Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2601.00706

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

Arda Sevinc, Rama Alassadi, Mustafa Sarisaman

physics.opticscond-mat.mtrl-sciquant-phSubmitted Dec 30, 2025• Announced Dec 31, 2025
arXivHTMLPDF

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.

Comments
26 pages, 14 figures, 4 table, accepted for publication in Scientific Reports

Related papers

Exploring Spectral Singularities in Dirac Semimetals: The Role of Non-Hermitian Physics and Dichroism

Mustafa Sarisaman, Murat Taş, Enes Talha Kırca

In this study, motivated by recent advancements in non-Hermitian physics, we explore new characteristics of Dirac semimetals (DSMs) using the spectral singularities by means of scattering techniques, with the goal of uncovering additional unique properties. To achieve this, we investigate how the axion texture of a DSM affects its topological properties by analyzing its interaction with electromagnetic waves. We examine the transverse electric (TE) mode configuration, where the magneto-electric effect induces a dichroic property in these materials. This behavior is particularly interesting and commonly seen in potential DSM candidates. Consequently, we report for the first time that a dichroic DSM generates 12 unique topological laser types. We discover that surface currents are generated by topological terms on the surface of the DSM slab. Furthermore, we examine how the θ term associated with axions in topological materials contributes to these topological properties. Our study reveals distinct topological role of the θ term more clearly than ever before. Our results confirm that the topological properties of DSMs with a single Dirac cone remain stable under external influences and that a topologically robust DSM laser can be developed accordingly

cond-mat.mes-hallCross-listedarXiv:2603.23001•Mar 25, 2026

Topological Eigenvalues: Unveiling Non-Hermitian Spectral Singularities

PAULO SÉRGIO DE ANDRADE

This paper explores the novel concept of topological eigenvalues within the realm of non-Hermitian quantum mechanics, focusing on their role in unveiling spectral singularities. Unlike conventional Hermitian systems, non-Hermitian Hamiltonians, which describe open systems with gain and loss, exhibit complex eigenvalues and unique spectral features such as exceptional points (EPs) where eigenvalues and their corresponding eigenvectors coalesce. We introduce the idea that certain eigenvalues in non-Hermitian systems possess an inherent topological character, dictated by the geometry of the parameter space and the winding properties of the characteristic polynomial. These topological eigenvalues are shown to be intimately linked to spectral singularities, which are non-Hermitian generalizations of bound states in the continuum or points of perfect reflection/transmission, characterized by infinite scattering amplitudes. We develop a theoretical framework to identify and characterize these topological eigenvalues, demonstrating how they emerge from the interplay of non-Hermiticity and underlying symmetries. Our findings reveal that the robust nature of these topological eigenvalues provides a new lens through which to understand the exotic phenomena observed in non-Hermitian systems, including the non-Hermitian skin effect and the breakdown of traditional bulk-boundary correspondence. This work opens new avenues for designing robust non-Hermitian devices and understanding fundamental aspects of open quantum systems.

•Nov 22, 2025•0 citations

Weyl solitons in three-dimensional optical lattices

Ce Shang, Yuanlin Zheng, Boris A. Malomed

Weyl fermions are massless chiral quasiparticles existing in materials known as Weyl semimetals. Topological surface states, associated with the unusual electronic structure in the Weyl semimetals, have been recently demonstrated in linear systems. Ultracold atomic gases, featuring laser-assisted tunneling in three-dimensional optical lattices, can be used for the emulation of Weyl semimetals, including nonlinear effects induced by the collisional nonlinearity of atomic Bose-Einstein condensates. We demonstrate that this setting gives rise to topological states in the form of Weyl solitons at the surface of the underlying optical lattice. These nonlinear modes, being exceptionally robust, bifurcate from linear states for a given quasimomentum. The Weyl solitons may be used to design an efficient control scheme for topologically protected unidirectional propagation of excitations in light-matter-interaction physics. After the recently introduced Majorana and Dirac solitons, the Weyl solitons proposed in this work constitute the third (and the last) member in this family of topological solitons.

