Dirac points, resulting in an effective mass of zero for the electrons.

3. What are the potential applications of massless electrons in graphene?

The unique properties of massless electrons in graphene make it a promising material for a variety of applications. These include high-speed electronics, ultra-sensitive sensors, and potential use in quantum computing.

4. Are there any limitations or challenges associated with massless electrons in graphene?

While the properties of massless electrons in graphene are promising, there are limitations and challenges that need to be addressed. These include the difficulty in controlling the Dirac points, the effects of impurities and defects on the electronic properties, and the challenge of integrating graphene into existing electronic devices.

5. How are scientists studying and manipulating massless electrons in graphene?

Scientists are using a variety of methods to study and manipulate massless electrons in graphene. These include scanning tunneling microscopy, which allows for the visualization of electronic states in graphene, and techniques such as doping and strain engineering to control the electronic properties of the material.

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