Magnetic crystals and helical liquids in alkaline-earth fermionic gases

TL;DR

This paper explores novel fractional insulating and conducting states in one-dimensional alkaline-earth fermionic gases with nuclear spin, revealing helical modes and magnetic order through analytical and numerical methods, with implications for cold-atom experiments.

Contribution

It introduces a hierarchy of fractional states in alkaline-earth gases, highlighting unique features for spin I > 1/2 and connecting them to fractional quantum Hall effects in a cold-atom context.

Findings

Gapless phases support helical modes

Gapped states exhibit density and magnetic order

Distinct features emerge for spin I > 1/2

Abstract

The joint action of a synthetic gauge potential and of atomic contact repulsion in a one-dimensional alkaline-earth(-like) fermionic gas with nuclear spin I leads to the existence of a hierarchy of fractional insulating and conducting states with intriguing properties. We unveil the existence and the features of those phases by means of both analytical bosonization techniques and numerical methods based on the density-matrix renormalization group algorithm. In particular, we show that the gapless phases can support helical modes, whereas the gapped states, which appear under certain conditions, are characterised both by density and magnetic order. Several distinct features emerge solely for spin I larger than 1/2, thus making their study with cold-atoms unique. We will finally argue that these states are related to the properties of an unconventional fractional quantum Hall effect in the thin-torus limit. The properties of this hierarchy of states can be experimentally studied in state-of-the-art cold-atom laboratories.