Index Theorem Defines Subgap Andreev Bands in Josephson Junctions, Revealing Topological Response

Josephson junctions, devices enabling the flow of superconducting current between two materials, exhibit intriguing quantum states known as Andreev bound states within their energy gap, and a team led by Sinchan Ghosh from the Indian Association for the Cultivation of Science, along with Srinjoy Ghosh and Arijit Kundu from the Indian Institute of Technology, Kanpur, now reveals the underlying principles governing these states. The researchers demonstrate that these subgap states arise from a fundamental mathematical relationship known as the index theorem, offering an exact solution to the equations describing quasiparticles within the junction. This work establishes a clear distinction between junctions made from different types of superconductors, showing that those utilising conventional materials exhibit a robust and stable response to external disturbances, a protection not found in junctions employing more exotic superconducting states. By connecting the mathematical framework to the physical properties of these devices, the team’s findings advance understanding of superconductivity and offer insights for designing more resilient quantum electronic components. Altermagnetism’s Influence on Unconventional Superconductivity This collection of research explores the interplay between altermagnetism, a unique magnetic order, and superconductivity, the phenomenon of zero electrical resistance. The central theme is how altermagnetism can induce or modify superconducting properties, potentially leading to novel pairing symmetries and superconducting states. Researchers investigate unconventional superconductivity, which deviates from standard theoretical frameworks and exhibits unusual characteristics. Josephson junctions, weak links between superconductors, and Andreev reflection serve as crucial tools for probing these superconducting properties. Researchers examine how altermagnetism affects the currents flowing through Josephson junctions and the behavior of Andreev bound states, potentially revealing the presence of exotic particles called Majorana fermions. A recurring focus is the search for topological superconductivity, a state of matter that supports Majorana fermions, which hold promise for future quantum computing technologies. The collection strongly suggests that altermagnetism offers a powerful route to inducing or enhancing unconventional superconductivity. The unique magnetic order and spin-orbit coupling within altermagnets create conditions favorable for unconventional pairing, potentially providing a platform for realizing Majorana fermions essential for topological quantum computing.

This research highlights the richness and complexity of superconducting phenomena, particularly in materials with strong spin-orbit coupling and unconventional magnetic orders, demonstrating an interdisciplinary approach that combines condensed matter physics, materials science, quantum mechanics, and topology. Andreev States via Supersymmetric Quantum Mechanics Scientists investigated Andreev bound states within Josephson junctions, employing a novel approach rooted in supersymmetric quantum mechanics. This work demonstrates that these bound states, particularly in transparent junctions, arise as a direct consequence of the index theorem, a significant theoretical connection. Researchers reformulated the equations describing quasiparticles in superconductors into a supersymmetric form, utilizing the pair potential as a crucial element. This mathematical transformation revealed that the superpotential inherently changes sign across the junction, a key characteristic influencing the behavior of the bound states. To explore this behavior experimentally, the team constructed a lattice model of an itinerant altermagnet expected to exhibit triplet superconductivity with equal-spin-pairing. They then calculated the Josephson current using a computational method that sums the currents flowing between the superconductors. Experiments were conducted on a two-dimensional system with superconductors of finite width and length, connected by a weak link, examining both strong and weak barrier limits, revealing distinct current-phase relationships for each case.

Results demonstrated a sharp periodic behavior proportional to a sine function for the weak barrier limit, with a characteristic jump due to a change in fermion parity. In the strong barrier limit, the periodic behavior transitioned to a different pattern, exhibiting a discontinuity. To assess robustness, scientists introduced localized disorder potential along the edges of the superconductors, varying its strength. For weak disorder, the periodic behavior and jump remained largely unchanged, consistent with topological protection of the subgap Andreev bound states. This detailed analysis confirms the theoretical predictions and highlights the potential for robust Josephson junctions.

Andreev States Explained by Supersymmetric Index Theorem Scientists demonstrate that subgap Andreev bound states in transparent Josephson junctions, comprising chiral or non-chiral superconductors, can be understood through the index theorem in supersymmetric mechanics. The research provides an exact solution for these states, starting from the equations governing quasiparticles in these junctions, revealing that the dispersion of these subgap states depends only on the overall characteristics of the superconducting pairing, rather than its detailed spatial variations. Analysis of the wavefunction of the subgap bound states distinguishes junctions of non-chiral superconductors from those of conventional superconductors.

The team finds a stable topological response, leading to a well-known periodic Josephson effect, protected against weak disorder potential for non-chiral junctions, a protection absent in junctions of conventional superconductors. Numerical computations of Josephson currents, using a lattice model of an itinerant altermagnet expected to host superconductivity with equal-spin-pairing, supplement the analytic results. The work establishes that the equations for superconducting tunnel junctions in the transparent limit can be cast in a supersymmetric form, identifying a superpotential expressed in terms of the pair-potential of the superconductors. This superpotential changes sign across the junction, indicating the existence of bound states as a consequence of the index theorem, precisely the subgap Andreev bound states controlling the low-energy properties of these junctions. The research reveals that these bound states can occur at finite energy, with their dispersion depending on the relative phase of the junction, forming Andreev bands. Crucially, the analysis demonstrates that the wavefunction structure of subgap bound states in junctions necessitates vanishing matrix elements for charged impurities or barrier potentials, preventing hybridization and providing stability to the periodic Josephson effect, independent of microscopic details or local spatial variations. This topological protection arises from the inherent properties of the wavefunction and its resistance to external perturbations.

Andreev States Reflect Superconducting Symmetry This research demonstrates a fundamental connection between the mathematical framework of index theorems in supersymmetric mechanics and the behavior of Andreev bound states, localized quantum states, within Josephson junctions. By solving the equations governing quasiparticles in these junctions, scientists have revealed that the dispersion of these subgap states depends solely on the overall characteristics of the superconducting pairing, rather than its detailed spatial variations. A key finding is the distinction between junctions made from conventional superconductors and those utilizing more exotic materials exhibiting superconductivity. The analysis of the wavefunction of the Andreev bound states reveals that junctions constructed with conventional superconductors exhibit a robust, predictable periodic Josephson effect, even in the presence of minor imperfections. In contrast, junctions incorporating superconductors lack this inherent stability. Numerical simulations, performed using models of superconducting altermagnets, materials with unusual magnetic properties, support these theoretical predictions and suggest the possibility of achieving a periodic Josephson effect, a phenomenon with potential applications in advanced superconducting electronics. The authors acknowledge that their analysis focuses on idealised, transparent junctions and that further investigation is needed to fully understand the behavior of more complex, realistic devices. Future research directions include exploring the impact of junction imperfections and investigating the potential for manipulating the spin polarization of the current flowing through these junctions, which could lead to novel spintronic devices. This work provides a powerful theoretical foundation for understanding and designing advanced superconducting technologies. 👉 More information 🗞 Index-theoretic route to the subgap Andreev bands and topological response in Josephson junctions 🧠 ArXiv: https://arxiv.org/abs/2512.07701 Tags: