Quantum Criticality in Monolayer Amorphous Carbon

TL;DR

This study demonstrates that monolayer amorphous carbon exhibits a unique quantum critical state near zero energy, characterized by multifractal wavefunctions and topologically protected extended states, marking a first in 2D amorphous systems.

Contribution

It provides the first evidence of Anderson criticality in a strictly 2D amorphous electronic system driven solely by topological disorder.

Findings

Disorder localizes low-energy electronic states in MAC.

A critical-like extended state exists near the band center ($E\,\sim\,0$).

Multifractal scaling relations are verified and supported by calculations.

Abstract

Amorphous solids represent the extreme limit of broken translational symmetry, in which the absence of long-range order removes well-defined crystal momenta and invalidates the Bloch description of electronic states. Monolayer amorphous carbon (MAC) has emerged as a unique realization of a strictly two-dimensional (2D) amorphous lattice defined by a structurally contiguous but topologically disordered $sp^2$-bonded random network devoid of any defined long-range crystal symmetry. From atomic-resolution measurements of multifractal wavefunctions, we show that disorder in MAC effectively localizes the low-energy part of the electronic spectrum but retains an extended critical-like state near the band centre ($E\sim 0$). We conjecture that this state is protected from topological disorder by remnant chiral symmetry surviving within the continuous random network, described by a Wess-Zumino-Witten (WZW) topological term. Near criticality, we verify the multifractal scaling relation $\eta = -\Delta_2$, providing quantitative agreement between independently measured spatial correlation decay and multifractal scaling exponents. Our results are confirmed by atomistic tight-binding calculations that closely mirror the multifractal scaling near $E\sim 0$. Our results establish MAC as the first strictly 2D amorphous electronic system to exhibit Anderson criticality driven purely by topological disorder