Metastable states of graphene Dirac fermion in potential barrier. (October 2019) - Kuwata, S; Takehisa, D
Abstract: Weak quantization of the Dirac equation under a potential barrier (with height V0 ) indicates that while the bound state of Dirac fermion (with energy E0 ∈ ℝ and mass m ) is allowed for | E 0 | < m, the Dirac fermion is metastable for | E 0 | > m . Under the condition V0 » m, which is well satisfied for typical graphene, it is found that the tunneling time Δ t and the lifetime τ for the metastable state are related as Δ t ≳ 2τ. As m decreases, it follows that Δ t /τ tends to increase and behaves as log(l/ m ) up to higher order logarithmic correction.