Topological Scaling of Nonlinear Injection current and the Quantized Circular Photogalvanic Effect (CPGE)in tilted multi Weyl semimetals(mWSMs)

TL;DR

This work develops a microscopic theory of nonlinear magneto-optical injection currents in tilted multi-Weyl semimetals under a magnetic field. By leveraging the Landau-level spectrum labeled by monopole charge $ν$ and applying a Kubo-type nonlinear response framework, it decomposes the dc-injection response into chiral-chiral, chiral-bulk, and bulk-bulk channels, uncovering universal $ν(ν+1)$ scaling and distinct resonant structures set by Landau-level selection rules and tilt. In the untitled limit, it derives compact analytic expressions with universal frequency thresholds that provide clear experimental fingerprints of higher-order Weyl topology. The results establish nonlinear injection currents as a sensitive transport probe of chiral Landau levels and multi-Weyl charge, with practical implications for gated devices and terahertz spectroscopy, and point to future work on disorder, finite temperature, and interactions.

Abstract

We develop a microscopic theory of nonlinear magneto-optical injection currents in multi-Weyl semimetals subjected to a uniform magnetic field. Using the Landau-level spectrum of a tilted multi-Weyl Hamiltonian with arbitrary monopole charge $ν$ as a starting point, we formulate a Kubo-type nonlinear response theory in the Landau-level basis and derive the second-order conductivity tensor. We identify distinct contributions originating from chiral-chiral, chiral-bulk, and bulk-bulk optical transitions, revealing characteristic monopole-charge scaling and sharp resonant structures governed by Landau-level selection rules and tilt-induced asymmetry. In the untilted limit, closed-form analytical expressions emerge that expose universal frequency thresholds and provide clear experimental signatures of higher-order Weyl topology. Our results establish nonlinear magneto-optical injection currents as a direct transport probe of chiral Landau levels and multi-Weyl topological charge.

Figures (3)

• Figure 1: The components of second-order DC conductivities $\beta^{xyz}$ and $\beta^{xxz}$( in the units of $\frac{e^3}{\hbar}$) as a function of the photon energy $\hbar\omega$. The plots are obtained for multi-Weyl nodes with finite tilting parameters($t_{\parallel},t_z \ne 0$) where chiral to chiral transitions becomes significant.The various curves illustrate the behaviour at different chemical potential.
• Figure 2: The photon-energy dependence of the second-order DC conductivity components $\beta^{xyz}$ and $\beta^{xxz}$ (in units of $e^3/\hbar$) is presented for multi-Weyl nodes in the untilted limit ($t_{\parallel}=0$, $t_z=0$), as derived from Eqs. (\ref{['beta_untilted_bulk']}) and (\ref{['chiral_bulk_analytic']}). The individual curves correspond to different chemical potentials.
• Figure 3: Schematic of a gated transport geometry for detecting nonlinear magneto-optical injection currents in a multi-Weyl semimetal. A multi-Weyl channel is contacted by metallic source and drain electrodes and electrostatically tuned through a gate oxide layer. A perpendicular magnetic field $\mathbf{B}=B_{0}\hat{z}$ quantizes the spectrum into chiral and bulk Landau levels, while illumination by a circularly polarized optical field $E(\omega)=E_{0}e^{i\Omega t}$ drives resonant inter-Landau level transitions. The resulting asymmetric carrier population generates a dc photocurrent $j_{\mathrm{dc}}$ along the channel, providing a direct transport probe of the second-order injection tensor $\beta^{\alpha\beta\gamma}(\omega)$ and its characteristic chiral-chiral, chiral-bulk, and bulk-bulk contributions discussed in the paper.