# Saddle-point von Hove singularity and dual topological insulator state in Pt$_2$HgSe$_3$

## TL;DR

This study reveals that Pt$_2$HgSe$_3$ hosts saddle-like topological surface states with van Hove singularities, and transitions between topological phases can be induced by structural modulation, making it a promising material for exploring exotic topological phenomena.

## Contribution

The paper demonstrates the existence of saddle-like topological surface states with van Hove singularities in Pt$_2$HgSe$_3$, and shows how structural changes can induce phase transitions to Dirac semimetals.

## Key findings

- Pt$_2$HgSe$_3$ hosts saddle-like surface states with van Hove singularities.
- Switching on spin-orbit coupling induces a topological insulator phase.
- Structural modulation can drive the material into a Dirac semimetal state.

## 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.