# Topology of Triple-Point Metals

## TL;DR

This paper explores the topological properties of triple-point metals, including electronic and phononic topological phases, and discusses their implications for transport phenomena and thermoelectric efficiency.

## Contribution

It provides a comprehensive classification of topological phases in triple-point metals and demonstrates their impact on electronic and phononic properties.

## Key findings

- Identification of topological fermions and bosons in triple-point metals
- Observation of Fermi arcs and Lifshitz transitions
- Enhanced thermoelectric performance due to topological effects

## Abstract

We discuss and illustrate the appearance of topological fermions and bosons in triple-point metals, where a band crossing of three electronic bands occurs close to the Fermi level. Topological bosons appear in the phonon spectrum of certain triple-point metals, depending on the mass of atoms that form the binary triple-point metal. We first provide a classification of possible triple-point electronic topological phases possible in crystalline compounds and discuss the consequences of these topological phases, seen in Fermi arcs, topological Lifshitz transitions and transport anomalies. Then we show how the topological phase of phonon modes can be extracted and proven for relevant compounds. Finally, we show how the interplay of electronic and phononic topologies in triple-point metals puts these \textit{metallic} materials into the list of the most efficient \textit{metallic} thermoelectrics known to date.