arXiv:1804.00837•Physical Review A•Apr 3, 2018•17 citations

Parity-time-symmetric quantum critical phenomena

Yuto Ashida, Shunsuke Furukawa, Masahito Ueda

Synthetic non-conservative systems with parity-time (PT) symmetric gain-loss structures can exhibit unusual spontaneous symmetry breaking that accompanies spectral singularity. Recent studies on PT symmetry in optics and weakly interacting open quantum systems have revealed intriguing physical properties, yet many-body correlations still play no role. Here by extending the idea of PT symmetry to strongly correlated many-body systems, we report that a combination of spectral singularity and quantum criticality yields an exotic universality class which has no counterpart in known critical phenomena. Moreover, we find unconventional low-dimensional quantum criticality, where superfluid correlation is anomalously enhanced owing to non-monotonic renormalization group flows in a PT-symmetry-broken quantum critical phase, in stark contrast to the Berezinskii-Kosterlitz-Thouless paradigm. Our findings can be experimentally tested in ultracold atoms and predict critical phenomena beyond the Hermitian paradigm of quantum many-body physics.

arXiv:1611.00396•Nature Communications•Jun 8, 2017•296 citations

Exploring topological double-Weyl semimetals with cold atoms in optical lattices

Xue-Ying Mai, Dan-Wei Zhang, Zhi Li +1 more

We explore the topological properties of double-Weyl semimetals with cold atoms in optical lattices. We first propose a tight-binding model of simulating the double-Weyl semimetal with a pair of double-Weyl points by engineering the atomic hopping in a three-dimensional optical lattice. We show that the double-Weyl points with topological charges of $\ifmmode\pm\else\textpm\fi{}2$ behave as the sink and source of Berry flux in momentum space connecting by two Fermi arcs and they are stabilized by the ${C}_{4h}$ point-group symmetry. By applying a realizable ${C}_{4}$ breaking term, we find that each double-Weyl point splits into two single-Weyl points and obtain rich phase diagrams in the parameter space spanned by the strengths of an effective Zeeman term and the ${C}_{4}$ breaking term, which contains a topological and a normal insulating phase and two topological Weyl semimetal phases with eight and four single-Weyl points, apart from the double-Weyl semimetal phase. Furthermore, we demonstrate with numerical simulations that (i) the mimicked double- and single-Weyl points can be detected by measuring the atomic transfer fractions after a Bloch oscillation; (ii) the Chern number of different quantum phases in the phase diagram can be extracted from the center shift of the hybrid Wannier functions, which can be directly measured with time-of-flight imaging; (iii) the band topology of the ${C}_{4}$-symmetric Bloch Hamiltonian can be detected simply from measuring the spin polarization at the high-symmetry momentum points with a condensate in the optical lattice. The proposed system would provide a promising platform for elaborating the intrinsic exotic physics of double-Weyl semimetals and the related topological phase transitions.

arXiv:1706.02063•Physical Review A•Jun 21, 2017•24 citations

Topics in topological band systems

Zhoushen Huang

The discovery of integer quantum Hall effect and its subsequent theoretical formulation heralded a new paradigm of thinking in condensed matter physics, which has by now blossomed into the rapidly growing field of topological phases. In this work we investigate several mutually related topics in the framework of topological band theory. In Chapter 2, we study solutions to boundary states on a lattice and see how they are related to the bulk topology. To elicit a real space manifestation of the non-trivial topology, the presence of a physical edge is not strictly necessary. We study two other possibilities, namely the entanglement spectrum associated with an imaginary spatial boundary, and the localization centers of Wannier functions, in Chapters 3,4, and 5. Topological classification through discrete indices is so far possible only for systems described by pure quantum states - in the existing scheme, quantization is lost for systems in mixed states. In Chapter 6, we present a program through which discrete topological indices can be defined for topological band systems at finite temperature, based on Uhlmann's parallel transport of density matrices. The potential of topologocal insulators in realistic applications lies in the existence of Dirac nodes on its surface spectrum. Dirac physics, however, is not exclusive to TI surfaces. In a recently discovered class of materials known as Weyl semimetals, energy nodes which emit linear dispersions also occur in the bulk material. In Chapter 7, we study the possibility of resonance states induced by localized impurities near the nodal energy in Weyl semimetals, which will help us in understanding the stability of density-of-state suppression at the energy nodes. Finally, in Chapter 8, we apply the topological characterization developed for noninteracting particles to a class of interacting spin models in 3D, which are generalizations of Kitaev's honeycomb model, and identify several exotic quantum phases such as spin metals and spin semimetals

