Graphene as an electronic membrane

TL;DR

This paper explores how the membrane-like properties of graphene influence its electronic behavior, revealing that curvature causes potential variations and that charge inhomogeneity stabilizes ripples, impacting both fundamental understanding and applications.

Contribution

It demonstrates the interplay between graphene's membrane curvature and electronic properties, highlighting how curvature induces potential variations and how charge inhomogeneity stabilizes ripples.

Findings

Curvature generates spatially varying electrochemical potential.

Charge inhomogeneity stabilizes ripple formation.

Graphene's membrane properties significantly affect its electronic behavior.

Abstract

Experiments are finally revealing intricate facts about graphene which go beyond the ideal picture of relativistic Dirac fermions in pristine two dimensional (2D) space, two years after its first isolation. While observations of rippling added another dimension to the richness of the physics of graphene, scanning single electron transistor images displayed prevalent charge inhomogeneity. The importance of understanding these non-ideal aspects cannot be overstated both from the fundamental research interest since graphene is a unique arena for their interplay, and from the device applications interest since the quality control is a key to applications. We investigate the membrane aspect of graphene and its impact on the electronic properties. We show that curvature generates spatially varying electrochemical potential. Further we show that the charge inhomogeneity in turn stabilizes ripple formation.