Anisotropy-Superconductivity Coupling in High-Entropy AgInSnPbBiTe₅: A Unified Theoretical Framework

Abstract

This work establishes quantitative relationships between magnetic anisotropy energy (E*)

and superconducting properties in high-entropy telluride AgInSnPbBiTe₅ through:

1. Modified McMillan formalism for Tₙ(E*)
2. Anisotropy-dependent Ginzburg-Landau theory
3. μSR-verified penetration depth scaling
4. Strong-coupling gap enhancement model

Key results:

• Tₙ reduction rate: -0.15 meV⁻¹
• Jₙ suppression threshold: E꜀* = 2.1 meV
• λ(0) scaling factor: +5% per meV E* Detailed Description

  This study presents a unified theoretical framework integrating:

  • Fourth-order anisotropy modeling with element-specific weightings (Sn/Ag-dominated K4=+0.34K4​=+0.34 meV, Bi/Pb-induced K6=−0.16K6​=−0.16 meV) 1

  • TF-μSR validation showing strong-coupling behavior (2Δ(0)/kBTc≈102Δ(0)/kB​Tc​≈10) and gap anisotropy (Δ(k)=Δ0[1+K4(αx4+αy4+αz4)+K6(αx2αy2αz2)]Δ(k)=Δ0​[1+K4​(αx4​+αy4​+αz4​)+K6​(αx2​αy2​αz2​)]) 1

  • Disorder-driven effects analogous to Pb-Bi alloys, where configurational disorder modifies gap structures and critical fields 78

  Key advances:
  ✓ Experimental-theoretical synergy: R2=0.98R2=0.98 agreement between μSR data and anisotropy model 1
  ✓ Anisotropy engineering: Gap maxima along ⟨100⟩⟨100⟩ and suppression along ⟨111⟩⟨111⟩ directions 1
  ✓ High-entropy tuning: Leveraging chemical disorder to enhance spin-orbit coupling and pairing anisotropy, akin to Pb-Bi systems