•Jan 1, 2014•0 citations
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 θθθ-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.
In this study, motivated by recent advancements in non-Hermitian physics, we explore new characteristics of Dirac semimetals (DSMs) using the spectral singularities by means of scattering techniques, with the goal of uncovering additional unique properties. To achieve this, we investigate how the axion texture of a DSM affects its topological properties by analyzing its interaction with electromagnetic waves. We examine the transverse electric (TE) mode configuration, where the magneto-electric effect induces a dichroic property in these materials. This behavior is particularly interesting and commonly seen in potential DSM candidates. Consequently, we report for the first time that a dichroic DSM generates 12 unique topological laser types. We discover that surface currents are generated by topological terms on the surface of the DSM slab. Furthermore, we examine how the θ term associated with axions in topological materials contributes to these topological properties. Our study reveals distinct topological role of the θ term more clearly than ever before. Our results confirm that the topological properties of DSMs with a single Dirac cone remain stable under external influences and that a topologically robust DSM laser can be developed accordingly
This paper explores the novel concept of topological eigenvalues within the realm of non-Hermitian quantum mechanics, focusing on their role in unveiling spectral singularities. Unlike conventional Hermitian systems, non-Hermitian Hamiltonians, which describe open systems with gain and loss, exhibit complex eigenvalues and unique spectral features such as exceptional points (EPs) where eigenvalues and their corresponding eigenvectors coalesce. We introduce the idea that certain eigenvalues in non-Hermitian systems possess an inherent topological character, dictated by the geometry of the parameter space and the winding properties of the characteristic polynomial. These topological eigenvalues are shown to be intimately linked to spectral singularities, which are non-Hermitian generalizations of bound states in the continuum or points of perfect reflection/transmission, characterized by infinite scattering amplitudes. We develop a theoretical framework to identify and characterize these topological eigenvalues, demonstrating how they emerge from the interplay of non-Hermiticity and underlying symmetries. Our findings reveal that the robust nature of these topological eigenvalues provides a new lens through which to understand the exotic phenomena observed in non-Hermitian systems, including the non-Hermitian skin effect and the breakdown of traditional bulk-boundary correspondence. This work opens new avenues for designing robust non-Hermitian devices and understanding fundamental aspects of open quantum systems.
Weyl fermions are massless chiral quasiparticles existing in materials known as Weyl semimetals. Topological surface states, associated with the unusual electronic structure in the Weyl semimetals, have been recently demonstrated in linear systems. Ultracold atomic gases, featuring laser-assisted tunneling in three-dimensional optical lattices, can be used for the emulation of Weyl semimetals, including nonlinear effects induced by the collisional nonlinearity of atomic Bose-Einstein condensates. We demonstrate that this setting gives rise to topological states in the form of Weyl solitons at the surface of the underlying optical lattice. These nonlinear modes, being exceptionally robust, bifurcate from linear states for a given quasimomentum. The Weyl solitons may be used to design an efficient control scheme for topologically protected unidirectional propagation of excitations in light-matter-interaction physics. After the recently introduced Majorana and Dirac solitons, the Weyl solitons proposed in this work constitute the third (and the last) member in this family of topological solitons.
