Altermagnetism creates unique surfaces for quantum computing

Researchers at Great Bay University and the University of Würzburg detail a path toward topological superconductivity by combining altermagnetism with a unique material structure. Their work describes how altermagnetic order in a topological insulator, potentially realized in the compound EuIn₂As₂, when paired with superconductivity, creates highly anisotropic superconducting properties and crystal-facet-dependent Bogoliubov Fermi surfaces. These surfaces offer distinct platforms to realize Majorana zero modes, crucial components not only at boundaries or vortex lines within the superconducting material. This approach utilizes altermagnetism-induced Bogoliubov Fermi surfaces to engineer topological superconductivity through crystal anisotropy and quantum confinement.

Altermagnetism in Topological Insulators Enables Novel Superconductivity

EuIn₂As₂ emerges as a promising candidate material for realizing a newly proposed form of topological superconductivity, stemming from the interplay between altermagnetism and conventional s-wave superconductivity. Critically, these surfaces are not uniform; their properties depend on the specific crystal facet observed, a phenomenon driven by the anisotropic nature of altermagnetism.

The authors state that this facet-dependent anisotropy is relevant to engineering topological superconductivity, specifically creating highly anisotropic superconducting gaps when altermagnetic order is combined with superconductivity. This anisotropy influences the creation of quasi-1D nanowires where the Bogoliubov Fermi surfaces undergo topological phase transitions due to quantum confinement, ultimately leading to the formation of Majorana zero modes (MZMs) at the nanowire’s ends.

Remarkably, the research extends beyond conventional MZM locations; the altermagnetic order allows for a transition between MZMs localized at vortex lines within the superconductor and those residing at the physical boundaries of the material. “The altermagnetic order drives not only vortex phase transitions but also topological phase transitions of Bogoliubov Fermi surfaces at side surfaces,” the authors write, highlighting a control mechanism beyond standard superconducting topological insulator systems.

This ability to transition between different MZM locations is a significant advancement. The model, authored by Fu, Chang-An Li, and Björn Trauzettel, incorporates a Hamiltonian that accounts for the altermagnetic order, represented by the term t_(AM)( cos k_x- cos k_y)ρ_zσ_z. The researchers explain that this term contrasts with similar terms found in higher-order topological insulators, as it induces anisotropic momentum shifts rather than simply eliminating surface Dirac cones.

Investigation of the normal-state Hamiltonian reveals that the altermagnetic order modifies the symmetry of the system, shifting it from the magnetic point group 4/mmm1^′ to 4^′/m^′m^′m, and resulting in an anisotropic Fermi surface. The authors’ findings provide a pathway for realizing and controlling topological superconductivity and MZMs by exploiting the impact of altermagnetism on topological surface states.

Bogoliubov Fermi Surfaces Formed at Crystal Facets in AMTI Hybrids

Researchers are investigating how altermagnetic order within this topological insulator, when combined with conventional superconductivity, generates unique electronic states at its crystal surfaces. This approach differs from previous attempts to create topological superconductors, which often rely on external magnetic fields or complex material interfaces. These crystal-facet-dependent Bogoliubov Fermi surfaces offer distinct platforms to realize Majorana zero modes (MZMs), crucial components for topological superconductivity.

EuIn_2As_2 as a Potential Platform for Altermagnetic Phases

Bo Fu of Great Bay University and colleagues are investigating the potential of the compound to host a novel form of topological superconductivity, driven by the interplay of altermagnetism and conventional superconductivity. Their work describes how manipulating the material could lead to the creation of highly anisotropic superconducting states, where the material’s properties change depending on the crystal surface examined. This anisotropy arises from the unique combination of altermagnetic order and the presence of a conventional s-wave superconductor in proximity, resulting in crystal-facet-dependent Bogoliubov Fermi Surfaces (BFSs).

The authors of the paper, Fu, Chang-An Li, and Björn Trauzettel, present a model incorporating a Hamiltonian that explicitly accounts for the altermagnetic influence. Remarkably, the calculations reveal that the altermagnetic order doesn’t limit MZM localization to the nanowire ends.

BdG Hamiltonian Models AMTI/Superconductor Heterostructures

The potential to engineer superconductivity with tailored surface properties has advanced with a new theoretical model linking altermagnetism to the formation of unique Bogoliubov Fermi surfaces (BFSs). This finding reveals that MZMs can be realized at vortex lines or boundaries, offering a new method for accessing these crucial components. The authors explain that EuIn₂As₂ exhibits zero-energy surface states in bulk nodal-ring phases and anisotropically shifted surface Dirac cones in topological insulating phases.

When combined with superconductivity, this arrangement generates crystal-facet-dependent BFSs at the material’s boundaries. These BFSs, not uniform across all surfaces, are central to the team’s proposal for realizing MZMs. The model details how the altermagnetic order significantly alters the symmetry of the topological insulator, breaking both time-reversal symmetry and four-fold rotation symmetry, which impacts the material’s Fermi surface and momentum-dependent spin polarization, creating a nodal structure and ultimately influencing the formation of the anisotropic superconducting gaps.

Anisotropic Surface States Characterize Altermagnetic Topological Insulators

Researchers are investigating this compound as a platform to observe altermagnetic topological insulator behavior, a theoretical framework detailed in recent work by Fu, Chang-An Li, and Björn Trauzettel. Unlike conventional topological insulators with uniformly distributed surface states, these materials exhibit anisotropically shifted Dirac cones, a distortion of the electronic structure dependent on the crystal’s surface orientation.

This facet-dependent behavior is a direct consequence of the altermagnetic order, a unique magnetic arrangement characterized by momentum-dependent spin splitting without net magnetization. This phase, characterized by ring-shaped constant energy contours in momentum space, is crucial for realizing Majorana zero modes (MZMs).

Quantum Confinement Drives Topological Transitions in Nanowires

Calculations demonstrate that the interplay between altermagnetism and superconductivity generates highly anisotropic superconducting gaps, manifesting as crystal-facet-dependent Bogoliubov Fermi surfaces (BFSs) at material boundaries, a critical departure from conventional topological insulators exhibiting uniformly distributed surface states. The research team proposes a quasi-one-dimensional nanowire geometry to further refine the behavior of these BFSs, leveraging quantum confinement to discretize the surface BFSs into a series of energy levels within the superconducting gap. The altermagnetic order thus acts as a control parameter to drive topological phase transitions of these surface states, ultimately generating MZMs at the wire ends in nontrivial phases.

Quantum confinement within these nanowires induces topological phase transitions, localizing MZMs at the nanowire’s ends. the altermagnetic order allows for a transition between two distinct types of MZMs: one type is located at the vortex line, while the other type is located at the physical boundaries.

Vortex Phase Transitions and Boundary-Localized MZMs in AMTI Systems

Their work centers on europium diindium diasenide, or EuIn₂As₂, a compound predicted to exhibit altermagnetic topological insulator properties, and details how Majorana zero modes (MZMs) can be realized in novel locations. By constructing quasi-one-dimensional nanowires from EuIn₂As₂, researchers predict quantum confinement will discretize the surface states, further refining the behavior of these MZMs and concentrating them at the nanowire’s extremities.

The research shows that this altermagnetic order doesn’t just influence vortex behavior, but actively participates in the topological phase transitions of the BFSs themselves, which is a departure from conventional topological superconductors where vortex-line physics operates independently.