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We theoretically study the lattice distortion induced first and second ordertopological phase transition in rectangular FeSe$_{x}$Te$_{1-x}$ monolayer.When compressing the lattice constant in one direction, our first principlescalculation shows that the FeSe$_x$Te$_{1-x}$ undergoes a band inversion at$\Gamma$ point in a wide dopping range, say $x\in(0.0,0.7)$, which ensurescoexistence of the topological band state and the high-T$_{\rm c}$superconductivity. This unidirectional pressure also leads to the C$_4$symmetry breaking which is necessary for the monolayer FeSe$_x$Te$_{1-x}$ tosupport Majorana corner states in the either presence or absence oftime-reversal symmetry. Particularly, we use $k\cdot p$ methods to fit the bandstructure from the first principles calculation and found that the edge statesalong the $(100)$ and $(010)$ directions have different Dirac energy due toC$_4$ symmetry breaking. This is essential to obtain Majorana corner states inD class without concerning the details of the superconducting pairingsymmetries and Zeeman form, which can potentially bring advantages in theexperimental implementation.

Lattice distortion induced first and second order topological phase transition in rectangular high-T$_{\rm c}$ superconducting monolayer