Massless fermions Klein tunneling

In summary, physicist Oskar Klein discovered in 1929 that Dirac electrons in graphene can tunnel through potential barriers almost completely, regardless of their width and energy height. This phenomenon, known as Klein tunneling, has been observed experimentally in graphene and has been further studied and expanded upon in various materials and dimensions. However, it should be noted that while electrons in graphene can tunnel through electric barriers, they cannot tunnel through dielectric barriers, as this requires the presence of a specific medium in which quasi-particles can exist. Despite this limitation, researchers have successfully created a graphene tunneling diode using a few atomic layers of boron nitride as a barrier, allowing for resonant tunnelling of quasi-particles.
  • #1
Stanley514
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QUOTE:
"In 1929, physicist Oskar Klein[1] obtained a surprising result by applying the Dirac equation to the familiar problem of electron scattering from a potential barrier. In nonrelativistic quantum mechanics, electron tunneling into a barrier is observed, with exponential damping. However, Klein’s result showed that if the potential is of the order of the electron mass, [PLAIN]https://upload.wikimedia.org/math/5/e/a/5ead404e0410a13fa323d3e8de6b2ced.png, the barrier is nearly transparent. Moreover, as the potential approaches infinity, the reflection diminishes and the electron is always transmitted."

These results were expanded to higher dimensions, and to other types of potentials, such as a linear step, a square barrier, etc. Many experiments in electron transport in graphene rely on the Klein paradox for massless particles.

https://en.wikipedia.org/wiki/Klein_paradox

QUOTE:
However, the Dirac electrons found in graphene can tunnel through energy barriers regardless of their width and energy height; a phenomenon called Klein tunneling, described theoretically for 3D massive Dirac electrons by the Swedish physicist Oskar Klein in 1929. Graphene was the first material in which Klein tunneling was observed experimentally, as massive Dirac electrons required energy barriers too large to be observed.

http://www.springer.com/about+springer/media/springer+select?SGWID=0-11001-6-1292222-0
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QUESTION:
If electrons in graphene can tunnel throug energy barriers regardless of their width and energy height, does it mean they could tunnel through any distance? So, we could make a graphene tunnel diode with 1 km distance between cathode and anode and an empty space (air) in between?
 
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  • #2
Your springer link has incorrect wording (for some reason). It's not electrons that are tunneling, but quasiparticles in graphene (of which, of course, electrons are the physical substratum, but electrons aren't actually tunneling). The potential barrier also is of an electrical nature, not just "any" barrier::http://arxiv.org/abs/cond-mat/0604323 "Such a barrier can be created by the electric field effect using a thin insulator or by local chemical doping".
 
  • #3
ddd123 said:
Your springer link has incorrect wording (for some reason). It's not electrons that are tunneling, but quasiparticles in graphene (of which, of course, electrons are the physical substratum, but electrons aren't actually tunneling). The potential barrier also is of an electrical nature, not just "any" barrier::http://arxiv.org/abs/cond-mat/0604323 "Such a barrier can be created by the electric field effect using a thin insulator or by local chemical doping".
They claim they created graphene tunneling diode with very thing layer of dielectric between graphene sheets.

http://www.researchgate.net/publication/260520206_High_performance_vertical_tunneling_diodes_using_graphenehexagonal_boron_nitridegraphene_hetero-structure

If electrons tunnel through dielectric, does it mean they do actually tunnel through, as you said? And if yes, then their unusual properties apply only to tunneling through electric barrier, but when they tunnel through dielectric, classical tunneling properties stay in the force?
 
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  • #4
Again, the electrons aren't tunneling, the graphene quasiparticles resulting from the collective behavior of the electrons are tunneling. If actual electrons were to tunnel, then the non-relativistic way of tunneling with exponential dampening of the amplitude applies, but it's most likely irrelevant to that article if the purpose is Klein tunneling.
 
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  • #5
ddd123 said:
Again, the electrons aren't tunneling, the graphene quasiparticles resulting from the collective behavior of the electrons are tunneling. If actual electrons were to tunnel, then the non-relativistic way of tunneling with exponential dampening of the amplitude applies, but it's most likely irrelevant to that article if the purpose is Klein tunneling.
So, graphene quasiparticles could tunnel through any kind of electric barrier (electric field?), but through dielectric barrier they tunnel on very small distance only, like regular tunneling particles?
 
