Altermagnet Josephson Junctions Enable Magnetic-Field-Free, Parity-Protected Qubits via Andreev-Bound-State Spectrum Control

Researchers are exploring new ways to build robust quantum computers, and a promising avenue lies in materials called altermagnets, which offer the potential to create superconducting circuits without relying on external magnetic fields. Sakineh Vosoughi-nia and Michał P. Nowak, both from AGH University of Krakow’s Academic Centre for Materials and Nanotechnology, investigate the behaviour of electrons within these altermagnetic materials to unlock their potential for quantum computing. Their work reveals how the unique properties of altermagnets shape the flow of electrons and, crucially, allows them to propose a novel type of superconducting qubit, dubbed the ‘altermon’, that operates without the need for magnetic fields, a significant step towards more stable and scalable quantum technologies. This innovative qubit design leverages the material’s inherent symmetry to protect quantum information, paving the way for more resilient quantum computations.

Altermagnetic Josephson Junction Calculations and Validation

This supplementary material provides detailed calculations and additional data supporting a new qubit design, the Altermon, based on an altermagnet Josephson junction. It rigorously justifies the theoretical model employed and validates the numerical results obtained through simulations. The material demonstrates that the qubit’s parity-protected operation extends beyond specific altermagnetic symmetries, expanding its potential applications. Scientists employed a down-folding method to derive the effective Hamiltonian describing the altermagnet’s electronic band structure, simplifying a two-band Hamiltonian for analytical calculations. This derivation provides a solid theoretical foundation and validates the approximations made in the main paper. The team presents data, including band structure analysis and qubit spectrum simulations, for the dxy symmetry, demonstrating that it also exhibits parity-protected behaviour, strengthening the qubit design’s robustness and versatility.

Altermagnetic Josephson Junctions and Andreev Bound States

Scientists engineered a novel approach to study superconducting circuits by utilizing altermagnetic materials, circumventing the need for traditional magnetic fields. The research centers on the Andreev bound state (ABS) spectrum within a Josephson junction incorporating an altermagnet, meticulously investigating how symmetry and geometric confinement influence low-energy excitations. The team distinguished between two altermagnetic symmetries, demonstrating that one induces spin splitting in the Andreev levels, while the other preserves spin degeneracy and exhibits splitting caused by intermode hybridization. To analyze the ABS, scientists developed analytical calculations based on the dispersion relation of the altermagnetic material, leveraging spin-polarized bands and spin-dependent Fermi velocities.

This allowed them to derive an altermagnet energy term, replacing the Zeeman energy used in conventional semiconductor nanowire Josephson junctions, and subsequently calculate the spin-resolved Andreev energies for a fully transparent junction. These analytical results, validated against numerical simulations, confirmed the accuracy of the model and the influence of junction length on spin splitting. When examining wider junctions, the team observed that coupling between modes resulted in a shift of the Andreev levels while preserving spin degeneracy. To confirm that this shift stemmed from band mixing rather than spin splitting, scientists constructed a two-mode Bogoliubov-de Gennes (BdG) Hamiltonian, introducing intermode coupling.

The close match between the BdG model and experimental data validated the hypothesis that band mixing is the primary cause of the observed shift. The research further demonstrated that applying a planar electric field along the altermagnetic segment controls the wave-function distribution, enabling precise tuning of the Andreev spectrum. This control is crucial for realizing a parity-protected qubit, termed the altermon, based on the altermagnetic Josephson junction.

Altermagnetism Splits Andreev Bound State Spectrum

Scientists have achieved a new route to engineer superconducting circuits without magnetic fields, utilizing a material property called altermagnetism. This work theoretically investigates the Andreev bound state (ABS) spectrum within Josephson junctions incorporating this altermagnetic material, revealing how its unique symmetry and geometric confinement shape the low-energy excitations. The research demonstrates a clear distinction between two altermagnetic symmetries; one produces spin splitting in the electronic bands, while the other preserves spin degeneracy and instead induces splitting of the ABS spectrum through intermode hybridization. Experiments studying the normal-region bandstructure revealed that pure dx2−y2-wave symmetry altermagnetism splits the band into two spin-resolved bands, while pure dxy-wave symmetry preserves spin degeneracy.

These modifications to the band structure were confirmed through analytical calculations using perturbation theory, aligning closely with the observed changes. Further investigation focused on Andreev levels, demonstrating that the dx2−y2 altermagnet term induces spin-polarized Andreev levels, a direct result of the spin splitting observed in the dispersion. The team analytically calculated these levels for a single-mode junction, achieving strong agreement with numerical results obtained from a lattice-based model. The research then expanded to consider wider junctions, revealing that when more than one mode is present, the coupling between bands leads to a shift in the Andreev levels while preserving spin degeneracy. A two-mode BdG Hamiltonian model was constructed to clarify this band mixing, and the resulting analytical predictions aligned closely with the numerical simulations, confirming that the observed shift is indeed caused by interband coupling.

Altermagnetic Josephson Junctions and Altermon Qubit Design

This research demonstrates a new approach to designing superconducting circuits, utilizing altermagnetic materials to create Josephson junctions without the need for external magnetic fields. Scientists have explored how the specific symmetry of altermagnetic order impacts the energy levels within these junctions, revealing distinct behaviours depending on the material’s arrangement. Specifically, one type of altermagnetism causes a splitting of electron spins, while another preserves spin but splits the overall energy spectrum due to interactions between different modes within the junction. Building on these findings, the team proposed a novel superconducting qubit, termed the altermon, which can be tuned electrically into a protected state, enhancing its stability and reducing errors. This electrical tunability, combined with inherent robustness, positions altermagnetic Josephson junctions as a promising platform for advanced quantum devices.