Saddle-point von Hove singularity and dual topological insulator state in Pt\(_2\)HgSe\(_3\)

Abstract

Saddle-point van Hove singularities in the topological surface states are interesting because they can provide a new pathway for accessing exotic correlated phenomena in topological materials. Here, based on first-principles calculations combined with a \(\mathbf {k \cdot p}\) model Hamiltonian analysis, we show that the layered platinum mineral jacutingaite (Pt\(_2\)HgSe\(_3\)) harbours saddle-like topological surface states with associated van Hove singularities. Pt\(_2\)HgSe\(_3\) is shown to host two distinct types of nodal lines without spin-orbit coupling (SOC) which are protected by combined inversion (\(I\)) and time-reversal (\(T\)) symmetries. Switching on the SOC gaps out the nodal lines and drives the system into a topological insulator state with nonzero weak topological invariant \(Z_2=(0;001)\) and mirror Chern number \(n_M=2\). Surface states on the naturally cleaved (001) surface are found to be nontrivial with a unique saddle-like energy dispersion with type II van Hove singularities. We also discuss how modulating the crystal structure can drive Pt\(_2\)HgSe\(_3\) into a Dirac semimetal state with a pair of Dirac points. Our results indicate that Pt\(_2\)HgSe\(_3\) is an ideal candidate material for exploring the properties of topological insulators with saddle-like surface states.