# Prediction of Nontrivial Band Topology and Superconductivity in Mg$_2$Pb

## TL;DR

This paper predicts that Mg$_2$Pb is a superconducting topological material with potential for topological superconductivity and Majorana fermions, based on first-principles calculations of its band structure and topological properties.

## Contribution

It is the first to identify Mg$_2$Pb as a superconducting topological material with a nontrivial band topology similar to HgTe, and proposes quantum well structures for spin-filtered edge currents.

## Key findings

- Mg$_2$Pb has a nontrivial topological band structure similar to HgTe.
- Mg$_2$Pb is predicted to become superconducting upon electron doping.
- A trivial to topological transition is predicted in Mg$_2$Sn$_{1-x}$Pb$_x$ at x~0.77.

## Abstract

The interplay of BCS superconductivity and nontrivial band topology is expected to give rise to opportunities for creating topological superconductors, achieved through pairing spin-filtered boundary modes via superconducting proximity effects. The thus-engineered topological superconductivity can, for example, facilitate the search for Majorana fermion quasiparticles in condensed matter systems. Here we report a first-principles study of Mg$_2$Pb and predict that it should be a superconducting topological material. The band topology of Mg$_2$Pb is identical to that of the archetypal quantum spin Hall insulator HgTe, while isostructural and isoelectronic Mg$_2$Sn is topologically trivial; a trivial to topological transition is predicted for Mg$_2$Sn$_{1-x}$Pb$_x$ for x~0.77. We propose that Mg$_2$Pb-Mg$_2$Sn quantum wells should generate robust spin-filtered edge currents in analogy to HgTe/CdTe quantum wells. In addition, our calculations predict that Mg$_2$Pb should become superconducting upon electron doping. Therefore, Mg$_2$Pb is expected to provide a practical material platform for studying emergent phenomena arising from the interplay of superconductivity and band topology.

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Source: https://tomesphere.com/paper/1703.03308