Quantum Criticality in Monolayer Amorphous Carbon

Amorphous solids represent the extreme limit of structural disorder, in which broken translational symmetry challenges the Bloch description of electronic states. In strictly two dimensions (2D), lattice disorder should lead to complete localization electronic states. In stark contrast, here we show that 2D monolayer amorphous carbon (MAC)– a chemically uniform but maximally disordered random network of π-conjugated carbon retains a quantum-critical extended state at the band centre (E ∼ 0)despite the absence of crystalline order. This is confirmed by correlating lattice disorder with local wavefunction structure in atomic-resolution scanning tunnelling microscopy and spectroscopy. Our statistical analysis of the wavefunction probability density reveals a diverging correlation length and verifies the multifractal scaling relation η = −∆ 2 – characteristic of Anderson criticality– in agreement with atomistic tight-binding calculations. We attribute the presence of this critical state to an emergent chiral symmetry of the continuous random network, described by a Wess-Zumino Witten (WZW) topological term that protects the band-centre. Our results thus identify topological disorder as stabilizing agent for quantum criticality in a strictly 2D amorphous system.