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arXiv · 2605.14349

Quantum Criticality in Monolayer Amorphous Carbon

Rejaul SK·Hanning Zhang·Artem K Grebenko·Arsen Herasymchuk·Ranjith Shivajirao·Hongji Zhang·Abee Nelson·Zheng Jue Tong·Gagandeep Singh·Naoto Kimiuchi·Yuta Sato·Kazutomo Suenaga·Chee Tat Toh·Rudolf A Romer·Shaffique Adam·Oleg V. Yazyev·Barbaros Ozyilmaz·Bent Weber
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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 $η= -Δ_2$, 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

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Rejaul SK, Hanning Zhang, Artem K Grebenko, Arsen Herasymchuk, Ranjith Shivajirao, Hongji Zhang, Abee Nelson, Zheng Jue Tong, Gagandeep Singh, Naoto Kimiuchi, Yuta Sato, Kazutomo Suenaga, Chee Tat Toh, Rudolf A Romer, Shaffique Adam, Oleg V. Yazyev, Barbaros Ozyilmaz, Bent Weber. 2026-05-14. Quantum Criticality in Monolayer Amorphous Carbon. https://arxiv.org/abs/2605.14349

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