Quantum mechanics

Hexagonal lattice

Antiferromagnetism

Acoustics

Lattice (music)

Thermodynamics

Physics

Finite element method

Quadrilateral

MAJORANA

Mathematics

Superconductivity

Condensed matter physics

Zigzag

Geometry

Combinatorics

Topology (electrical circuits)

Asymmetry

Physical Review Letters

We propose a realization of the lattice-symmetry-assisted second-order topological superconductors with corner Majorana zero modes (MZM) based on two-dimensional topological insulators (2DTI). The lattice symmetry can naturally lead to the anisotropic coupling of edge states along different directions to the in-plane magnetic field and conventional $s$-wave pairings, thus leading to a single MZM located at the corners for various lattice patterns. In particular, we focus on the 2DTI with ${D}_{3d}$ lattice symmetry and found different types of gap opening for the edge states along the armchair and zigzag edges in a broad range of parameters. As a consequence, a single MZM exists at the corner between the zigzag and armchair edges, and is robust against weakly broken lattice symmetry. We propose to realize such corner MZMs in a variety of polygon patterns, such as triangles and quadrilaterals. We further show their potentials in building the Majorana network through constructing the Majorana $Y$ junction under an in-plane magnetic field.

Lattice-Symmetry-Assisted Second-Order Topological Superconductors and Majorana Patterns