Emergent Weyl Fermions in an Orbital Multipolar Ordering Phase

TL;DR

This paper explores how orbital multipolar orderings in a diamond lattice induce emergent Weyl fermions from degenerate band nodes, revealing new topological phases driven by interactions in orbital systems.

Contribution

It demonstrates that orbital multipolar orderings can split degenerate band nodes into Weyl fermions, providing a novel mechanism for topological phase emergence in orbital systems.

Findings

Triply degenerate band nodes split into Weyl fermions due to orbital ordering.

Interaction-driven transition to an insulating phase with quadrupolar order.

Spin-$1/2$ case shows ferromagnetic transition and similar orbital-driven phases.

Abstract

Multipolar orderings in degenerate orbital systems offer unique opportunities for emergent topological phases. The phase diagram of interacting spinless fermions in a $p$-band diamond lattice at unit filling is first studied to elucidate the essential role of orbital multipolar orderings in the evolution of multifold degenerate band nodes. The free band structure around the Brillouin zone center is described by two quadratic band nodes each with a threefold degeneracy, which are spanned by the bonding and anti-bonding $p$-orbital multiplets, respectively. Upon switching on interactions, the triply degenerate band node is split into a pair of Weyl fermions with opposite chirality due to the onset of orbital multipolar orderings. Further raising interactions ultimately drives the system into an insulating phase with the orbital quadrupolar ordering. Our study is then generalized to spin-$1/2$ fermions, which has direct relevance with solid-state materials. The system develops full spin polarization through a ferromagnetic transition at tiny interactions, leaving the remaining orbital sector activated. The ensuing transitions take place in the orbital sector as a natural consequence, qualitatively recovering the phase diagram of spinless fermions. Our findings shed new light on the realization of emergent novel fermions with a prospect being a frontier at the confluence of topology, orbital physics and strong correlation.