Grokene: Graphene-Derived 2D Superconductor

• Grokene is a two-dimensional graphene-derived superlattice engineered with interstitial dopants and lattice buckling to exhibit near-room-temperature superconductivity.
• Its discovery utilizes an AI-guided workflow combining precise DFT, DFPT, and many-body calculations to validate strong electron-phonon coupling and electronic structure perturbations.
• Despite a mean-field T_c above 300 K, intrinsic 2D phase fluctuations limit observable superconductivity, prompting engineering strategies such as few-layer stacking and substrate gating.

Grokene is a two-dimensional graphene-derived superlattice predicted to display ambient-pressure, near-room-temperature superconductivity. Identified via an AI-guided materials discovery workflow employing a fine-tuned LLM and advanced electronic structure calculations, Grokene is notable for its high electron-phonon coupling and robust theoretical support for superconductivity above ambient conditions. Its structural, electronic, and superconducting properties are substantiated by first-principles calculations and many-body theory, but key limitations arise from phase fluctuations intrinsic to two-dimensional systems, especially evidenced by the Berezinskii-Kosterlitz-Thouless (BKT) transition. Multiple strategies are proposed for engineering Grokene to optimize its superconducting performance in practical contexts (Team et al., 2 Jan 2026).

1. Atomic and Electronic Structure

Grokene is constructed from a 4×4 graphene supercell with 6.25 at.% interstitial alkali-analog dopants introduced. Density functional theory (DFT) relaxations (PBE+D3, force < 10⁻³ eV/Å, energy < 10⁻⁶ eV) reveal a deviation from ideal P6/mmm symmetry, yielding P6/m2 due to lattice buckling near dopants. The in-plane lattice parameters are measured as $a = 9.84$ Å and $b = 8.52$ Å, with the dopant positioned at $z = 1.85 \pm 0.05$ Å above the carbon plane. The computed formation enthalpy is $\Delta H_f = -0.06 \pm 0.02$ eV/atom. Phonon dispersion curves exhibit no imaginary modes, and ab initio molecular dynamics in the NVT ensemble (300 K, 1 fs steps, up to 50 ps) confirm dynamical stability of the lattice.

Electronic band structure calculations demonstrate significant perturbation of Dirac cones by dopant-induced effects, pushing the Fermi level to a pronounced van Hove singularity. The density of states at the Fermi level is $N(E_F) = 0.15 \pm 0.02$ states/eV/Ų, in agreement with HSE06/GW benchmarks within 10%.

2. AI-Guided Materials Discovery Workflow

Grokene's identification leverages the Grok-3 LLM, fine-tuned on the Materials Project as of August 2025. This workflow integrates equivariant graph neural network (GNN) embeddings, density of states (DOS) summaries, and an electron-phonon coupling (EPC) meta-predictor. Precision@1 and recall values are reported as 0.41 and 0.37, respectively, for time-split validation (train: 2019–2023, test: 2024–2025), supporting automated and reproducible materials screening.

The closed-loop workflow encompasses:

• Pre-filtering by formation enthalpy threshold ($\Delta H_f < 0.1$ eV/atom),
• Optimization for Fermi-surface nesting near van Hove points,
• Density functional perturbation theory (DFPT) and electron-phonon Wannier (EPW) refinement using GPAW (80 Ry cutoff, $48 \times 48 \times 1$ k-mesh, $12 \times 12 \times 1$ q-mesh, Gaussian smearing 0.03 Ry),
• Final many-body validation via the full isotropic Eliashberg equations and static random phase approximation (RPA) to preclude competing charge/spin density wave instabilities.

Audit trail and data integrity are maintained by anchoring all input/output hashes, parameters, and logs on the Solana blockchain.

3. Superconducting Properties and Calculations

Quantitative superconductivity metrics for Grokene are calculated from the EPW-interpolated Eliashberg spectral function $\alpha^2F(\omega)$, yielding an electron-phonon coupling constant $\lambda = 3.8 \pm 0.3$ and logarithmic-averaged phonon frequency $\omega_{\text{log}} = 1650 \pm 100$ K. Applying the McMillan–Allen–Dynes formula with $\mu^* = 0.10 \pm 0.02$, the mean-field critical temperature is $T_{\text{MF}} \approx 325 \pm 40$ K.

