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"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, [Broken] 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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# Massless fermions Klein tunneling

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