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Exploring Spectral Singularities and Topological Lasers in PT-Symmetric Weyl Semimetals

Arda Sevinc, Rama Alassadi, Mustafa Sarisaman

TL;DR

The paper develops a transfer-matrix framework for PT-symmetric topological Weyl semimetals that couples non-Hermitian photonics with axion electrodynamics to realize topological lasers. Spectral singularities of the TE-mode scattering in a Weyl slab define laser threshold states, with the $\theta$-term quantizing gain and enabling 12 distinct laser configurations via Kerr/Faraday-induced mode coupling. Using TaAs as a concrete material, the study finds that PT symmetry substantially lowers the required gain and that axion-induced currents form cyclotron-like topological patterns in the gain/loss regions, providing measurable signatures of the topological phase. These insights open routes to robust, tunable topological lasers for quantum information and advanced photonics applications.

Abstract

This paper investigates the unique properties of PT-symmetric Topological Weyl Semimetals (TWS) within the framework of non-Hermitian physics, focusing on their potential for generating topological lasers. By exploring the role of spectral singularities and their relationship to exceptional points, we examine how these materials, characterized by Weyl nodes and topologically protected surface states, can support novel optical phenomena such as unidirectional propagation and enhanced lasing. Through a theoretical model based on the transfer matrix approach, we reveal how the interplay between the PT symmetry and the axion term introduces new dynamics, leading to 12 distinct topological laser configurations. The study also investigates the impact of the $θ$-term on spectral singularities, showing how it quantizes the system's gain values and influences the topological properties of the lasers. By applying our model to the TaAs material, a known Weyl semimetal, we uncover previously unreported effects, demonstrating the potential of PT-symmetric TWS materials for advanced optoelectronic applications. We show that the axion-induced cyclotron-like Hall current in a PT-symmetric TWS medium, revealing its topological characteristics and distinct flow patterns in the gain and loss regions, which serve as indicators of the system's topological symmetry. Our findings open new avenues for the development of robust, tunable, and efficient topological lasers with applications in quantum information processing and beyond.

Exploring Spectral Singularities and Topological Lasers in PT-Symmetric Weyl Semimetals

TL;DR

The paper develops a transfer-matrix framework for PT-symmetric topological Weyl semimetals that couples non-Hermitian photonics with axion electrodynamics to realize topological lasers. Spectral singularities of the TE-mode scattering in a Weyl slab define laser threshold states, with the -term quantizing gain and enabling 12 distinct laser configurations via Kerr/Faraday-induced mode coupling. Using TaAs as a concrete material, the study finds that PT symmetry substantially lowers the required gain and that axion-induced currents form cyclotron-like topological patterns in the gain/loss regions, providing measurable signatures of the topological phase. These insights open routes to robust, tunable topological lasers for quantum information and advanced photonics applications.

Abstract

This paper investigates the unique properties of PT-symmetric Topological Weyl Semimetals (TWS) within the framework of non-Hermitian physics, focusing on their potential for generating topological lasers. By exploring the role of spectral singularities and their relationship to exceptional points, we examine how these materials, characterized by Weyl nodes and topologically protected surface states, can support novel optical phenomena such as unidirectional propagation and enhanced lasing. Through a theoretical model based on the transfer matrix approach, we reveal how the interplay between the PT symmetry and the axion term introduces new dynamics, leading to 12 distinct topological laser configurations. The study also investigates the impact of the -term on spectral singularities, showing how it quantizes the system's gain values and influences the topological properties of the lasers. By applying our model to the TaAs material, a known Weyl semimetal, we uncover previously unreported effects, demonstrating the potential of PT-symmetric TWS materials for advanced optoelectronic applications. We show that the axion-induced cyclotron-like Hall current in a PT-symmetric TWS medium, revealing its topological characteristics and distinct flow patterns in the gain and loss regions, which serve as indicators of the system's topological symmetry. Our findings open new avenues for the development of robust, tunable, and efficient topological lasers with applications in quantum information processing and beyond.
Paper Structure (16 sections, 39 equations, 14 figures, 4 tables)

This paper contains 16 sections, 39 equations, 14 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Interaction of Electromagnetic Waves with a Single TWS Slab
  3. $\mathcal{PT}$-Symmetric TWS
  4. Various Spectral Singularity Configurations: Types of Topological Lasers
  5. A. Plus Mode Spectral Singularity Configuration: Plus-Mode Topological TWS Laser
  6. B. Minus Mode Spectral Singularity Configuration: Minus-Mode Topological TWS Laser
  7. C. Bimodal Spectral Singularity Configuration: Bimodal Topological TWS Laser
  8. D. Random Spectral Singularity Configurations: Random Topological TWS Lasers
  9. Effect of $\mathcal{PT}$ symmetry on TWS Laser Types
  10. Axion-Induced Current $\vec{\mathcal{J}}_{\theta}$ and its Topological Character
  11. Concluding Remarks
  12. Appendix
  13. A. Spectral Singularities: A Brief Overview
  14. B. Modified Maxwell Equations
  15. C. Computation of Conductivities
  16. ...and 1 more sections

Figures (14)

  • Figure 1: (Color online) The TE mode configuration for the interaction of an electromagnetic wave with the Weyl semimetal slab (Left panel). The wave is emitted on the slab by an angle $\phi$ which is measured from the normal to the surface, and direction of the polarization is rotated by an angle of $\phi_F$ and $\phi_K$ inside and outside of the slab respectively. On the right panel, Fermi arcs due to Weyl nodes for an individual slab are presented.
  • Figure 2: (Color online) Configurations of a single layer optically active TWS slab (side view).
  • Figure 3: Figure displays the $\theta$-terms corresponding to each specific medium. Colored region specifies TWS. Notice that $\theta$-term is linearly proportional to $2 \mathtt{b}$, where $\mathtt{b}$ implies the distance between Weyl nodes.
  • Figure 4: (Color online) The TE mode configuration for the interaction of an electromagnetic wave with the Weyl semimetal slab (Left panel). The wave is emitted on the slab by an angle $\phi$ which is measured from the normal to the surface, and direction of the polarization is rotated by an angle of $\phi_F$ and $\phi_K$ inside and outside of the slab respectively. On the right panel, Fermi arcs due to Weyl nodes for an individual slab are presented.
  • Figure 5: (Color Online) The figure shows the spectral singularity configurations and laser output modes of the Plus Mode (left panel), Minus Mode (middle panel) and Bimodal case (right panel) in the TWS medium. Waves with amplitudes $B_{1}^{(+)}$ and $A_{3}^{(+)}$ are output from the left and right sides in the Plus Mode, amplitudes $B_{1}^{(-)}$ and $A_{3}^{(-)}$ for the Minus Mode, and amplitudes $B_{1}^{(+)}$, $B_{1}^{(-)}$, $A_{3}^{(+)}$, and $A_{3}^{(-)}$ for the Bimodal case, respectively.
  • ...and 9 more figures