Tunneling and transmission resonances of a Dirac particle by a double barrier

TL;DR

This paper investigates the tunneling and scattering of a Dirac particle through double barriers, revealing how transmission resonances alter energy resonance shapes and affect time-delay characteristics.

Contribution

It introduces a detailed analysis of Dirac particle tunneling through double barriers using scattering matrix formalism, highlighting the impact of transmission resonances on energy profiles.

Findings

Transmission resonances modify Lorentzian energy resonance shapes.

Additional maxima appear in transmission coefficients at resonance energies.

Maxima of Wigner time-delay depend on resonance positions.

Abstract

We calculate the tunneling process of a Dirac particle across two square barriers separated a distance $d$, as well as the scattering by a double cusp barrier where the centers of the cusps are separated a distance larger than their screening lengths. Using the scattering matrix formalism, we obtain the transmission and reflection amplitudes for the scattering processes of both configurations. We show that, the presence of transmission resonances modifies the Lorentizian shape of the energy resonances and induces the appearance of additional maxima in the transmission coefficient in the range of energies where transmission resonances occur. We calculate the Wigner time-delay and show how their maxima depend on the position of the transmission resonance.