Reduction of topological $\mathbb{Z}$ classification in cold atomic systems

TL;DR

This paper proposes ultracold dipolar fermions in optical lattices as a promising platform to experimentally observe the reduction of topological classification from Z to Z_4, with detailed methods for detection.

Contribution

It introduces a feasible experimental setup using ultracold dipolar fermions to observe topological classification reduction in cold atomic systems.

Findings

High controllability of ultracold dipolar fermions enables observation of Z to Z_4 reduction.

Detection methods include local radio frequency spectroscopy and spin expectation measurements.

Edge modes reappear around dislocations despite the reduction.

Abstract

One of the most challenging problems in correlated topological systems is a realization of the reduction of topological classification, but very few experimental platforms have been proposed so far. We here demonstrate that ultracold dipolar fermions (e.g., $^{167}$Er, $^{161}$Dy, and $^{53}$Cr) loaded in an optical lattice of two-leg ladder geometry can be the first promising testbed for the reduction $\mathbb{Z}\to\mathbb{Z}_4$, where solid evidence for the reduction is available thanks to their high controllability. We further give a detailed account of how to experimentally access this phenomenon; around the edges, the destruction of one-particle gapless excitations can be observed by the local radio frequency spectroscopy, while that of gapless spin excitations can be observed by a time-dependent spin expectation value of a superposed state of the ground state and the first excited state. We clarify that even when the reduction occurs, a gapless edge mode is recovered around a dislocation, which can be another piece of evidence for the reduction.