Topological semimetal in a fermionic optical lattice

TL;DR

This paper predicts a new topological semimetal state in fermionic optical lattices with orbital degrees of freedom, characterized by a parity-protected gapless point with unique Berry flux, and explores its transition to a topological insulator under interactions.

Contribution

It introduces a novel topological semimetal phase in optical lattices with D4 symmetry, characterized by a parity-protected degeneracy and Berry flux, expanding the understanding of quantum states in engineered systems.

Findings

Discovery of a parity-protected gapless topological semimetal in optical lattices.

Universal emergence of this state in D4 symmetric lattices with orbital hybridization.

Transition to a topological insulator with chiral edge modes under repulsive interactions.

Abstract

Optical lattices play a versatile role in advancing our understanding of correlated quantum matter. The recent implementation of orbital degrees of freedom in chequerboard and hexagonal optical lattices opens up a new thrust towards discovering novel quantum states of matter, which have no prior analogs in solid state electronic materials. Here, we demonstrate that an exotic topological semimetal emerges as a parity-protected gapless state in the orbital bands of a two-dimensional fermionic optical lattice. The new quantum state is characterized by a parabolic band-degeneracy point with Berry flux $2\pi$, in sharp contrast to the $\pi$ flux of Dirac points as in graphene. We prove that the appearance of this topological liquid is universal for all lattices with D$_4$ point group symmetry as long as orbitals with opposite parities hybridize strongly with each other and the band degeneracy is protected by odd parity. Turning on inter-particle repulsive interactions, the system undergoes a phase transition to a topological insulator whose experimental signature includes chiral gapless domain-wall modes, reminiscent of quantum Hall edge states.