# Dual topology in Jacutingaite Pt$_2$HgSe$_3$

## TL;DR

This paper demonstrates that the mineral Jacutingaite (Pt$_2$HgSe$_3$) exhibits a dual topological phase, combining weak topological insulator and mirror-protected topological crystalline insulator properties, supported by density-functional calculations.

## Contribution

It identifies dual topological phases in Jacutingaite and Pd$_2$HgSe$_3$, and develops tight-binding models to describe their topological surface states.

## Key findings

- Jacutingaite is a dual topological insulator.
- Pd$_2$HgSe$_3$ shares similar topological properties.
- Tight-binding models effectively capture the surface spectral features.

## Abstract

Topological phases of electronic systems often coexist in a material, well-known examples being systems which are both strong and weak topological insulators. More recently, a number of materials have been found to have the topological structure of both a weak topological insulator and a mirror-protected topological crystalline insulator. In this work, we first focus on the naturally occurring mineral called Jacutingaite, Pt$_2$HgSe$_3$, and show based on density-functional calculations that it realizes this dual topological phase and that the same conclusion holds for Pd$_2$HgSe$_3$. Second, we introduce tight-binding models that capture the essential topological properties of this dual topological phase in materials with three-fold rotation symmetry and use these models to describe the main features of the surface spectral density of different materials in the class.