Spectral analysis of the magneto-optical response in valley polarized Pb$_{1-x}$Sn$_x$Se

TL;DR

This study investigates the valley-dependent magneto-optical response in Pb$_{1-x}$Sn$_x$Se alloys, revealing an anomaly in interband transitions linked to valley differences and interference effects, supported by theoretical modeling.

Contribution

It provides the first detailed analysis of valley-specific magneto-optical behavior in Pb$_{1-x}$Sn$_x$Se, combining experimental data with a theoretical fit using the Mitchell-Wallis model.

Findings

Anomalous absorption strength ratio between valleys under magnetic field.

Carrier density differences influence valley-dependent optical responses.

Theoretical modeling accurately fits experimental spectral data at high magnetic fields.

Abstract

Since the last century, considerable efforts have been devoted to the study of valley-degenerate narrow gap semiconductors, such as the Pb$_{1-x}$Sn$_x$Se alloy. This material possesses band edges at the $L$-points of their Brillouin zone, yielding a valley degeneracy of four. However, in (111)-oriented films, it is still not fully understood how differences between the longitudinal valley, oriented along the growth axis, and the oblique valleys, oriented at an angle with respect to that axis, appear in infrared magneto-optical spectroscopy. In this work, we report a magneto-optical study on this family of alloys, focusing on an anomaly in the interband transition of the absorption strength ratio between longitudinal and oblique valleys under a magnetic field applied along the [111] direction. Based on the Mitchell-Wallis model, we provide a theoretical fit for the experimental transmission data, which quantitatively explains the spectral shape of the data at magnetic fields as high as 35T. In particular, we attribute this anomalous absorption strength variation to the carrier density difference between the two types of valleys as well as the field-dependent multiple-beam interference or the Fabry-P\'{e}rot interference. Our analysis also allows for the extraction of the real and imaginary parts of the dielectric function.