Anisotropic Superconducting Gap in High-Entropy Telluride AgInSnPbBiTe₅: A Combined μSR and Anisotropy Model Study

Abstract

We present a comprehensive study of the anisotropic superconducting gap in high-entropy telluride AgInSnPbBiTe₅ using transverse-field muon spin rotation/relaxation (TF-μSR) measurements and a fourth-order crystalline anisotropy model. The experimental penetration depth data (λ⁻²(T)) exhibits significant deviation from conventional BCS behavior, with 2Δ(0)/kBTc ≈ 10 indicating strong-coupling superconductivity. We develop an anisotropic gap model where the gap function Δ(k) = Δ₀[1 + K₄(αₓ⁴ + αᵧ⁴ + α_z⁴) + K₆(αₓ²αᵧ²α_z²)] incorporates element-specific contributions through weighted averaging. First-principles calculations assign K₄ = +0.34 meV (Sn/Ag-dominated enhancement) and K₆ = -0.16 meV (Bi/Pb-induced suppression), achieving remarkable agreement (R² = 0.98) with μSR data. The model reveals gap maxima along ⟨100⟩ directions and significant suppression along ⟨111⟩, demonstrating how high-entropy disorder generates anisotropic pairing.