Emergence of triplet orbital pairing and non-Abelian states in ultracold multi-orbital optical lattices with quadratic band touching

TL;DR

This paper predicts the emergence of non-Abelian p-wave orbital pairing states in ultracold multi-orbital optical lattices with quadratic band touching, which could enable topological quantum computation.

Contribution

It demonstrates the absence of singlet orbital pairing and the emergence of triplet orbital pairing in specific lattice systems, revealing new non-Abelian ground states.

Findings

Triplet orbital pairing states are predicted in checkerboard and kagome lattices.

These states are non-Abelian and fully gapped, suitable for topological quantum computation.

The results are applicable to a broad class of multi-orbital systems.

Abstract

It is found that all the {\em singlet orbital pairing} instabilities are {\em absent} in a class of spin-polarized multi-orbital systems with quadratic band touching, which opens the way for {\em triplet orbital pairing} order. The ground states are found to be {\em non-Abelian} states with p-wave orbital pairing in checkerboard (away from 1/2 filling) and kagome (above 1/3 filling) lattices with {\em isotropic} attractive interaction which can be realized in ultracold multi-orbital optical lattices. The special property of such systems is generalized to more classes of multi-orbital systems, where the fully-gapped {\em non-Abelian} states are possibly the ground states. Those findings are helpful in achieving topological quantum computation.