Synthetic non-conservative systems with parity-time (PT) symmetric gain-loss structures can exhibit unusual spontaneous symmetry breaking that accompanies spectral singularity. Recent studies on PT symmetry in optics and weakly interacting open quantum systems have revealed intriguing physical properties, yet many-body correlations still play no role. Here by extending the idea of PT symmetry to strongly correlated many-body systems, we report that a combination of spectral singularity and quantum criticality yields an exotic universality class which has no counterpart in known critical phenomena. Moreover, we find unconventional low-dimensional quantum criticality, where superfluid correlation is anomalously enhanced owing to non-monotonic renormalization group flows in a PT-symmetry-broken quantum critical phase, in stark contrast to the Berezinskii-Kosterlitz-Thouless paradigm. Our findings can be experimentally tested in ultracold atoms and predict critical phenomena beyond the Hermitian paradigm of quantum many-body physics.
We explore the topological properties of double-Weyl semimetals with cold atoms in optical lattices. We first propose a tight-binding model of simulating the double-Weyl semimetal with a pair of double-Weyl points by engineering the atomic hopping in a three-dimensional optical lattice. We show that the double-Weyl points with topological charges of $\ifmmode\pm\else\textpm\fi{}2$ behave as the sink and source of Berry flux in momentum space connecting by two Fermi arcs and they are stabilized by the C4h{C}_{4h}C4h​ point-group symmetry. By applying a realizable C4{C}_{4}C4​ breaking term, we find that each double-Weyl point splits into two single-Weyl points and obtain rich phase diagrams in the parameter space spanned by the strengths of an effective Zeeman term and the C4{C}_{4}C4​ breaking term, which contains a topological and a normal insulating phase and two topological Weyl semimetal phases with eight and four single-Weyl points, apart from the double-Weyl semimetal phase. Furthermore, we demonstrate with numerical simulations that (i) the mimicked double- and single-Weyl points can be detected by measuring the atomic transfer fractions after a Bloch oscillation; (ii) the Chern number of different quantum phases in the phase diagram can be extracted from the center shift of the hybrid Wannier functions, which can be directly measured with time-of-flight imaging; (iii) the band topology of the C4{C}_{4}C4​-symmetric Bloch Hamiltonian can be detected simply from measuring the spin polarization at the high-symmetry momentum points with a condensate in the optical lattice. The proposed system would provide a promising platform for elaborating the intrinsic exotic physics of double-Weyl semimetals and the related topological phase transitions.
The discovery of integer quantum Hall effect and its subsequent theoretical formulation heralded a new paradigm of thinking in condensed matter physics, which has by now blossomed into the rapidly growing field of topological phases. In this work we investigate several mutually related topics in the framework of topological band theory. In Chapter 2, we study solutions to boundary states on a lattice and see how they are related to the bulk topology. To elicit a real space manifestation of the non-trivial topology, the presence of a physical edge is not strictly necessary. We study two other possibilities, namely the entanglement spectrum associated with an imaginary spatial boundary, and the localization centers of Wannier functions, in Chapters 3,4, and 5. Topological classification through discrete indices is so far possible only for systems described by pure quantum states - in the existing scheme, quantization is lost for systems in mixed states. In Chapter 6, we present a program through which discrete topological indices can be defined for topological band systems at finite temperature, based on Uhlmann's parallel transport of density matrices. The potential of topologocal insulators in realistic applications lies in the existence of Dirac nodes on its surface spectrum. Dirac physics, however, is not exclusive to TI surfaces. In a recently discovered class of materials known as Weyl semimetals, energy nodes which emit linear dispersions also occur in the bulk material. In Chapter 7, we study the possibility of resonance states induced by localized impurities near the nodal energy in Weyl semimetals, which will help us in understanding the stability of density-of-state suppression at the energy nodes. Finally, in Chapter 8, we apply the topological characterization developed for noninteracting particles to a class of interacting spin models in 3D, which are generalizations of Kitaev's honeycomb model, and identify several exotic quantum phases such as spin metals and spin semimetals