Graphene is a single-layer honeycomb lattice of carbon atoms that had been predicted but was thought impossible to isolate. Using an extremely simple ‘mechanical exfoliation’ method—repeatedly peeling graphite with Scotch tape—Geim and Novoselov obtained a true monolayer. Hall-effect and other transport measurements showed that its charge carriers behave like massless Dirac particles and possess mobilities far exceeding those of silicon. The work opened the door to ultra-fast transistors, transparent conductive films and a wealth of basic-physics tests such as the quantum Hall effect at room temperature. It also launched the now vast research field of two-dimensional materials.

In their 2004 Science paper the laureates identified monolayers transferred onto SiO₂/Si wafers by optical-interference contrast and verified single-layer thickness with AFM and Raman spectroscopy. The band structure shows linear dispersion near the K points, so charge carriers act as massless fermions with a Fermi velocity of ~1×10^6 m/s and room-temperature mobilities above 2×10^4 cm^2/Vs. Phenomena such as a minimum conductivity of 4e^2/h and the observation of an integer quantum Hall effect confirmed graphene as a Dirac fermion system. This unique combination of electronic behavior, tensile strength (≈130 GPa), thermal conductivity (>3000 W/mK) and optical transparency (~97.7 %) has spurred research into RF devices, flexible electronics and reinforcing composites. Moreover, the idea of stacking atomically thin crystals into van der Waals heterostructures grew directly from this work, providing a versatile platform for two-dimensional materials physics.

Monolayers obtained by mechanical exfoliation exhibit ~2.3 % optical absorption on 300 nm SiO₂, consistent with πα≈π/137. h-BN-encapsulated devices suppress charged-impurity scattering, achieving μ>10^5 cm^2/Vs and enabling integer QHE observation near 300 K. Shubnikov–de Haas oscillations around the Dirac point yield a Berry phase of π, while p–n junction studies report Klein-tunnelling-dominated rectification. EPG and DFT analyses show curvature-induced gaps <10 meV and spin–orbit coupling of order tens of µeV, implying long spin-relaxation lengths. These attributes underpin proposals for topological qubits and THz plasmonic devices, and, through van der Waals epitaxy, stimulate studies of MoS₂/graphene/h-BN superlattices and twist-bilayer flat-band superconductivity, broadening the landscape of strongly correlated 2D phenomena.