What basically is Klein tunneling ?

[phywithAK]

Recently, in my quantum physics classes i was introduced to the concept of tunneling of particle through a barrier potential and about transmission probability.
Our instructor mentioned about something known as "Klein tunneling".
Can somebody explain to me what is Klein tunneling and why behavior of the particle which is tunneling changes when barrier potential is approximately equal to rest mass energy,
V≅MC² .

 

[drvrm]

Recently, in my quantum physics classes i was introduced to the concept of tunneling of particle through a barrier potential and about transmission probability.

one has to look up the following

We investigate Klein tunneling for the α−T3 model, which interpolates between graphene and the dice lattice via parameter α. We study transmission across two types of electrostatic interfaces: sharp potential steps and sharp potential barriers. We find both interfaces to be perfectly transparent for normal incidence for the full range of the parameter α for both interfaces. For other angles of incidence, we find that transmission is enhanced with increasing α. For the dice lattice, we find perfect, all-angle transmission across a potential step for incoming electrons with energy equal to half of the height of the potential step. This is analogous to the “super”, all-angle transmission reported for the dice lattice for Klein tunneling across a potential barrier.

Klein tunneling in the α−T3 model
E. Illes and E. J. Nicol
Phys. Rev. B 95, 235432 – Published 26 June 2017

 

[drvrm]

that 1929 paper may be interesting...

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.

Read more at: https://phys.org/news/2011-11-secrets-tunneling-energy-barriers.html#jCp

 

[phywithAK]

that 1929 paper may be interesting...

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.

Read more at: https://phys.org/news/2011-11-secrets-tunneling-energy-barriers.html#jCp

Thanks drvrm for this interesting link, so because of the electrons behaving as massless particles they no longer follow the classical physics energy equation
E=P²/2M ,
and tend to follow relativistic mechanics. So that would mean they would not also follow Schrödinger's equation also.