Symmetry-broken superconducting configurations from density functional theory for bcc and hcp metals and Nb₃Sn

We recently proposed a unified theoretical framework for superconductivity that broadens the applicability of Bardeen–Cooper–Schrieffer theory to both conventional and unconventional superconductors. Within this framework, superconductivity arises from the formation of a symmetry-broken superconducting configuration (SCC) generated by atomic perturbations of the normal conducting configuration (NCC). The SCC emerges through electron–phonon interactions and gives rise to distinct straight one-dimensional tunnels (SODTs) in the SCC–NCC charge density difference of electrons and/or holes. These SODTs originate from regular and systematic atomic displacements between the SCC and NCC, a phenomenon revealed by density functional theory (DFT) calculations. To further verify this framework, we performed DFT-based calculations for 12 hexagonal close-packed (hcp) elements (Be, Mg, Sc, Y, Ti, Zr, Hf, Tc, Re, Ru, Os, and Zn), 5 body-centered cubic (bcc) elements (V, Nb, Ta, Mo, and W), and the compound Nb₃Sn, all examined at 0 K and 0 GPa. Most materials exhibit robust SODTs consistent with known superconducting behavior, while Mg, Sc, and Y are identified as marginal cases, showing functional-dependent SODT signatures indicative of extremely weak superconducting instabilities at ambient pressure. These results support the usefulness of SODTs as a qualitative real-space descriptor of superconductivity-compatible electronic structures within the current limitations of DFT.