| 1. |
- Sayyad, Sharareh, et al.
(författare)
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Symmetry-protected exceptional and nodal points in non-Hermitian systems
- 2023
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Ingår i: SciPost Physics. - 2542-4653. ; 15:5
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Tidskriftsartikel (refereegranskat)abstract
- One of the unique features of non-Hermitian (NH) systems is the appearance of NH degeneracies known as exceptional points (EPs). The extensively studied defective EPs occur when the Hamiltonian becomes non-diagonalizable. Aside from this degeneracy, we show that NH systems may host two further types of non-defective degeneracies, namely, non-defective EPs and ordinary (Hermitian) nodal points. The non-defective EPs manifest themselves by i) the diagonalizability of the NH Hamiltonian at these points and ii) the non-diagonalizability of the Hamiltonian along certain intersections of these points, resulting in instabilities in the Jordan decomposition when approaching the points from certain directions. We demonstrate that certain discrete symmetries, namely parity-time, parity-particle-hole, and pseudo-Hermitian symmetry, guarantee the occurrence of both defective and non-defective EPs. We extend this list of symmetries by including the NH time-reversal symmetry in two-band systems. Two-band and four-band models exemplify our findings. Through an example, we further reveal that ordinary nodal points may coexist with defective EPs in NH models when the above symmetries are relaxed.
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| 2. |
- Stålhammar, Marcus, 1994-, et al.
(författare)
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Classification of exceptional nodal topologies protected by PT symmetry
- 2021
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Ingår i: Physical Review B. - : American Physical Society (APS). - 2469-9950 .- 2469-9969. ; 104:20
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Tidskriftsartikel (refereegranskat)abstract
- Exceptional degeneracies, at which both eigenvalues and eigenvectors coalesce, and parity-time (PT) symmetry, reflecting balanced gain and loss in photonic systems, are paramount concepts in non-Hermitian systems. We here complete the topological classification of exceptional nodal degeneracies protected by PT symmetry in up to three dimensions and provide simple example models whose exceptional nodal topologies include previously overlooked possibilities such as second-order knotted surfaces of arbitrary genus, third-order knots, and fourth-order points.
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| 3. |
- Stålhammar, Marcus, 1994-, et al.
(författare)
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Emergent Chern-Simons interactions in 3+1 dimensions
- 2024
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Ingår i: Physical Review B. - : American Physical Society (APS). - 2469-9950 .- 2469-9969. ; 109:6
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Tidskriftsartikel (refereegranskat)abstract
- Parity-violating superconductors can support a low-dimension local interaction that becomes, upon condensation, a purely spatial Chern-Simons term. Solutions to the resulting generalized London equations can be obtained from solutions of the ordinary London equations with a complex penetration depth, and suggest several remarkable physical phenomena. The problem of flux exclusion by a sphere brings in an anapole moment, the problem of current-carrying wires brings in an azimuthal magnetic field, and the problem of vortices brings in currents along the vortices. We demonstrate that interactions of this kind, together with a conceptually related dimensionally reduced Chern-Simons interaction, can arise from physically plausible microscopic interactions.
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| 4. |
- Stålhammar, Marcus, 1994-, et al.
(författare)
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Fractal nodal band structures
- 2023
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Ingår i: Physical Review Research. - 2643-1564. ; 5:4
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Tidskriftsartikel (refereegranskat)abstract
- Non-Hermitian systems exhibit interesting band structures, where novel topological phenomena arise from the existence of exceptional points at which eigenvalues and eigenvectors coalesce. One important open question is how this would manifest at noninteger dimension. Here, we report on the appearance of fractal eigenvalue degeneracies and Fermi surfaces in Hermitian and non-Hermitian topological band structures. This might have profound implications on the physics of black holes and Fermi surface instability driven phenomena, such as superconductivity and charge density waves.
