Topological superconductivity is a major focus in condensed matter physics since it can host Majorana fermions, which are key components for future fault-tolerant quantum computers. Within this field, Weyl topological superconductivity is a unique state that features protected Bogoliubov point gap nodes and surface Fermi arcs. However, realizing this state in materials is challenging, as it typically requires on complex band structures and a delicate relativistic effect known as spin-orbit coupling.
A recent study published in the National Science Review offers a simpler and more universal mechanism. A collaborative team led by Fan Yang at the Beijing Institute of Technology and Congjun Wu at Westlake University found that Weyl topological superconductivity can naturally emerge from repulsive electron interactions in a three-dimensional (3D) cubic lattice.
The geometry of frustration
In highly studied two-dimensional (2D) square lattices, such as those related to high-temperature cuprate superconductors, electron repulsion often leads to 2D d-wave pairing. In this square layout, the sign of the superconducting wavefunction alternates between positive and negative along the x and y axes.
But applying this alternating pattern to a 3D cubic lattice creates a physical conflict, usually known as geometric frustration. It is mathematically impossible to simultaneously assign mutually opposite signs along all three spatial axes (x, y, and z) at the same time.
To resolve this conflict, the system undergoes a natural phase compromise. Studying theoretical models within both weak and strong coupling approaches, the researchers demonstrated that the electrons settle into a chiral d+id pairing state. Instead of flipping completely between positive and negative, the phase shifts evenly by 120 degrees among the three axes.
An octupolar solution
Unlike previously known chiral superconductors, this specific 120-degree arrangement does not generate a net orbital angular momentum. Instead, the electron pairs develop what is known as an octupolar component.
This unique symmetry is inherently related to the eight gapless Weyl points situated along the body diagonal directions of the crystal. Because these nodes act as alternating positive and negative magnetic monopoles in momentum space, the system acts as an octupolar Weyl topological superconductor.
A new frontier for materials
By removing the requirement for spin-orbit coupling, this discovery simplifies the search for Weyl topological superconductors. It also opens a new frontier for studying unconventional superconductivity in 3D strongly correlated systems. The theoretical framework points to strongly correlated cubic compounds and 3D cold-atom quantum simulations as prime experimental candidates.
National Science Review
Computational simulation/modeling