Topological quantum phase transitions of ultracold fermions in optical lattices

TL;DR

This paper explores topological quantum phase transitions in ultracold fermions within optical lattices, focusing on how these transitions depend on pairing symmetry, and proposes measurable signatures for their detection.

Contribution

It introduces the concept of topological quantum phase transitions in ultracold fermions, emphasizing their occurrence with non-zero angular momentum pairing and providing phase diagrams and measurable indicators.

Findings

Topological transitions occur only for p-wave, d-wave, and f-wave pairings.

Phase diagrams show where these topological transitions are most prominent.

Measurable quantities like momentum distribution and superfluid density can indicate topological phases.

Abstract

We consider the possibility of topological quantum phase transitions of ultracold fermions in optical lattices, which can be studied as a function of interaction strength or atomic filling factor (density). The phase transitions are connected to the topology of the elementary excitation spectrum, and occur only for non-zero angular momentum pairing (p-wave, d-wave and f-wave), while they are absent for s-wave. We construct phase diagrams for the specific example of highly anisotropic optical lattices, where the proposed topological phase transitions are most pronounced. To characterize the existence of these topological transitions, we calculate several measurable quantities including momentum distribution, quasi-particle excitation spectrum, atomic compressibility, superfluid density, and sound velocities.