Role of effective mass anisotropy in realizing a hybrid nodal-line fermion state

Understanding the role of lattice geometry in shaping topological states and their properties is of fundamental importance to condensed matter and device physics. Here, we demonstrate how an anisotropic crystal lattice drives a topological hybrid nodal line in transition metal tetraphosphides MP4 (M = transition metal). MP4 constitutes a unique class of black phosphorus materials formed by intercalating transition metal ions between the phosphorus layers without destroying the characteristic anisotropic band structure of the black phosphorous. Based on the first-principles calculations and k center dot p theory, we show that MP4 harbors a single hybrid nodal line formed between anisotropic M d and P states with oppositely oriented effective masses. The nodal line consists of both type-I and type-II nodal band crossings whose nature and location are determined by the effective mass anisotropies of the intersecting bands. We further discuss a possible topological phase transition to exemplify the formation of the hybrid nodal-line state in MP4. Our results offer a comprehensive study for understanding the interplay between structural motifs-driven mass anisotropies and topology in anisotropic lattice materials to realize hybrid semimetal states.