Non-euclidean Interfaces Enable Exploration of Infinite Graphene Lattice Orientations

The complex interplay between two-dimensional materials and metal surfaces dictates the properties of advanced heterostructures, but traditional research has struggled to fully understand the range of possible arrangements at these interfaces. Li-Qun Shen, Hao-Jin Wang, and Mengzhao Sun, along with colleagues at Yue Chai’s institution, now demonstrate a breakthrough in mapping these arrangements by employing curved, non-Euclidean surfaces, specifically copper, as a model system. Their innovative approach combines advanced microscopy with a powerful machine-learning framework to translate images into detailed three-dimensional surface reconstructions, revealing a unified principle governing how these surfaces form. This work not only resolves longstanding questions about copper’s behaviour, but also establishes a new, generalisable method for understanding and controlling the reconstruction of interfaces between metals and two-dimensional materials, paving the way for improved materials design.

Graphene Growth and Copper Surface Analysis

The research team characterized graphene growth and the copper substrate using techniques including transmission electron microscopy and scanning tunneling microscopy, likely supplemented by X-ray photoelectron spectroscopy, low-energy electron diffraction, and atomic force microscopy. Computer vision and image analysis, including Poisson equation solving, were used to analyse patterns and features in microscopy images. The study highlights that oxygen adsorption significantly reconstructs copper surfaces, influencing graphene nucleation and growth. Graphene growth appears to occur through the attachment of carbon clusters, and strategies to promote growth from a single nucleus are being explored to create large-area single-crystal graphene.

Lower background pressure during chemical vapor deposition is crucial for controlling nucleation density, and techniques like continuous oxygen supply can accelerate growth. Graphene layers induce local lattice expansion in the underlying copper, and evaporative loss of copper during growth can limit quality. Graphene can stabilize copper surface facets, and proton assistance during growth can lead to ultra-flat films. The research also considers concepts like Wulff construction and Herring’s principles, which relate to crystal shape and surface energy minimization, to understand how graphene modifies the copper surface.

Copper-nickel alloys are used to promote fast growth of single-crystalline graphene, and graphene coating improves copper’s oxidation resistance. Achieving high-quality, large-area graphene requires controlling nucleation density, preparing the copper surface carefully, optimizing growth pressure and temperature, and selecting an appropriate carbon source. Careful control of oxygen levels is also essential, as is minimizing copper evaporation during growth.

Curved Surfaces Reveal Reconstruction Thermodynamics

Scientists have achieved a breakthrough in understanding interfacial reconstruction by utilizing curved two-dimensional copper surfaces, a non-Euclidean interface, to explore a continuous spectrum of lattice orientations. Integrating multimodal microscopy with a deep-learning framework allowed the team to translate scanning electron microscopy data into accurate three-dimensional surface morphologies, enabling precise identification of crystal facets. The research demonstrates that reconstruction is governed by a unified thermodynamic mechanism, where high-index facets correspond to specific local minima within the surface energy landscape. Observations of graphene growth on copper revealed that as a spherical cap expands, it forces symmetry breaking and selectively exposes stable facets, resulting in the formation of well-aligned step bunches. These step bunches, composed of high-index facets, transform a smooth dome into a polygonal, faceted mound, capturing the continuous landscape of surface reconstruction in a single experiment. Detailed analysis using electron backscatter diffraction and atomic force microscopy quantitatively characterized the faceted morphology, confirming that secondary steps intersect primary steps at specific angles, constrained by a common crystallographic zone axis.

Graphene Growth Dictates Copper Surface Reconstruction

This research overcomes limitations in studying material interfaces by employing curved copper surfaces to explore the complete range of crystallographic orientations during graphene growth. The team combined experimental techniques with machine learning-enhanced computational modelling to reveal how graphene induces reconstruction of the underlying copper surface. Results demonstrate that the formation of high-index facets on the copper corresponds to stable, low-energy configurations, establishing a clear link between surface orientation and thermodynamic stability. The study provides a comprehensive map of all possible reconstructed facets for graphene on copper, resolving a long-standing challenge in understanding this material system. The researchers validated their findings through a robust comparison between experimental observations and theoretical predictions, confirming the energy-driven nature of the reconstruction process. While focused on copper and graphene, the methodology, using non-Euclidean geometries to investigate continuous parameter spaces, offers a broadly applicable framework for studying interfacial reconstruction in diverse two-dimensional materials and metal combinations.