# Super-Klein tunneling of Klein-Gordon particles

## TL;DR

This paper analyzes super-Klein tunneling of Klein-Gordon particles, deriving conditions for total transmission through potential barriers and confirming predictions with numerical calculations.

## Contribution

It introduces an analytical impedance matching condition for super-Klein tunneling in Klein-Gordon systems, including effects of scalar and vector potentials.

## Key findings

- Super-Klein tunneling occurs at half the barrier potential energy.
- Impedance matching leads to omnidirectional total transmission.
- Numerical results confirm theoretical predictions.

## Abstract

We study the total transmission of quantum particles satisfying the Klein-Gordon equation through a potential barrier based on the classical wave propagation theory. We deduce an analytical expression for the wave impedance for Klein-Gordon particles. From the condition that the impedance is matched throughout the space, we show that super-Klein tunneling, which refers to the omnidirectional total transmission of particles through a potential barrier when the energy of the particle is equal to the half of the barrier potential, should occur in these systems. We also derive a condition for total transmission of Klein-Gordon particles in the presence of both scalar and vector potentials and discuss the influence of weak scattering at the interfaces on super-Klein tunneling. The theoretical predictions are confirmed by explicit numerical calculations of the transmittance based on the invariant imbedding method.