Motivated by the wealth of proposals and realizations of nontrivial topological phases in ${\mathrm{EuCd}}_2{\mathrm{As}}_2$, such as a Weyl semimetallic state and the recently controversially discussed semimetallic versus semiconductor behavior in this system, we analyze in this work the role of the delicate interplay of Eu magnetism, strain, and pressure on the realization of such phases. For that we invoke a combination of a group theoretical analysis with ab initio density functional theory calculations and uncover a rich phase diagram with various nontrivial topological phases beyond a Weyl semimetallic state, such as axion and topological crystalline insulating phases, and discuss their realization.

• Received 23 August 2023
• Revised 6 November 2023
• Accepted 13 November 2023

DOI:https://doi.org/10.1103/PhysRevB.108.235113