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| 5. |
- Stålhammar, Marcus, 1994-
(författare)
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Knots and Transport in Topological Matter
- 2022
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Topology has manifestations in physics ranging from the field of condensed matter to photonics. This dissertation provides a two-fold study on the impact of topology in Hermitian and non-Hermitian band structures. Salient examples include the notion of topological invariants and knots, which are both used to describe characteristics of eigenvalue intersections. The first part focuses on Hermitian topological phases of matter, where general methods predicting transport properties in both gapped and gapless phases are presented. The second part turns to non-Hermitian phases and revolves around the topological properties of their exceptional eigenvalue degeneracies. Through a generic construction originating in knot theory, it is shown that such degeneracies take the form of knots, which furthermore bound open Fermi surfaces coinciding with the respective Seifert surfaces. This construction is then extended and applied in a similar fashion to parity-time-symmetric systems, where the exceptional points form surfaces and curves of any topology, as well as points. These theoretical descriptions constitute a fruitful platform to study dissipative systems—in particular in optics where parity-time symmetry implies a balance between gain and loss in photonic crystals—but also give rise to interesting connections to gravity in the context of analogue black holes.
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| 6. |
- Stålhammar, Marcus, 1994-
(författare)
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Knotted Nodal Band Structures
- 2019
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- It is well known that in conventional three dimensional (3D) Hermitian two band models, the intersections between the energy bands are generically given by points. The typical example are Weyl semimetals, where these singular points can be effectively described as Weyl fermions in the low energy regime. By explicitly imposing discrete symmetries or fine-tuning, the intersection can form higher- dimensional nodal structures, e.g. nodal lines. By instead considering dissipative contributions to such a system, the degeneracies will generically take the form of closed 1D curves, consisting of exceptional points, i.e. points where the Hamiltonian becomes defective. By constructing the Hamiltonian in a particular way, the 1D exceptional curves can host non-trivial topology, i.e. they can form links or knots in the Brillouin zone. In stark contrast to line nodes occurring in Hermitian systems, which inevitably rely on discrete symmetries or fine tuning, the exceptional knots are generically stable towards any small perturbation. In further contrast to point singularities and unknotted circles, the topology of knots cannot be characterized by usual integer valued invariants. Instead, the complexity of the knottedness is captured by polynomial type invariants, making the physical classification and interpretation of these system challenging. To this end, the study of knotted nodal band structures naturally brings two different aspects of topology together – mathematical knot theory on the one hand, and the physical theory of topological phases on the other hand.This licentiate thesis focuses on providing the necessary theoretical background to understand the two accompanying publications entitled Knotted non-Hermitian metals, written by Johan Carlström, together with the author of this thesis, Jan Carl Budich and Emil J. Bergholtz, published in Physical Review B on April 24 2019, and Hyperbolic nodal band structures and knot invariants, written by the author of this thesis, together with Lukas Rødland, Gregory Arone, Jan Carl Budich and Emil J. Bergholtz, published in SciPost Physics August 8 2019. An introduction to gapless topological phases in the Hermitian regime, focusing on Weyl semimetals, their classification and surface states, is provided. Then, the light is brought to non-Hermitian operators and the differences from their conventional Hermitian counterpart, such as the two different set of eigenvectors bi-orthogonal to each other, exceptional eigenvalue degeneracies and some of their consequences, are explained. Afterwards, these operators are applied to dissipative physical system, and some of the striking differences from the conventional Hermitian systems are highlighted, the main focus being the possibly non-trivial topology of the 1D exceptional eigenvalue degeneracies. In order to be somewhat self contained, a brief conceptual introduction to the utilized concepts of knot theory is given, and lastly, further research directions and possible experimental realization of the considered systems are discussed.
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| 7. |
- Stålhammar, Marcus, 1994-, et al.
