# Magnetoterahertz Response and Faraday Rotation from Massive Dirac Fermions in the Topological Crystalline Insulator Pb$_{0.5}$Sn$_{0.5}$Te

## TL;DR

This study uses magneto-terahertz spectroscopy to analyze bulk carriers in Pb$_{0.5}$Sn$_{0.5}$Te, revealing distinct Dirac and conventional bands and their unique responses to magnetic fields, advancing understanding of topological crystalline insulators.

## Contribution

It provides a novel quantitative analysis of bulk carriers in Pb$_{0.5}$Sn$_{0.5}$Te, distinguishing Dirac from conventional bands and their magnetic field responses.

## Key findings

- Identification of p-type Dirac and n-type conventional carriers.
- Different cyclotron resonance behaviors for the two carrier types.
- Opposite field dependence of scattering rates for p- and n-type carriers.

## Abstract

Pb$_{1-x}$Sn$_x$Te has been shown to be an interesting tunable topological crystalline insulator system. We present a magneto-terahertz spectroscopic study of thin films of Pb$_{0.5}$Sn$_{0.5}$Te. The complex Faraday rotation angle and optical conductivity in the circular basis are extracted without any additional assumptions. Our quantitative measures of the THz response allow us to show that the sample studied contains two types of bulk carriers. One is $p$-type and originates in 3D Dirac bands. The other is $n$-type and appears to be from more conventional 3D bands. These two types of carriers display different cyclotron resonance dispersions. Through simulating the cyclotron resonance of hole carriers, we can determine the Fermi energy and Fermi velocity. Furthermore, the scattering rates of $p$-type and $n$-type carriers were found to show opposite field dependences, which can be attributed to their different Landau level broadening behaviors under magnetic field. Our work provides a new way to isolate real topological signatures of bulk states in Dirac and Weyl semimetals.