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• W3048463309 abstract "Dirac materials are of great interest as condensed matter realizations of the Dirac and Weyl equations. In particular, they serve as a starting point for the study of topological phases. This physics has been extensively studied in electronic systems such as graphene, Weyl, and Dirac semimetals. In contrast, recent studies have highlighted several examples of Dirac-like cones in collective excitation spectra, viz. in phonon, magnon, and triplon bands. These cannot be directly related to the Dirac or Weyl equations as they are bosonic in nature with pseudounitary band bases. We address this issue by constructing a generic deformation scheme that maps any fermionic Hamiltonian and its spectrum to that of a bosonic problem. In particular, we show that any Dirac-like equation can be deformed into a suitable bosonic form. The resulting bosonic spectra bear a two-to-one relation to that of the parent Dirac system. Their dispersions inherit several interesting properties including conical band touching points and a gap-opening role for ‘mass’ terms. The relationship also extends to the band eigenvectors with the bosonic states carrying the same Berry connections as the parent fermionic states. The bosonic bands thus inherit topological character as well. If the parent fermionic system has nontrivial topology that leads to midgap surface states, the bosonic analog also hosts surface states that lie within the corresponding band gap. The proposed bosonic Dirac structure appears in several known models. In materials, it is realized in Ba2CuSi2O6Cl2 and possibly in CoTiO3 as well as in paramagnetic honeycomb ruthenates. Our results allow for a rigorous understanding of Dirac phononic and magnonic systems and enable concrete predictions, e.g., of surface states in magnonic topological insulators and Weyl semimetals.Received 4 March 2018Accepted 5 June 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.033035Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasMagnonsPhysical SystemsDirac semimetalTopological materialsCondensed Matter & Materials Physics" @default.
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• W3048463309 date "2020-07-08" @default.
• W3048463309 modified "2023-10-16" @default.
• W3048463309 title "Dirac Hamiltonians for bosonic spectra" @default.
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• W3048463309 doi "https://doi.org/10.1103/physrevresearch.2.033035" @default.
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