2018/02/22 by P. Sathish Kumar, R. Ganesh, Igor F. Herbut
Materials Science · Physics and Astronomy · #Berry connection and curvature #Chemical and Physical Properties of Materials #Conical surface #Dirac (video compression format) #Dirac equation #Dirac fermion #Dirac sea #Eigenvalues and eigenvectors #Graphene research and applications #Hamiltonian (control theory) #Topological Materials and Phenomena #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevresearch.2.033035
published as Phys. Rev. Research 2, 033035 (2020) · 10 pages, supersedes arXiv:1802.08269
openalex created_date 2018/03/06 · arxiv created 2020/01/18 · openalex publication_date 2020/07/08 · arxiv updated 2020/08/11 · openalex updated_date 2026/08/05
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 Ba 2 CuSi 2 O 6 Cl 2 and possibly in CoTiO 3 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.