It is claimed that electrons in graphene are effectively massless at certain points and tunnel "through barriers of any height and width". If they are "massless", what is their De Broglie wavelength equal to? If it is equal to infinity, does it mean they exist "anywhere in the Universe"? 

Quote

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.

https://phys.org/news/2011-11-secrets-tunneling-energy-barriers.html

What is the "barrier width" and its difference from the "barrier height"? If electrons in graphene can tunnel through the barriers of any width, does it mean they can completely negate any distances?

Edited May 1, 20205 yr by Moreno

Effective mass is not the same as inertial mass.
It is the mass the electron 'appears' to have when subjected to certain fields/forces.
See here...

https://en.wikipedia.org/wiki/Effective_mass_(solid-state_physics)

 

The earliest ( easiest ? ) way quantum tunneling was described to me ( back in 2nd year ) is if you consider the wave nature of the electron as described by a wave packet. If that wave packet is 'wider' than the potential barrier, then some part of the wave packet will lie outside the barrier.
IOW there is a finite probability of finding the electron outside the barrier.
( and as simplistic as this is, it still assumes you are familiar with some aspects of QM )