Lattice distortion induced first- and second-order topological phase transition in a rectangular high-T_{c} superconducting monolayer

We theoretically study the lattice distortion induced first- and second-order topological phase transition in rectangular FeSe_{x}Te_{1−x} monolayer. When compressing the lattice constant in one direction, our first-principles calculation shows that the FeSe_{x}Te_{1−x} undergoes a band inversion at Γ point in a wide doping range, say x∈(0.0,0.7), which indicates the first-order topological phase transition of its electronic band structure. Meanwhile, because the unidirectional pressure breaks C_{4} symmetry, the topological edge states along the (100) and (010) directions have different Dirac energy. Given the high-temperature superconductivity of FeSe_{x}Te_{1−x} monolayer, we found that the C_{4} symmetry breaking is essential to support Majorana corner states in either presence or absence of time-reversal symmetry. Especially in the case of breaking time-reversal symmetry, we can obtain a single Majorana zero mode at each corner without concerning the details of the superconducting pairing symmetries and applied Zeeman form, which can potentially bring advantages in the experimental implementation.