Topical Review: The rise of Klein tunneling in low-dimensional materials and superlattices

TL;DR

This review discusses recent progress in Klein tunneling phenomena in low-dimensional materials and superlattices, highlighting theoretical criteria, new material examples, and experimental platforms demonstrating its universality.

Contribution

It establishes a unified framework for Klein tunneling across various materials and wave systems, extending understanding beyond graphene to other low-dimensional structures.

Findings

Klein tunneling criteria based on pseudospin conservation

Multiple types of Klein tunneling identified in diverse materials

Potential for testing in various artificial and natural lattice systems

Abstract

We review recent advances in Klein and anti-Klein tunneling in one- and two-dimensional materials. Using a general tight-binding framework applied to multiple periodic systems, we establish the criteria for the emergence of Klein tunneling based on the conservation of an effective reduced pseudospin. The inclusion of higher-order terms in the wave vector leads to nontrivial matching conditions for wave scattering at interfaces. We further examine the emergence of multiple types of Klein tunneling in two-dimensional materials beyond graphene, including phosphorene and borophene, as well as in one-dimensional systems such as Su-Schrieffer-Heeger lattices. Finally, we discuss how these tunneling phenomena can be tested in both synthesized and artificial lattices, including elastic metamaterials, optical, photonic, phononic, and superconducting platforms, demonstrating the universality of Klein tunneling across different wave natures and length scales.