[Paper Review] Hydrostatic Pressure Dependence of the Superconducting and Structural Properties of MgB2

J. S. Schilling, J. D. Jorgensen+5 more|arXiv (Cornell University)|Oct 12, 2001

Superconductivity in MgB2 and Alloys4 references5 citations

TL;DR

This study investigates the hydrostatic pressure dependence of superconducting and structural properties in MgB2 using high-pressure resistivity and X-ray diffraction. It reveals that Tc decreases linearly with pressure up to 20 GPa, with dTc/dP ≈ -1.5 K/GPa, and shows excellent agreement between experimental Tc(P) data and McMillan formula predictions using pressure-dependent electron-phonon coupling and phonon frequency. The results confirm MgB2 as a conventional BCS superconductor with strong electron-phonon coupling, and suggest Tc could reach zero at ~60 GPa, supporting the phonon-mediated pairing mechanism.

ABSTRACT

In this paper we report parallel in situ neutron powder diffraction and Tc(P) measurements versus pressure on the same MgB2 sample in a He-gas apparatus to 0.6 GPa; in addition, we present Tc(P) measurements in a helium-loaded diamond-anvil-cell to 20 GPa on the same sample. Our results are compared with those of other groups. The high precision achieved in these measurements allows a quantitative evaluation of the change in Tc as a function of the changes in structure. Our results are consistent with electron-phonon pairing in MgB2.

Motivation & Objective

• To determine the hydrostatic pressure dependence of the superconducting transition temperature Tc in MgB2.
• To measure structural changes under pressure using X-ray diffraction to link lattice compression to electronic and superconducting properties.
• To test whether the pressure dependence of Tc supports a phonon-mediated BCS pairing mechanism.
• To assess the role of anisotropic compression on electron-phonon coupling and Fermi surface features in layered MgB2.
• To compare experimental Tc(P) data with theoretical predictions from the McMillan formula using pressure-dependent parameters.

Proposed method

• High-pressure resistivity measurements were performed up to 20 GPa using a helium gas pressure medium to minimize shear stresses.
• X-ray diffraction was used to measure lattice parameters and volume changes under hydrostatic pressure.
• The McMillan formula was applied with pressure-dependent electron-phonon coupling λ(V) and average phonon frequency ⟨ω⟩(V), derived from Grüneisen parameter analysis.
• The Grüneisen parameter γ = -dln⟨ω⟩/dlnV ≈ 2.36 was extracted from high-pressure data at 0.7 GPa to model phonon softening.
• The logarithmic volume derivative of resistivity dlnρRT/dlnV ≈ +4.05 was calculated and compared with experimental dlnρRT/dP ≈ -3%/GPa to validate the electron-phonon model.
• A least-squares fit of Tc vs. relative volume V/V0 was used to estimate the pressure at which Tc → 0 K.

Experimental results

Research questions

• RQ1 How does hydrostatic pressure affect the superconducting transition temperature Tc in MgB2?
• RQ2 To what extent do structural changes under pressure influence electron-phonon coupling and superconductivity?
• RQ3 Does the pressure dependence of Tc align with predictions from the McMillan formula for a BCS superconductor?
• RQ4 What is the role of anisotropic lattice compression in modifying the electronic structure and Fermi surface in MgB2?
• RQ5 Can the observed Tc(P) behavior be explained by changes in phonon frequencies and electron-phonon coupling alone?

Key findings

• Tc decreases linearly with pressure at a rate of dTc/dP ≈ -1.5 K/GPa up to 20 GPa, consistent with BCS theory.
• The McMillan formula, using volume-dependent λ(V) ∝ (V/V0)^3.72 and ⟨ω⟩(V) ∝ (V/V0)^-2.36, shows excellent agreement with experimental Tc(P) data.
• Tc is predicted to extrapolate to zero at approximately 60 GPa, corresponding to V/V0 ≈ 0.76.
• The measured pressure derivative of resistivity dlnρRT/dP ≈ -3%/GPa is in good agreement with the theoretical prediction dlnρRT/dlnV ≈ +4.05, supporting a consistent electron-phonon model.
• The Grüneisen parameter γ ≈ 2.36, derived from high-pressure X-ray data, explains the strong phonon softening and its impact on Tc.
• The results rule out hole superconductivity models, as Tc decreases under pressure despite negligible change in hole carrier concentration.