Multiorder topological superfluid phase transitions in a two-dimensional optical superlattice

Abstract

Higher-order topological superfluids have gapped bulk and symmetry-protected Majorana zero modes with various localizations. Motivated by recent advances, we present a proposal for synthesizing multi-order topological superfluids that support various Majorana zero modes in ultracold atomic gases. For this purpose, we use the two-dimensional optical superlattice that introduces a spatial modulation to the spin-orbit coupling in one direction, providing an extra degree of freedom for the emergent higher-order topological state. We find the topologically trivial superfluids, first-order and second-order topological superfluids, as well as different topological phase transitions among them with respect to the experimentally tunable parameters. Besides the conventional transition characterized by the Chern number associated with the bulk gap closing and reopening, we find the system can support the topological superfluids with Majorana corner modes, but the topological phase transition undergoes no gap-closing of bulk bands. Instead, the transition is refined by the quadrupole moment and signaled out by the gap-closing of edge states. The proposal is based on the $s$-wave interaction and is valid using existing experimental techniques, which unifies multi-order topological phase transitions in a simple but realistic system.

arXiv comment8 pages, 5 figures

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• Sublattice-enriched tunability of bound states in second-order topological insulators and superconductors
• Sublattice-sensitive Majorana Modes
• Tunable boson-assisted finite-range interaction and engineering Majorana corner modes in optical lattices
• Majorana corner states in an attractive quantum spin Hall insulator with opposite in-plane Zeeman energy at two sublattice sites