Strain Induced One-Dimensional Landau-Level Quantization in Corrugated Graphene

TL;DR

This paper demonstrates that ripples in graphene induce effective pseudomagnetic fields leading to zero-energy Landau levels, resulting in flat bands in one dimension, confirmed through microscopy and theoretical modeling.

Contribution

It provides experimental and theoretical evidence that graphene ripples generate pseudomagnetic flux causing one-dimensional Landau-level quantization.

Findings

Zero-energy Landau levels form when pseudomagnetic flux exceeds flux quantum.

Flat bands appear in one direction but not in the perpendicular direction.

Fermi velocities in the perpendicular direction remain unaffected.

Abstract

Theoretical research has predicted that ripples of graphene generates effective gauge field on its low energy electronic structure and could lead to zero-energy flat bands, which are the analog of Landau levels in real magnetic fields. Here we demonstrate, using a combination of scanning tunneling microscopy and tight-binding approximation, that the zero-energy Landau levels with vanishing Fermi velocities will form when the effective pseudomagnetic flux per ripple is larger than the flux quantum. Our analysis indicates that the effective gauge field of the ripples results in zero-energy flat bands in one direction but not in another. The Fermi velocities in the perpendicular direction of the ripples are not renormalized at all. The condition to generate the ripples is also discussed according to classical thin-film elasticity theory.