The secrets of tunneling through energy barriers

November 7, 2011

Electrons moving in graphene behave in an unusual way, as demonstrated by 2010 Nobel Prize laureates for physics Andre Geim and Konstantin Novoselov, who performed transport experiments on this one-carbon-atom-thick material. A review article, just published in EPJ B, explores the theoretical and experimental results to date of electrons tunneling through energy barriers in graphene.

As good an at room temperature as copper graphene is, it also outperforms all other known materials as a heat conductor. It is both very dense due to its structure and almost completely transparent, making it suitable, among other applications, for touch screens and light panels.

What could partly explain graphene's properties is that electrons travelling inside the material behave as if they were massless. Their behavior is described by the so-called massless Dirac equation that is normally used for high-energy particles such as neutrinos nearing the speed of light. However, electrons in graphene move at a constant speed 300 times smaller than that of light.

In this review, P.E. Allain and J.N. Fuchs, both from the Université Paris-Sud, focus on the tunneling effect occurring when Dirac electrons found in graphene are transmitted through different types of energy barriers. Contrary to the laws of classical mechanics, which govern larger scale particles that cannot cross energy barriers, electron tunneling is possible in quantum mechanics – though only under restricted conditions, depending on the width and energy height of the barrier.

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.

Explore further: Bilayer graphene is another step toward graphene electronics

More information: Allain PE, Fuchs JN (2011). Klein tunneling in graphene: optics with massless electrons. European Physical Journal B (EPJ B). DOI 10.1140/epjb/e2011-20351-3

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not rated yet Nov 07, 2011
"electron tunneling is possible in quantum mechanics". does anyone know physically how it work?
2.7 / 5 (3) Nov 07, 2011
A well known example of Klein tunneling is the tunneling through Josephson's junction or - even more illustrative - the passing of superfluous helium through porous membranes and its climbing across various barriers, i.e. tunneling through gravitational potential.


The so-called supersolidity and the crunching of cold snow could be the effects of the same category. The snow is too hot for some permanent quantum effects, so that the ballistic transport of water molecules at the surface of snow flakes takes place in it only temporarily.
1.8 / 5 (4) Nov 07, 2011
does anyone know physically how it work
The dense aether model enables to imagine the vacuum like density fluctuations of hypothetical dense gas. The density fluctuations are random and when two such
fluctuations appear together, they're behaving like temporal tunnel or microscopic worm hole, enabling to jump particles across trench of potential energy.

It's similar to the escapement of fish from nearly full bucket, when the surface of water undulates in it wildly. At the moment, when surface wave spills over the brim of bucket, the fish can escape from it. But the Klein tunneling is a bit more tricky than this simple analogy.
1.5 / 5 (4) Nov 07, 2011
The Klein tunneling applies to situation, when the fish itself changes into surface wave, which interferes with the surface barrier. The peeling of carbon layer from graphene results into mutual compression of movable electrons. Such electrons are moving collectively like elastic network of mutually repulsing balls. The charge is transfered through the array of such electrons in a longitudinal waves and we cannot say exactly, which particular electron is responsible for its transfer. The carrier velocity is independent to their energy and it remains a much higher then the barrier. Because the repulsive forces between electrons in graphene are comparable to the attractive forces between electrons and carbon atom nuclei, they can switch their positions freely. At the case of thin potential barrier such electrons aren't required to tunnel through it - they can escape into lower layers of atoms like so-called valence electrons and expel the hole from the other side of barrier at distance.
1.3 / 5 (4) Nov 07, 2011
You can imagine, whereas the graphene isn't bulk superconductor, it actually exhibits so-called pseudogap state, being composed of many isolated and temporal islands of superconductive phase which are appearing and dissapearing again randomly across the surface of graphene flake. The energetic barriers in undoped graphene are rather low, in the range of few hundreds of milielectronvolts. But if we would dope the graphene via charge injection in the opposite way at both sides, we can increase the height of potential barrier and we can achieve the similar situation, like at the case of Josephson junction. After then we can measure the Josephson current tunneling through undoped region of graphene stripe even at the room temperature. We actually achieved a room temperature superconductivity - just at the very small area between electrodes, which are injecting electrons and holes into graphene.
3 / 5 (2) Nov 08, 2011
Are we are living at Josephson junction?
not rated yet Nov 08, 2011
Callippo, J Prins claims to have done something similar with diamond doping to achieve room temperature superconductivity.

5 / 5 (1) Nov 08, 2011
"electron tunneling is possible in quantum mechanics". does anyone know physically how it work?
The uncertainty principle states that we cannot know both the exact position and momentum of a particle. Consider the barrier as the observer in this case. If the obstacle is small enough, there is a finite chance that the particle will be on either side of the obstacle. Hence, that is the chance it will appear on the other 'side' of the barrier. For sufficiently thin barriers around the plank distance, the height could be infinitely high, for thicker ones, or barriers of non-step shape, you must solve Schrodinger's equation as an integral for every combination of thickness as you move up the 'wall' to determine the probability of tunneling.
1 / 5 (1) Nov 09, 2011
does anyone know physically how it work? ..The uncertainty principle states that we cannot know both the exact position and momentum of a particle.
This explanation is OK with respect to mainstream physics, but this is how the tunnelling works mathematically. The real physical interpretation covers some geometric insights too, which is not contained in formal explanation.
1 / 5 (1) Nov 09, 2011
Callippo, J Prins claims to have done something similar with diamond doping to achieve room temperature superconductivity.


Yep, I know about it and IMO it's the most significant finding of contemporary physics after cold fusion (and as such ignored with mainstream physicists too). It's closely related to the graphene superconductivity model above explained.


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