Pressure weakens coupling strength in In and Sn elemental superconductors

The pressure dependence of the thermodynamic critical field <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>B</a:mi><a:mi mathvariant="normal">c</a:mi></a:msub></a:math> in elemental indium (In) and tin (Sn) superconductors was studied by means of muon-spin rotation/relaxation. Pressure enhances the deviation of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:msub><c:mi>B</c:mi><c:mi mathvariant="normal">c</c:mi></c:msub><c:mrow><c:mo>(</c:mo><c:mi>T</c:mi><c:mo>)</c:mo></c:mrow></c:mrow></c:math> from the parabolic behavior expected for a typical type-I superconductor, suggesting a weakening of the coupling strength <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi>α</e:mi><e:mo>=</e:mo><e:mrow><e:mo>〈</e:mo><e:mi mathvariant="normal">Δ</e:mi><e:mo>〉</e:mo></e:mrow><e:mo>/</e:mo><e:msub><e:mi>k</e:mi><e:mi mathvariant="normal">B</e:mi></e:msub><e:msub><e:mi>T</e:mi><e:mi mathvariant="normal">c</e:mi></e:msub></e:mrow></e:math> (<i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mo>〈</i:mo><i:mi mathvariant="normal">Δ</i:mi><i:mo>〉</i:mo></i:mrow></i:math> is the average value of the superconducting energy gap, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:msub><k:mi>T</k:mi><k:mi mathvariant="normal">c</k:mi></k:msub></k:math> is the transition temperature, and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msub><m:mi>k</m:mi><m:mi mathvariant="normal">B</m:mi></m:msub></m:math> is the Boltzmann constant). As pressure increases from 0.0 to <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"><o:mrow><o:mo>≃</o:mo><o:mn>3.0</o:mn></o:mrow></o:math> GPa, <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"><p:mi>α</p:mi></p:math> decreases linearly, approaching the limiting weak-coupling Bardeen-Cooper-Schrieffer (BCS) value <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"><q:mrow><q:msub><q:mi>α</q:mi><q:mi>BCS</q:mi></q:msub><q:mo>≃</q:mo><q:mn>1.764</q:mn></q:mrow></q:math>. Analysis of the data within the framework of Eliashberg theory reveals that only part of the pressure effect on <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"><r:mi>α</r:mi></r:math> can be attributed to the hardening of the phonon spectra, reflected by a decrease in the electron-phonon coupling constant. Nearly 40% of the effect is caused by an increased anisotropy of the superconducting energy gap. Published by the American Physical Society 2024