Unveiling the Chiral States in Multi-Weyl Semimetals through Magneto-Optical Spectroscopy

TL;DR

This work addresses how higher-order Weyl nodes in multi-Weyl semimetals manifest in magneto-optical and transport properties by deriving a generic Landau level spectrum that includes tilt and computing the magneto-optical conductivity via the Kubo formalism. It presents explicit LL expressions with $m$-fold chiral zeroth LLs and nonlinear LL spacing, and computes the conductivity tensor components for bulk, chiral, and chiral-to-bulk transitions, linking them to Kerr and Faraday spectra through Fresnel boundary conditions. A key finding is that chiral signatures in the conductivity grow with the Weyl node order $m$ and that the tilting parameter $w_z, w_{\parallel}$ shapes spectral features near tilted Dirac cone energies, enabling tunable magneto-optical responses. The results provide a robust framework for identifying topological chiral states in mWSMs and indicate potential applications in non-reciprocal optics and topological photonics.

Abstract

This study investigates the transport parameters in multi-Weyl semimetals, focusing on their magneto-optical properties and the role of chiral states. The tilting parameter is identified as a key factor in higher-order Weyl nodes, significantly influencing the magneto-optical response. We obtain a generic Landau-level expression for multi-Weyl semimetals, establishing a robust framework for analyzing their quantum transport properties. A comprehensive expression for the conductivity tensor components is presented, uncovering distinctive low-frequency peaks and other features shaped by the tilting parameter. Our findings reveal that the signatures of chiral states in the conductivity tensors become increasingly pronounced with the Weyl node order. Particularly, the tilting parameter is shown to impact Faraday rotation, at energies near the tilted Dirac cone energies. These results provide critical insights into the magneto-optical behavior of multi-Weyl semimetals and their potential for exploring topological phenomena.

Figures (6)

• Figure 1: The LL dispersion (in eV) about the $k_z$ direction (in units of 1/$\mathring{\rm A})$ highlighting the emergence of robust $m$ chiral states. Parameters are taken from Table. [\ref{['Table1']}] with $\mathcal{Q}=0.25$ (in units of 1/$\mathring{\rm A})$ and $\eta=-1$.
• Figure 2: The conductivity tensor $\sigma_L\;\& \; \sigma_H$ in units of $e^2/h$: From left to right m=1,2,3,4. Conductivity tensor components show enhanced chiral signatures with higher Weyl node orders and distinct Faraday rotation near tilted Dirac cone energies, highlighting the tilting parameter's role in mWSMs' magneto-optical behavior. The parameters are taken as $T=5$ K, the quantity '$0_+$' is set to $0_+=w_\parallel/5$ for $m=1,2$ and $0_+=w_\parallel/2$ for $m=3,4$ with $w_\parallel$ given in table \ref{['Table1']}, the magnetic length is normalised to $l_B=1$ and the rest of parameters are taken from Table [\ref{['Table1']}].
• Figure 3: This figure maps the LLs spectrum (in eV) and the JDOS as a function of the frequency in the same eV units, illustrating transitions between chiral states and from chiral states to bulk states. For demonstration, we took $m=3$.
• Figure 4: Schematic illustrating the Faraday and Kerr rotation in thin mWSMs, providing a framework to derive the Fresnel coefficients.
• Figure 5: Depiction of the polarization vectors for s- and p-polarized waves in the medium 1. The red arrows indicate the polarization vectors $\epsilon_{p_1}^\pm$ when projected on the $(k_x-k_y)$ plane.