Quantum Monte Carlo Reveals Graphene Resonating Valence Bond Pairing Energy Depends on Length Satisfying L = N·a

The unusual electronic properties of graphene continue to fascinate physicists, and recent research investigates the potential for resonating valence bond (RVB) pairing within this material. S. Azadi, A. Principi, T. D. Kühne, and M. S. Bahramy explore this phenomenon using advanced quantum Monte Carlo simulations, revealing a surprising link between graphene’s geometry and electron pairing. Their calculations demonstrate that the energy associated with RVB pairing critically depends on the shape of the graphene sample, specifically its length relative to the carbon-carbon bond length. This work establishes that a finite energy gap near the Fermi level is essential for stabilising electron pairing, uncovering a geometry-driven mechanism that governs electron behaviour in confined graphene nanostructures and advances understanding of its potential for novel electronic devices.

Graphene’s RVB State via Quantum Monte Carlo

Scientists are investigating the potential for unconventional superconductivity in graphene by exploring the resonating valence bond (RVB) state, a theoretical framework describing strong electron interactions. This research focuses on accurately simulating strongly correlated electron systems, where the interactions between electrons significantly influence the material’s properties. Researchers carefully define effective core potentials and atomic orbital basis sets to accurately represent the electronic structure of graphene, aiming to understand how electron correlation influences the electronic properties of graphene and determine if RVB states can lead to novel superconducting behavior. They investigated the resonating valence bond (RVB) state within confined graphene structures, constructing rectangular samples deliberately avoiding symmetry to observe how the energy gap near the Fermi level responds to dimensional constraints. They discovered that the energy gap vanishes when the sample length corresponds to an integer multiple of the carbon-carbon bond length, while a finite gap emerges otherwise, playing a crucial role in stabilizing electron pairing. 2 milli-Hartree per atom at the thermodynamic limit, demonstrating a geometry-driven mechanism for electron pairing. They constructed the RVB wave function using a Jastrow term, which accounts for short-range Coulomb interactions, and an antisymmetrized geminal power determinant, which describes the singlet pairs. They employed both Jastrow-Slater-determinant and Jastrow-antisymmetrized-geminal-power approaches to evaluate the energy associated with electron pairing within the graphene structure, constructing rectangular samples specifically designed without rotational symmetry to observe how the energy gap near the Fermi level responds to changes in sample size. Data demonstrates that stable RVB pairing occurs only when a finite energy gap exists near the Fermi level. Diffusion Monte Carlo calculations predicted an absolute pairing energy of approximately 0.

48 milli-Hartree per atom at the thermodynamic limit. This research reveals a geometry-driven mechanism for electron pairing within confined graphene nanostructures, highlighting the crucial role of sample size and shape in determining electronic properties. The study clarifies that the size dependence of single-particle energy states differs in nanoscale graphene compared to infinite systems, suggesting that correlation-driven phenomena, such as spin-liquid states and superconductivity, are strongly size-dependent.

Geometry Drives Electron Pairing in Graphene

This research demonstrates that the shape of confined graphene nanostructures directly influences electron pairing. Specifically, the simulations showed that when the length of the graphene sample along one axis corresponds to a multiple of a specific distance related to the carbon-carbon bond length, the energy gap vanishes, suppressing electron pairing. The team calculated the pairing energy, finding a value of approximately 0.

48 milli-Hartree per atom in the thermodynamic limit, indicating a preference for a non-metallic ground state. These findings suggest that controlling the geometry of graphene nanostructures offers a pathway to engineer materials with tailored electronic characteristics. The authors acknowledge that their calculations were performed on finite system sizes, and future work will focus on exploring the implications of this geometry-driven gap opening, including its effect on massless Dirac fermions, Berry curvature, valley physics, and the suppression of Klein tunneling.