Graphene: structure, properties and synthesis

Graphene is carbon in its simplest two-dimensional form. Each carbon atom is sp² hybridised: three of its electrons form σ bonds to three neighbours in the plane, 120° apart and 1.42 Å long, and the fourth sits in a p orbital perpendicular to the sheet. The p orbitals of all the atoms overlap into the π system that gives graphene its electronic properties (Castro Neto et al. 2009).

The atoms form a honeycomb. It is not a Bravais lattice on its own: it is a hexagonal lattice with a two-atom basis, the A and B sublattices. The cell vectors a₁ and a₂ are 2.46 Å long (√3 × 1.42 Å) and 60° apart, so the cell holds two atoms in 5.24 Ų, which works out at 3.82 × 10¹⁵ atoms per cm² and 0.76 mg per m² (calculated).

Stack graphene sheets on top of one another, every second sheet shifted so that half its atoms sit over hexagon centres, and you have graphite (AB or Bernal stacking), with the layers 0.335 nm apart (Sun et al. 2017) and held only by van der Waals forces. That weak bonding between layers is why a single sheet can be peeled off.

1. Mechanical exfoliation. Graphite is peeled apart with adhesive tape; this gave the first few-atom-thick crystals, of remarkably high quality (Novoselov et al. 2004). It is still the route for the best research devices.
2. Liquid-phase and shear exfoliation. Graphite is exfoliated in a solvent whose surface energy matches graphene’s, such as NMP, giving about 1 wt % monolayers (Hernandez et al. 2008); high-shear mixing scales this from hundreds of millilitres to hundreds of litres (Paton et al. 2014).
3. Graphene oxide and reduction. Graphite is oxidised (Hummers & Offeman 1958), split into graphene oxide in water and reduced; easy to scale, but the product stays defective (Luong et al. 2020). See the graphene oxide page.
4. Chemical vapour deposition (CVD). Methane on copper foil gives centimetre-scale films that are mostly one layer, less than 5 % of the area thicker (Li et al. 2009); roll-to-roll transfer makes 30-inch films (Bae et al. 2010).
5. Epitaxy on SiC. Heating silicon carbide in about 1 bar of argon drives off silicon from the Si face and leaves graphene films (Emtsev et al. 2009).
6. Flash Joule heating. A current pulse turns coal, carbon black or plastic waste into gram-scale turbostratic graphene in less than a second (Luong et al. 2020).

• Electronic. The π and π* bands touch at the corners of the Brillouin zone (the K points), where they are linear in momentum: the Dirac cones. Graphene is therefore a zero-gap semimetal whose carriers move at about 10⁶ m s⁻¹ as if they had no mass (Castro Neto et al. 2009). A gate tunes the carriers continuously from electrons to holes, up to 10¹³ cm⁻² (Novoselov et al. 2004).
• Quantum Hall effect. In a magnetic field graphene shows a half-integer quantum Hall effect, σxy = ±4(N + ½)e²/h, a direct signature of its Dirac carriers (Novoselov et al. 2005; Zhang et al. 2005).
• Mobility. About 10,000 cm² V⁻¹ s⁻¹ at room temperature on SiO₂ in the first devices (Novoselov et al. 2004); on atomically flat h-BN, mobility and carrier uniformity are almost an order of magnitude better (Dean et al. 2010).
• Mechanical. Nanoindentation of suspended sheets gave a Young’s modulus of 1.0 TPa and an intrinsic strength of 130 GPa, “the strongest material ever measured” (Lee et al. 2008).
• Thermal. Suspended single layers conduct heat at (4.84–5.30) × 10³ W m⁻¹ K⁻¹ at room temperature (Balandin et al. 2008).
• Optical. One layer absorbs πα = 2.3 % of white light, a value set by the fine-structure constant (Nair et al. 2008).
• Barrier. A defect-free monolayer is impermeable to standard gases, including helium (Bunch et al. 2008).

The 2004 Science paper showed films a few atoms thick that were stable in air, metallic and of high quality, with a strong ambipolar field effect (Novoselov et al. 2004). The following year two groups measured the half-integer quantum Hall effect, confirming that graphene’s carriers behave as massless Dirac fermions (Novoselov et al. 2005; Zhang et al. 2005).

Graphene opened the field of 2D materials. The same peeling and transfer methods gave insulating h-BN, semiconducting MoS₂ and many more, and these layers can be restacked in a chosen order into van der Waals heterostructures (Geim & Grigorieva 2013), including twisted bilayer graphene.

• Transparent electrodes. Roll-to-roll CVD films reached about 125 Ω per square at 97.4 % transmittance (Bae et al. 2010).
• Composites. Graphene sheets in polystyrene conduct electricity above about 0.1 vol % (Stankovich et al. 2006).
• Electronics and physics. High-mobility devices on h-BN (Dean et al. 2010), moiré superlattices and twisted bilayers (Cao et al. 2018).
• Thermal management. Its thermal conductivity makes it an excellent material for thermal management (Balandin et al. 2008).
• Membranes and barriers. Impermeable sheets (Bunch et al. 2008) and graphene oxide laminates that sieve ions (Joshi et al. 2014).
• Quality control. Raman spectroscopy counts layers and measures defects without damage (Ferrari et al. 2006); a monolayer at 532 nm has FWHM(2D) ≤ 35 cm⁻¹ and I(2D)/I(G) ≥ 2 (Muñoz-Vargas et al. 2025).

For a paper, slide or poster, start from the honeycomb: two atoms per cell, bonds of 1.42 Å, and the cell vectors of 2.46 Å if you want to show the lattice. The Dirac physics figure above adds the Brillouin zone and the Dirac cone, the production figure shows how it is made and the Raman figure how it is checked; each opens as an editable LabCanvas figure. The structure drawing is a high-resolution SVG of the figure editor’s graphene object, which you can tilt, ripple or switch to h-BN, MoS₂ or MXene. The crystal structure drawing shows graphite, the AB stack of graphene sheets, from its crystal file and opens in the figure editor, where you can change the style, the number of cells and the view. The 3D model opens in the LabCanvas 3D Studio, where you can add layers or a twist and export a high-resolution image.