Microscopic Origin Achieves Clear Formulation of Orbital Magnetization in Chiral Superconductors

Chiral superconductivity, a fascinating state breaking time-reversal symmetry, is gaining prominence as a potential avenue for novel technologies. Jihang Zhu from the University of Washington and Chunli Huang from the University of Kentucky, alongside colleagues, have now tackled a long-standing problem: understanding the microscopic origin of orbital magnetization within these unusual superconductors. Despite being a fundamental consequence of chiral superconductivity, a clear explanation of this magnetization has remained elusive due to the complex behaviour of quasiparticles. This new research is significant because it provides a unifying theory, applicable to materials like rhombohedral multilayer graphene , where spin-orbit coupling is minimal , and reveals how superconductivity can dramatically alter existing orbital magnetization, even identifying a unique collective mode contributing to the effect.

Chiral Superconductors and Bogoliubov Quasiparticle Magnetization

Scientists have demonstrated a novel microscopic theory explaining orbital magnetization within chiral superconductors, addressing a long-standing conceptual challenge in the field. This breakthrough unifies the effects of interband coherence, crucial for orbital magnetization in normal crystals, with the intrinsic orbital moments arising from the Cooper-pair condensate in superconducting materials. Researchers tackled the difficulty that Bogoliubov quasiparticles lack definite electric charge, preventing a straightforward interpretation of orbital magnetization as circulating currents. The team achieved this by systematically accounting for virtual transitions between normal and Bogoliubov quasiparticles, moving beyond traditional Fermi-surface descriptions and fully respecting gauge invariance and conservation laws.
Applying this theory to rhombohedral tetralayer graphene, the study reveals that the onset of superconductivity can either enhance or suppress the normal-state orbital magnetization, a behaviour critically dependent on the material’s bandstructure. This finding is particularly significant given the recent observation of chiral superconductivity in this material, which possesses negligible spin-orbit coupling, providing an ideal platform for testing the theoretical framework. Furthermore, the research identifies a generalized clapping mode, coherent fluctuations between opposite chiral windings of the p-wave order parameter, possessing a gap determined by the sublattice winding form factor. This unique collective mode, intrinsic to chiral superconductors, contributes to orbital magnetization by influencing the photon vertex.

Experiments show that the dressed photon vertex appears naturally within the microscopic theory, guaranteeing gauge invariance and current conservation, essential for accurate modelling. The work establishes a comprehensive Hamiltonian, incorporating both the electromagnetic coupling and the multiband structure of Bogoliubov quasiparticles, allowing for a detailed analysis of orbital magnetization. Researchers found that when rhombohedral tetralayer graphene hosts three disjoint Fermi pockets, superconductivity enhances orbital magnetization, while a simply connected Fermi surface leads to suppression, providing experimentally verifiable predictions. The study unveils that measurements of orbital magnetization relative to the quarter-metal phase would serve as a direct test of the proposed theory, potentially confirming the presence of intrinsic chiral superconductivity. Specifically, combined nano-SQUID and quantum oscillation measurements could validate the contrasting behaviours predicted for different bandstructures. This research opens avenues for exploring topological quantum computation, leveraging the unique properties of chiral superconductors and their associated orbital magnetization, and establishes a new understanding of how superconductivity and orbital magnetism interact in complex materials.

Bogoliubov Quasiparticle Transitions and Orbital Magnetization reveal fundamental

Scientists developed a microscopic theory to formulate orbital magnetization in chiral superconductors, addressing a long-standing conceptual challenge. The research tackled the difficulty arising from Bogoliubov quasiparticles lacking definite electric charge, preventing simple interpretation of orbital magnetization as circulating currents. Researchers moved beyond traditional Fermi-surface descriptions, systematically accounting for virtual transitions between normal and Bogoliubov quasiparticles, as illustrated in their Figure 1a. This innovative approach incorporates both the intrinsic orbital moment of Cooper pairs and interband coherence induced by the crystal lattice, crucial for understanding orbital response in crystalline superconductors.

The study pioneered a method employing a three-band model, conduction bands c and c’, and a valence band v, to illustrate interband processes contributing to orbital magnetization. Only the c band was considered superconducting, enabling classification of transitions as normal-normal (NN), Bogoliubov-Bogoliubov (BB), or mixed normal-Bogoliubov (NB and BN), detailed in Section III of their work. Applying this theory to rhombohedral tetralayer graphene, the team investigated how superconductivity impacts orbital magnetization, finding that its effect depends sensitively on the normal-state bandstructure. Experiments employed a phenomenological attractive p-wave pairing model, revealing that superconductivity enhances orbital magnetization when the quarter metal hosts three disjoint Fermi pockets.

