Superconductivity in the Intercalated Graphite Compound CaC₆ and the Roeser–Huber Formalism

The superconducting transition temperature, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mi>c</mi></msub></semantics></math></inline-formula>, of the graphite intercalation compound, Ca<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="normal">C</mi><mn>6</mn></msub></semantics></math></inline-formula>, was calculated using the Roeser–Huber (RH) formalism. This method was adapted to alloys with complex crystal structures by identifying symmetric paths for the superconducting charge carriers (Cooper pairs) and incorporating interactions with neighboring atoms through phonon coupling. The evaluation of the lowest energy levels, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>Δ</mo><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></msub></semantics></math></inline-formula>, along all relevant crystallographic directions reveals a slight anisotropy between the in-plane and out-of-plane directions, consistent with the experimental observation of the gap anisotropy by point contact spectroscopy. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mi>c</mi></msub></semantics></math></inline-formula> values obtained for Ca<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="normal">C</mi><mn>6</mn></msub></semantics></math></inline-formula>, Ca<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="normal">C</mi><mn>6</mn></msub></semantics></math></inline-formula> with applied high pressure, and Yb<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="normal">C</mi><mn>6</mn></msub></semantics></math></inline-formula> show good agreement with experimental data, thereby supporting both the validity of the RH approach and its predictive capability in describing superconductivity within complex crystal structures.