Realization of high-order topological phase transition in 2D metal-organic frameworks

In two-dimensional (2D) scale, controllable topological phase transition between a conventional topological quantum state and a higher-order one has been a challenge currently. Herein, based on first-principles, we report 2D metal-organic frameworks (MOFs) are ideal choice for realizing such topological phase transition. Taking MOF candidate Pd₃(C₆S₆)₂as an example, a semimetallic band structure is present at the equilibrium state. Under moderate compressive strain, it features a nontrivial energy gap and corner states, which is evidenced as a second-order topological insulator (SOTI). In addition, the band order for its low-energy bands switches at moderate tensile strain, during which topological phase transition from SOTI and topological semimetal to double Weyl semimetal (DWSM) happens, accompanied by the change in real Chern number formνR=1toνR=0. At the critical point for the phase transition, the system can be characterized as a 2D pseudospin-1 fermion. Beside Pd₃(C₆S₆)₂, we further identify the ferromagnetic monolayer Fe₃(C₆S₆)₂can also take the DWSM-to-SOTI phase transition, where the topological fermions and corresponding edge/corner states could be fully spin-polarized. This work has for the first time realized topological transition between conventional topological quantum state and a higher-order one in both nonmagnetic and magnetic MOFs.