(författare)
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Magneto-Optical Conductivity in Generic Weyl Semimetals
- 2020
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 102:23
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Tidskriftsartikel (refereegranskat)abstract
- Magneto-optical studies of Weyl semimetals have been proposed as a versatile tool for observing low-energy Weyl fermions in candidate materials including the chiral Landau level. However, previous theoretical results have been restricted to the linearized regime around the Weyl node and are at odds with experimental findings. Here, we derive a closed form expression for the magneto-optical conductivity of generic Weyl semimetals in the presence of an external magnetic field aligned with the tilt of the spectrum. The systems are taken to have linear dispersion in two directions, while the tilting direction can consist of any arbitrary continuously differentiable function. This general calculation is then used to analytically evaluate the magneto-optical conductivity of Weyl semimetals expanded to cubic order in momentum. In particular, systems with arbitrary tilt, as well as systems hosting trivial Fermi pockets are investigated. The higher-order terms in momentum close the Fermi pockets in the type-II regime, removing the need for unphysical cutoffs when evaluating the magneto-optical conductivity. Crucially, the ability to take into account closed over-tilted and additional trivial Fermi pockets allows us to treat model systems closer to actual materials and we propose a simple explanation why the presence of parasitic trivial Fermi pockets can mask the characteristic signature of Weyl fermions in magneto-optical conductivity measurements.
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| 8. |
- Stålhammar, Marcus, 1994-, et al.
(författare)
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PT symmetry-protected exceptional cones and analogue Hawking radiation
- 2023
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Ingår i: New Journal of Physics. - : IOP Publishing. - 1367-2630. ; 25:4
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Tidskriftsartikel (refereegranskat)abstract
- Non-Hermitian Hamiltonians, which effectively describe dissipative systems, and analogue gravity models, which simulate properties of gravitational objects, comprise seemingly different areas of current research. Here, we investigate the interplay between the two by relating parity-time-symmetric dissipative Weyl-type Hamiltonians to analogue Schwarzschild black holes emitting Hawking radiation. We show that the exceptional points of these Hamiltonians form tilted cones mimicking the behavior of the light cone of a radially infalling observer approaching a black hole horizon. We further investigate the presence of tunneling processes, reminiscent of those happening in black holes, in a concrete example model. We interpret the non-trivial result as the purely thermal contribution to analogue Hawking radiation in a Schwarzschild black hole. Assuming that our particular Hamiltonian models a photonic crystal, we discuss the concrete nature of the analogue Hawking radiation in this particular setup.
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| 9. |
- Yang, Kang, et al.
(författare)
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Homotopy, Symmetry, and Non-Hermitian Band Topology
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Non-Hermitian matrices are ubiquitous in the description of nature ranging from classical dissipative systems, including optical, electrical, and mechanical metamaterials, to scattering of waves and open quantum many-body systems. Seminal K-theory classifications of non-Hermitian systems based on line and point gaps have deepened the understanding of many physical phenomena. However, ample systems remain beyond this description; reference points and lines are in general unable to distinguish whether multiple non-Hermitian bands exhibit band crossings and braids. To remedy this we consider the complementary notions of non-Hermitian band gaps and separation gaps that crucially include a broad class of multi-band scenarios, enabling the description of generic band structures with symmetries. With these concepts, we provide a unified and systematic classification of both gapped and nodal systems in the presence of physically relevant parity-time (PT) and pseudo-Hermitian symmetries using homotopy theory. This uncovers new fragile phases and, remarkably, also implies new stable phenomena stemming from the topology of both eigenvalues and eigenvectors. In particular, we reveal different Abelian and non-Abelian phases in PT-symmetric systems, described by frame and braid topology. The corresponding invariants are robust to symmetry-preserving perturbations that do not close band gaps, and they also predict the deformation rules of nodal phases. We further demonstrate that spontaneous PT symmetry breaking is captured by a Chern-Euler description, a fingerprint of unprecedented non-Hermitian topology. These results open the door for theoretical and experimental exploration of a rich variety of novel topological phenomena in a wide range of physical platforms.
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