Conversely, when the Fermi surface is simply connected, superconductivity suppresses orbital magnetization, providing experimentally testable predictions verifiable through nano-SQUID and quantum oscillation measurements. Scientists identified a generalized clapping mode, coherent fluctuations reversing superconducting chirality between winding sectors, with a gap determined by the sublattice winding form factor. This collective mode, unique to chiral superconductors, contributes to orbital magnetization by dressing the photon vertex, and its observation would confirm intrinsic chiral superconductivity in the quarter-metal phase. The research harnessed nano-SQUID measurements previously used to directly visualize orbital magnetization in the quarter-metal phase, providing a crucial baseline for comparison.

Graphene reveals tunable superconducting orbital magnetization

Scientists have uncovered a detailed microscopic theory explaining orbital magnetization in chiral superconductors, a phenomenon attracting considerable interest as a potential platform for novel technologies. The research, focused on rhombohedral multilayer graphene, provides a unique opportunity to understand this complex behaviour due to its negligible spin-orbit coupling. Experiments revealed that the onset of superconductivity can either enhance or suppress the normal-state orbital magnetization, a finding critically dependent on the material’s bandstructure. This sensitivity offers a pathway to tune the material’s properties for specific applications.

The team measured contributions to orbital magnetization arising from normal-normal transitions, finding that this component represents a background inherited from the normal parent state. Data shows that the normal-normal contribution, MNN z (k), exhibits a strong presence at the zone corner (kx= ky= 0), where the Berry curvature is at its highest. Further analysis identified a generalized clapping mode, a collective excitation unique to chiral superconductors, corresponding to coherent fluctuations between opposite chiral windings of the p-wave order parameter. This mode, with a gap determined by the sublattice winding form factor, contributes to the orbital magnetization by influencing the photon vertex.

Results demonstrate that the mixed normal-Bogoliubov transitions, denoted MNB z (k), are a primary mechanism by which superconductivity modifies the orbital magnetization. Scientists recorded a value of 61.886 μB per electron for MNB z, while the normal-normal contribution, MNN z, measured 8.612 μB per electron. The team also quantified the normal-normal contribution from conduction bands, MNNc z, at 62.142 μB per electron, and the mixed Bogoliubov-normal contribution, MNcN z, at 16.336 μB per electron. Tests prove that the Bogoliubov-Bogoliubov contribution, MBB z, reaches 16.593 μB per electron, with a peak magnitude nearly two orders of magnitude larger than the background.

Measurements confirm that the dominant contribution to MBB z originates from the region where the electron and hole Fermi surfaces overlap, a crucial observation for understanding the material’s behaviour. The study details how, in the normal state, the orbital magnetization vanishes inside the trigonally warped Fermi surface due to Pauli blocking, but this constraint is softened in the superconducting phase. Specifically, the research shows that for a chosen value of g, the BCS probability factor varies rapidly, reducing the available phase space for interband transitions and suppressing the orbital magnetization in this channel. The breakthrough delivers a detailed momentum-space distribution of these contributions, providing a direct test of the developed theory through experimental measurements of orbital magnetization relative to the quarter-metal phase.

Orbital Magnetization in Chiral Graphene Superconductors

Scientists have developed a novel theory explaining orbital magnetization within chiral superconductors, a state of matter garnering attention for potential technological applications. This research addresses a long-standing challenge in understanding how orbital magnetization, a consequence of broken time-reversal symmetry, arises at a microscopic level, particularly given the unusual properties of quasiparticles in superconductors. The team unified concepts of normal-state orbital magnetization with the intrinsic orbital moments present in the superconducting condensate, offering a comprehensive framework for analysing this phenomenon. Applying this theory to rhombohedral tetralayer graphene, the researchers discovered that the onset of superconductivity can either amplify or diminish the existing normal-state orbital magnetization, a sensitivity dependent on the material’s bandstructure.

Furthermore, they identified a unique collective mode, a ‘clapping mode’, linked to coherent fluctuations within the chiral superconducting order parameter, which contributes to orbital magnetization by influencing how photons interact with the system. This mode is specific to chiral superconductors and represents a distinctive characteristic of this phase. The authors acknowledge a limitation in their work, noting the phenomenological nature of the pairing mechanism employed; identifying the precise microscopic origin of superconductivity in rhombohedral multilayer graphene remains an open question. Future research, as suggested by the team, should focus on experimentally measuring the orbital magnetization in relation to the quarter-metal phase, providing a crucial test of their theoretical predictions. These findings are significant as they provide a detailed microscopic understanding of orbital magnetization in chiral superconductors, potentially guiding the development of new materials and devices based on this exotic state of matter.