Geometry-controlled engineering of the low-temperature proximity effect in normal metal–superconductor junctions

• Munisa A. Tomayeva,
• Vyacheslav D. Neverov,
• Andrey V. Krasavin,
• Alexei Vagov and
• Mihail D. Croitoru

Beilstein J. Nanotechnol. 2025, 16, 2265–2273, doi:10.3762/bjnano.16.155

• length scale set by the superconducting coherence length ξs[5][59][60]. In the SC, near the NS boundary, the superconducting order parameter Δs(z) is governed by the self-consistent Bogoliubov–de Gennes equations. Linearizing these equations under the assumption of a weak perturbation (i.e., Δs(z

• decay of the Cooper pair amplitude, the effective transparency of the junction, and the induced proximity gap in the normal region. Employing a fully numerical self-consistent solution of the Bogoliubov–de Gennes equations, we analyzed a variety of boundary geometries without relying on simplifying

• interface governs the transparency of the clean NS junction and thus influences the proximity effect. These results deepen our understanding of how geometry and the proximity effect interact, which is important for the design and optimization of superconducting hybrid devices. Keywords: Bogoliubov–de

Hartree–Fock interaction in superconducting condensate fractals

• Edward G. Nikonov,
• Yajiang Chen,
• Mauro M. Doria and
• Arkady A. Shanenko

Beilstein J. Nanotechnol. 2025, 16, 2177–2182, doi:10.3762/bjnano.16.150

• solve the Bogoliubov–de Gennes equations and show that, beyond the half-filling, the HF potential significantly enhances the self-similar spatial oscillations of the order parameter while simultaneously reducing its average value and altering its critical exponent. Consequently, the critical temperature

• for quasicrystalline superconductors are to the inclusion of the HF potential in the fundamental microscopic equations. Our work addresses this open problem through an investigation of the superconducting Fibonacci chain, a standard prototype for quasiperiodic systems. Bogoliubov–de Gennes Equations

• state ν, σ, respectively. The quasiparticle wave functions obey the Bogoliubov–de Gennes equations where εν is the quasiparticle energy. As a result of the diagonalization, one obtains where fν is the Fermi–Dirac distribution of bogolons with the quasiparticle energy εν. The quantum number ν enumerates

Interplay between pairing and correlations in spin-polarized bound states

• Szczepan Głodzik,
• Aksel Kobiałka,
• Anna Gorczyca-Goraj,
• Andrzej Ptok,
• Grzegorz Górski,
• Maciej M. Maśka and
• Tadeusz Domański

Beilstein J. Nanotechnol. 2018, 9, 1370–1380, doi:10.3762/bjnano.9.129

• Green’s functions can be computed numerically from the solution of the Bogoliubov–de Gennes equations of this model (Equation 10). The net spin current turns out to be predominantly sensitive to the Majorana end-modes. Its differential conductance can thus distinguish the polarized Majorana