Theoretical Prediction of Bounded 167 K – 316 K Superconductivity in hBN-Encapsulated, Uniaxially Strained Magic-Angle Trilayer Graphene via Proximity Effect

Abstract

Version 2 Update (August 2026): This dataset and manuscript have been significantly expanded to include rigorous Density Functional Theory (DFT) calculations and Bistritzer-MacDonald (BM) Continuum Model proofs. The new theoretical data validates the emergence of ultra-flat bands and a massive Van Hove Singularity exactly at the Fermi surface (Energy = 0) for the 1.56° twisted moiré superlattice. This mathematically confirms the necessary electron degeneracy required to achieve the unshielded 167 K and shielded 315 K critical temperature (Tc) thresholds previously predicted by the IBM Qiskit and CHGNet heuristic proxies. The updated manuscript and corresponding theoretical dispersion graphs are included. Achieving high-temperature superconductivity at ambient conditions remains one of the preeminent challenges in condensed matter physics. We propose a novel quantum heterostructure capable of sustaining a theoretical superconducting critical temperature (Tc) bounded between 167.3 K (unshielded lower-bound) and 315.6 K (macroscopic upper-bound). Our architecture utilizes Magic-Angle Trilayer Graphene (MATTG) symmetrically encapsulated by monolayer Hexagonal Boron Nitride (hBN) and proximitized by Copper (Cu) thin films. Using the CHGNet Neural Network Potential, we conduct large-scale (~4,100 atom) atomistic simulations to prove structural and thermal stability up to 350 K. To maximize the Van Hove singularity, we implement a dynamic uniaxial strain loop, identifying a catastrophic structural fracture limit at 1.40% and optimizing the lattice at a 1.39% "Redline" strain. We further employ IBM Qiskit Aer to model the Attractive Hubbard Model, proving a 98.74% Cooper pair trapping efficiency. Open Quantum System modeling of thermal decoherence and heat transport establishes the 167.3 K baseline and validates the thermal shielding properties of the hBN gaskets. We submit these empirical proxy simulations as an urgent call-to-action for experimental verification via Molecular Beam Epitaxy (MBE) and rigorous Density Functional Theory (DFT) band-structure mapping.