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Higher-order topological superconductors and superfluids hostlower-dimensional Majorana corner and hinge states since novel topologyexhibitions on boundaries. While such topological nontrivial phases have beenexplored extensively, more possible schemes are necessary for engineeringMajorana states. In this paper we propose Majorana corner states could berealized in a two-dimensional attractive quantum spin-Hall insulator withopposite in-plane Zeeman energy at two sublattice sites. The appropriate Zeemanfield leads to the opposite Dirac mass for adjacent edges of a square sample,and naturally induce Majorana corner states. This topological phase can becharacterized by Majorana edge polarizations, and it is robust againstperturbations on random potentials as long as the edge gap remains open. Ourwork provides a new possibility to realize a second-order topologicalsuperfluid in two dimensions and engineer Majorana corner states.

Majorana corner states in an attractive quantum spin Hall insulator with opposite in-plane Zeeman energy at two sublattice sites