Klein Tunneling

Klein Tunneling ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Outline ,[object Object],[object Object],[object Object],[object Object],[object Object]

Classical Picture Kinetic Energy = E Mass of the ball = m H E < mgH E = mgH E > mgH

Tunneling ,[object Object],[object Object],[object Object]

Quantum tunneling effect ,[object Object],[object Object],[object Object]

Quantum tunneling effect ,[object Object],[object Object],Tunneling = Transmission through the potential barrier V Ψ (x) Ψ ʹ (x) E < V

Tunneling Source: http://en.wikipedia.org/wiki/Quantum_tunneling Reflection Interference fringes Transmission Tunneling

Klein Tunneling ,[object Object],[object Object],[object Object]

Tunneling in Graphene ,[object Object],[object Object],[object Object]

Absence of backscattering ,[object Object],[object Object],Conduction band Valence band d min 0 x y

Absence of backscattering ,[object Object],[object Object],Conduction band Valence band e - Potential barrier

Band structure d U E F Conduction band Valence band U 0 0 x

Absence of backscattering ,[object Object],[object Object],[object Object],[object Object]

Klein tunneling ,[object Object],[object Object],[object Object],d min Electron-like (E,p y ) Hole-like (E,p y ) Conduction band Valence band

Klein tunneling ,[object Object],Condition:

Transmission resonance ,[object Object],[object Object],No transmission resonance Conduction band Valence band e - Potential barrier P y =0

Bipolar junctions ,[object Object],n++ Si (back gate) top gate SiO 2 PMMA Ti/Au graphene Ti/Au Ti/Au Lead Lead

Bipolar junctions ,[object Object],[object Object],In the Valence band inside the barrier ( p -doped region) In the Conduction band outside the barrier ( n -doped region) d U E F Conduction band Valence band U 0 0 x

Bipolar junctions ,[object Object],U 0 E F x n n p d U Fermi momenta in both the n and p regions are given by: d ≈ 80 nm † † Measured by Huard et al (2007) for their device.

Bipolar junctions ,[object Object],[object Object],[object Object]

Bipolar junctions ,[object Object],[object Object],[object Object],† Cheianov and Fal’ko, 2006

Applications of tunneling ,[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object]

Dr. Leo Esaki (b. 1925, Osaka, Japan)

Klein Tunneling

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Klein Tunneling