Saddle-like topological surface states on the TT'X family of compounds (T, T' = Transition metal, X= Si, Ge)

TL;DR

This paper predicts saddle-like topological surface states in the TT'X family of compounds, revealing a transition from nodal-line semimetals to strong topological insulators upon including spin-orbit coupling, with unique surface state features.

Contribution

It identifies and characterizes saddle-like topological surface states in TT'X compounds, expanding understanding of topological phases beyond conventional Dirac cones.

Findings

Presence of nodal-line semimetal states in TT'X compounds without SOC.

Existence of drumhead surface states with saddle-like dispersion.

Transition to strong topological insulators with SOC inclusion.

Abstract

Topological nodal-line semimetals are exotic conductors that host symmetry-protected conducting nodal-lines in their bulk electronic spectrum and nontrivial drumhead states on the surface. Based on first-principles calculations and an effective model analysis, we identify the presence of topological nodal-line semimetal states in the TT'X family of compounds (T, T' = transition metal, X= Si, or Ge) in the absence of spin-orbit coupling (SOC). Taking ZrPtGe as an exemplar system, we show that this material harbors a single nodal line on the $k_y=0$ plane, which is protected by the $M_y$ mirror plane symmetry. Surface electronic structure calculations further reveal the existence of a drumhead surface state nested inside the nodal line projection on the (010) surface with a saddle-like energy dispersion. When the SOC is included, the nodal line gaps out and the system transitions to a strong topological insulator state with $Z_2=(1;000)$. The topological surface state evolves from the drumhead surface state via the sharing of its saddle-like energy dispersion within the bulk energy gap. These features differ remarkably from those of the currently known topological surface states in topological insulators such as Bi$_2$Se$_3$ with Dirac-cone-like energy dispersions.