Electron-phonon interactions and Helmholtz free energy in confined systems: Advancing low-dimensional superconductors for quantum technologies

• Quantitative modeling of Helmholtz Free energy in low-dimensional superconductors. • Impact of electron-phonon interaction on superconductivity. • Dimensional confinement and subband effects analyzed. • Inclusion of defect and anharmonic contributions. • Relevance to quantum technologies and material design. The thermodynamic and superconducting properties of low-dimensional superconductors are profoundly influenced by electron–phonon interactions, which play a critical role in determining the Helmholtz free energy. Therefore, the quantitative study of Helmholtz free energy using electron–phonon interactions in low-dimensional superconductors is essential to comprehending and improving superconducting materials which are also the building blocks of developing quantum technologies. This article presents a quantitative analysis of our theoretically developed model with the impact of electron–phonon coupling on the Helmholtz free energy in low-dimensional superconductors. Using Green’s function methods and advanced many-body theory, we thoroughly examine the changes in the free energy landscape caused by changes in electron–phonon coupling strengths, temperature variation, effects of defects, and system dimensionality with the confinement phenomenon. The analysis also encompasses the behavior of electron–phonon interactions in quantum wells, offering insights into energy confinement and the effects of temperatures. The findings indicate notable changes in thermodynamic properties, especially in systems characterized by reduced dimensionality with the confinement of electrons in one dimension. The findings also underscore the significant impact of electron–phonon interactions on enhancing superconducting performance and establishing a framework for customizing superconducting material properties. The proposed quantitative model based on Helmholtz free energy and electron–phonon interactions provides a powerful framework for exploring the properties of low-dimensional superconductors, especially as they relate to practical applications in quantum technology.