# Klein tunnelling and Hartman effect in graphene junctions with proximity exchange field

## TL;DR

This paper theoretically investigates spin-dependent Klein tunnelling and the Hartman effect in graphene junctions with proximity-induced exchange fields, analyzing how a spectral gap influences tunnelling properties.

## Contribution

It introduces a detailed theoretical analysis of Klein tunnelling and the Hartman effect in graphene with proximity exchange fields, considering the impact of a spectral gap.

## Key findings

- Klein tunnelling is spin-dependent in these systems.
- The spectral gap significantly affects tunnelling behavior.
- Group delay and Hartman effect are analyzed in the context of graphene junctions.

## Abstract

Tunnelling of electrons in graphene-based junctions is studied theoretically. Graphene is assumed to be deposited either directly on a ferromagnetic insulator or on a few atomic layers of boron nitride which separate graphene from a metallic ferromagnetic substrate. Such junctions can be formed by appropriate external gating of the corresponding system. To describe low-energy electronic states near the Dirac points, certain effective Hamiltonians available in the relevant literature are used. These Hamiltonians include staggered potential and exchange interaction due to ferromagnetic substrates. Tunnelling in the systems under consideration is then spin-dependent. The main focus is on Klein tunnelling and also on the group delay and the associated Hartman effect. The impact of a gap induced in the spectrum at the Dirac points on tunnelling is analysed in detail.