Metastable states of graphene Dirac fermion in potential barrier

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 |E0| < m, the Dirac fermion is metastable for |E0| > m. Under the condition V0 » m, which is well satisfied for typical graphene, it is found that the tunneling time Δt and the lifetime τ for the metastable state are related as Δt ≳ 2τ. As m decreases, it follows that Δt/τ tends to increase and behaves as log(l/m) up to higher order logarithmic correction.