A Thermodynamic Pinning Criterion for Two-Dimensional Structural Superlubricity

• URL: http://arxiv.org/abs/2607.19732v1
• Date: Wed, 22 Jul 2026 04:00:22 GMT
• Title: A Thermodynamic Pinning Criterion for Two-Dimensional Structural Superlubricity
• Abstract summary: Incommensurability and elastic reconstruction do not by themselves define a structurally superlubric phase.<n>We define fully sliding and pinned zero-temperature phases by $limsup_Atoinfty_rm depmax(A)=0$ and $liminf_Atoinfty_rm depmin(A)>0$.
• Score: 1.669738660194889
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Incommensurability and elastic reconstruction do not by themselves define a structurally superlubric phase. We define fully sliding and pinned zero-temperature phases by $\limsup_{A\to\infty}τ_{\rm dep}^{\max}(A)=0$ and $\liminf_{A\to\infty}τ_{\rm dep}^{\min}(A)>0$, respectively; $Λ_n=|V_n|G_{n,i}[D_{\rm rel}^{-1}(\mathbf q_n)]_{ij}G_{n,j}$ measures only reconstruction susceptibility. Translational covariance then proves that a clean, smooth, infinite moiré continuum can reconstruct without acquiring a bulk sliding barrier. We restore atomic sampling in a two-dimensional discrete model of graphene/hBN and test both a diffusion quantum Monte Carlo first-star potential and a 15-harmonic Leven potential across three rational approximants and five directions. No physical-coupling equilibrium or metastable barrier is resolved. The Leven spectrum raises the largest tested $Λ$ from $0.142$ to $0.212$, while artificial scaling through $Λ=1$ reaches uncontrolled strain before a size-independent threshold appears. The tested zero-temperature in-plane models are therefore consistent with an elastically relaxed sliding regime; $Λ=1$ is a reconstruction scale, not a static phase criterion.

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