Beyond mean-field, numerical solutions of the self-consistent isotropic Eliashberg equations on the Matsubara axis yield $T_c = 310 \pm 25$ K and a superconducting gap $\Delta(0) \approx 45 \pm 5$ meV, corresponding to $2 \Delta(0)/k_B T_c \approx 3.4 \pm 0.5$. These metrics demonstrate Grokene's strong theoretical potential for ambient-pressure, room-temperature superconductivity.

4. Phase Fluctuations and the BKT Transition

The strict two-dimensionality of Grokene introduces notable phase fluctuations. Long-range superconductivity is limited by vortex–antivortex excitations, leading to a BKT-type transition. Superfluid stiffness, calculated from the EPC-renormalized two-dimensional carrier density ($n_{2D} = (3.5 \pm 1.0) \times 10^{13}$ cm$^{-2}$) and effective mass ($m^* = 1.3 \pm 0.2\, m_e$), determines the BKT transition temperature via $k_B T_{BKT} = (\pi/2) J_s$, with $J_s \simeq \hbar^2 n_{2D}/(4 m^*)$. The resulting $T_{BKT} \approx 120 \pm 30$ K is substantially below the mean-field $T_c$, indicating that superconductivity in monolayer Grokene is observable well below predicted pairing temperatures due to phase disorder.

5. Pathways for Engineering Superconducting Transition Temperature

Several strategies are proposed to enhance $T_{BKT}$ toward room temperature:

1. Few-Layer Stacking: Bilayer Grokene, with weak interlayer Josephson coupling, increases superfluid stiffness, estimating $T_{BKT}$ in the $180$–$200$ K range.
2. Substrate/Gate Engineering: Use of high-$\kappa$ dielectrics or ionic liquid gating enhances screening, potentially raising $n_{2D}$ and lowering $m^*$.
3. Superlattice Optimization: Adjustment of dopant coverage or supercell geometry to shift the Fermi level further into van Hove singularity can elevate $\lambda$ and $\omega_{\text{log}}$ (exemplified by Rb-analog variants with $\lambda \approx 4.1$, $T_{\text{MF}} \approx 340$ K).
4. Controlled Doping: Mixed or co-intercalated dopant species enable tuning of soft-mode phonon frequencies, increasing spectral weight in $\alpha^2F(\omega)$ at low $\omega$.

A plausible implication is that experimental realization of multistacked or optimally doped Grokene could yield observable superconductivity at substantially elevated temperatures, provided phase coherence is preserved.

6. Experimental Considerations and Reproducibility

Synthesis suggestions include vapor-phase alkali doping of CVD or exfoliated graphene under ultrahigh vacuum ($T = 350$–$420$ K, $P = 10^{-8}$–$10^{-7}$ Torr), followed by annealing ($300$–$350$ K) and inert capping (graphene/h-BN) to prevent oxidation. NEB calculations yield a dopant migration barrier of $0.42 \pm 0.05$ eV, indicating metastability at room temperature for the required dopant periodicity. Monte Carlo simulations predict clustering only above $\sim10$–$12$\% coverage.

Measurement priorities include in situ phonon spectroscopy for $\alpha^2F(\omega)$ characterization and superfluid stiffness assessments by THz conductivity, kinetic inductance, and muon spin resonance. Iterative feedback from ARPES, phonon, and transport measurements is critical for refining both the AI pipeline and the experimental window, mitigating previous reproducibility pitfalls in room-temperature superconductor claims. All workflow steps from structure search to convergence scans are fully scripted and version-controlled; input/output hashes and data integrity are anchored via blockchain audit.

7. Significance and Future Directions

Grokene exemplifies the integration of LLM-driven materials proposal, rigorous electron-phonon coupling analysis (DFPT, EPW), and comprehensive many-body validation in reproducible superconductor discovery. Grokene's predicted ambient-pressure and near-room-temperature pairing, with potential improvements via engineering phase coherence, represents a compelling target for experimental realization. Open challenges include confirming stability, verifying predicted superconducting properties in the laboratory, and scaling synthesis methods for device applications (Team et al., 2 Jan 2026).