Nobel Lecture: Graphene: Materials in the Flatland^*

Much like the world described in Abbott’s Flatland, graphene is a two-dimensional object. And, as “Flatland” is “a romance of many dimensions,” graphene is much more than just a flat crystal. It possesses a number of unusual properties which are often unique or superior to those in other materials. In this brief lecture I would like to explain the reason for my (and many other people’s) fascination with this material, and invite the reader to share some of the excitement I’ve experienced while researching it.

Figure 1

The crystal structure of graphene—carbon atoms arranged in a honeycomb lattice.

Figure 2

The micromechanical cleavage technique (“Scotch-tape” method) for producing graphene. Top row: Adhesive tape is used to cleave the top few layers of graphite from a bulk crystal of the material. Bottom left: The tape with graphitic flakes is then pressed against the substrate of choice. Bottom right: Some flakes stay on the substrate, even on removal of the tape.

Figure 3

Thin graphitic flakes on a surface of $\mathrm{Si}/{\mathrm{SiO}}_2$ wafer (300 nm of ${\mathrm{SiO}}_2$, purple color). The different colors correspond to flakes of differing thicknesses, from $\sim 100\mathrm{nm}$ (the pale yellow ones) to a few nanometers (a few graphene layers—the most purple ones). The scale is given by the distance between the lithography marks ($200\mu \mathrm{m}$).

Figure 4

Optical micrographs of various 2D crystals (top row) and their crystal structures (bottom row). Left: Flakes of boron nitride on top of an oxidized Si wafer (290 nm of ${\mathrm{SiO}}_2$, the image taken using narrow band yellow filter, $\lambda =590\mathrm{nm}$). The central crystal is a monolayer. Center: A device prepared from monolayer and bilayer ${\mathrm{NbSe}}_2$ crystals on an oxidized Si wafer (290 nm of ${\mathrm{SiO}}_2$). Right: Flakes of ${\mathrm{MoS}}_2$ on top of an oxidized Si wafer (90 nm of ${\mathrm{SiO}}_2$). The piece at the bottom-right corner is a monolayer. Color coding for the crystal structures at the bottom: yellow spheres $=$ boron, purple $=$ nitrogen, large white spheres $=$ niobium, red $=$ selenide, blue $=$ molybdenum, and small white spheres $=$ sulfur.

Figure 5

Chemically modified graphene. One can add different species (such as hydrogen or fluorine) to graphene scaffolding. Carbon atoms are represented by blue spheres.

Figure 6

2D-based heterostructures. $\mathrm{\text{Blue spheres}}=\mathrm{\text{carbon atoms}}$, $\mathrm{\text{yellow}}=\mathrm{\text{boron}}$, $\mathrm{\text{purple}}=\mathrm{\text{nitrogen}}$, $\mathrm{\text{white}}=\mathrm{\text{niobium}}$, and $\mathrm{\text{red}}=\mathrm{\text{selenide}}$.

Figure 7

The low-energy band structure of graphene.

Figure 8

Hall conductivity as a function of the carrier concentration.

Figure 9

Crystal structure of bilayer graphene.

Figure 10

The band structure of bilayer graphene in the vicinity of the $K$ point.

Figure 11

Dr. Sheldon Cooper (Jim Parsons) “…either isolating the terms of his formula and examining them individually or looking for the alligator that swallowed his hand after Peter Pan cut it off.” From The Big Bang Theory, series 3, episode 14 “The Einstein Approximation.” Photo: Sonja Flemming/CBS ©2010 CBS Broadcasting Inc.

Figure 12

Production of graphene membranes for TEM support application. Graphene, grown on metal (a) is covered with a layer of plastic (b). The sacrificial metal layer is etched away and graphene on plastic is fished on a standard TEM grid (c). Upon the removal of the plastic layer (d) the graphene membrane can be exposed to a solution of biomolecules (e) which adsorb on the surface of graphene (f) and can be studied in a TEM.

Figure 13

Ambipolar field effect in graphene.