Graphene as an electronic membrane

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 [1,2]. While observations of rippling [3,4,5] added another dimension to the richness of the physics of graphene, scanning single electron transistor images displayed prevalent charge inhomogeneity [6]. 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.Since its unexpected isolation [1], free standing graphene, a single atomic layer of carbon atoms forming a 2D honeycomb lattice, has risen as an intriguing and promising metamaterial. Not only the charming notion of manipulating relativistic fermions on a table top but also the potential of the graphene-based electronics, is propelling the current enthusiasm [2,7]. However, for the graphene-based electronics it is vital to understand the interplay and connection among observed real material aspects.The observations of ripples in suspended graphene using transmission electron microscopy (TEM) [3] and in graphene on SiO 2 substrate using scanning tunneling microscopy (STM) [4,5] summon the membrane aspect of graphene to the foreground. Statistical mechanics of membranes has long been an important branch of soft condensed matter physics [8], with its application to biological systems being one of its driving forces. However, it has been irrelevant for the study of conventional 2D electronic systems which are buried in the semiconductor heterojunction structure. Graphene being a single layer of carbon atoms that can be gated, it forms the first example of an electronic membrane that is subject to direct probes.Electron-hole puddles in graphene imaged by scanning single electron transistor (SET) [6] suggest that such charge inhomogeneity should play an important role in limiting the transport characteristics of graphene. One cause of such charge inhomogeneity could be remote charged impurities in the substrate as it was noted in Refs. [9,10]. By building an effective theory based on microscopic calculations, we find the corrugations to generate inhomogeneous electrochemical potential directly on the graphene membrane; thus identify corrugations as another cause of charge inhomogeneity. We predict control over irregular corrugations to improve the transport properties of graphene greatly. At present, the technology for stabilizing perfectly flat graphene is not available. One possibility is to epitaxially grow monolayer graphene in a controlled manner. While current epitaxial growth technique only yields ...

Quantum effects in graphene monolayers: Path-integral simulations

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Electron scattering on microscopic corrugations in graphene

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Step-edge-induced resistance anisotropy in quasi-free-standing bilayer chemical vapor deposition graphene on SiC

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