  • #6
I think the quasiparticles also tunnel Klein-like through the dielectric barrier (not sure, the abstract isn't very clear). It's just the electrons that tunnel normally.
 
  • #7
ddd123 said:
I think the quasiparticles also tunnel Klein-like through the dielectric barrier (not sure, the abstract isn't very clear). It's just the electrons that tunnel normally.
1) Could this quasiparticles carry energy or information while they tunnel?
2) Could you use just an empty air as a dielectric (in principle)?
3) If they Klain-tunneling through a dielectric barrier, what maximal thickness of such barrier could be acheived?
 
  • #8
The answer to 1) is yes. The Dirac theory predicts 2) - yes; 3) - infinite. But graphene is a realistic case, it's probably different. You should ask in the atomic and solid state subforum.
 
  • #9
The (quasi-)electrons in graphene behave like 2D Dirac particles. However, the arrangement they are talking about in this article is a 3D structure. So that's certainly not Klein tunneling.Furthermore, you certainly can't use a dielectric barrier. Rather, the barrier has to be "vacuum like", i.e. graphene like in our case , up to some applied electric potential.

In graphene, the electrons only behave Dirac like in a small energy band around the Dirac point. This limits the height of the barrier. So there will be no complete transmission.
 
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  • #10
So, Klein tunneling (of electrons or charged quasiparticles) through the air is not possible under any practical conditions?
This one article mentions Photonic Klein tunneling through a dielectric slab.
http://arxiv.org/pdf/1101.3519.pdf

And if it would be possible, what distance could we achieve?

If common tunneling of electrons through dielectric barrier is possible, then why Klain tunneling of either electrons or quasi-particles is impossible?
 
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  • #11
Klein tunnelling is possible for electrons through air (or even better vacuum), but not for quasi-particles for the simple reason that the definition of a quasi particle requires a specific medium (like graphene). No specific medium, no quasi-particles, hence also no tunnelling of quasi particles through no medium (=vacuum).
 
  • #12
DrDu said:
Klein tunnelling is possible for electrons through air (or even better vacuum), but not for quasi-particles for the simple reason that the definition of a quasi particle requires a specific medium (like graphene). No specific medium, no quasi-particles, hence also no tunnelling of quasi particles through no medium (=vacuum).
But they claim created graphene tunneling diode in which quasiparticles(?) tunnel through dielectric barrier (just few atoms thick). How do you explain that?

QUOTE:
Here we report resonant tunnelling of Dirac fermions through a boron nitride barrier, a few atomic layers thick, sandwiched between two graphene electrodes.
http://www.nature.com/ncomms/journal/v4/n4/full/ncomms2817.html
 

Related to Massless fermions Klein tunneling

1. What are "massless fermions"?

"Massless fermions" refer to particles that have zero rest mass and exhibit fermionic behavior, meaning they follow the laws of quantum mechanics and have half-integer spin. Examples of massless fermions include neutrinos and certain types of quarks.

2. What is Klein tunneling?

Klein tunneling is a phenomenon in quantum mechanics where a particle with high energy and momentum can pass through a potential barrier with 100% probability, even if classical physics would suggest that the particle should be reflected. It was first predicted by physicist Oskar Klein in the 1920s.

3. How do massless fermions exhibit Klein tunneling?

Massless fermions exhibit Klein tunneling due to their unique properties, such as having zero rest mass and obeying the laws of quantum mechanics. These properties allow them to behave as both particles and waves, giving them a higher probability of passing through a potential barrier.

4. What are the applications of massless fermions Klein tunneling?

Massless fermions Klein tunneling has potential applications in various fields such as electronics, quantum computing, and particle physics. It could also help us better understand the behavior of particles at the quantum level.

5. Are there any challenges in studying massless fermions Klein tunneling?

Yes, there are challenges in studying massless fermions Klein tunneling, including the difficulty in experimentally observing and manipulating these particles due to their unique properties. Additionally, there is ongoing research and debate about the exact mechanisms behind Klein tunneling and its potential implications.

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