English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Employing a combination of first-principles calculations and low-energyeffective models, we present a comprehensive investigation on the electronicstructure of Pb$_{10}$(PO$_{4}$)$_{6}$O$_{4}$, which exhibits remarkablequasi-one-dimensional flat-band around the Fermi level that contains novelmulti-dimensional fermions. These flat bands predominantly originate from$p_x/p_y$ orbital of the oxygen molecules chain at $4e$ Wyckoff positions, andthus can be well-captured by a four-band tight-binding model. Furthermore, theabundant crystal symmetry inherent to Pb$_{10}$(PO$_{4}$)$_{6}$O$_{4}$ providesan ideal platform for the emergence of various multi-dimensional fermions,including a 0D four-fold degenerated Dirac fermion with quadratic dispersion, a1D quadratic/linear nodal-line (QNL/LNL) fermion along symmetric $k$-paths, 1Dhourglass nodal-line (HNL) fermion linked to the Dirac fermion, and a 2Dsymmetry-enforced nodal surface (NS) found on the $k_z$=$\pi$ plane. Moreover,when considering the weak ferromagnetic order, Pb$_{10}$(PO$_{4}$)$_{6}$O$_{4}$transforms into a rare semi-half-metal, which is characterized by the presenceof Dirac fermion and HNL fermion at the Fermi level for a single spin channelexhibiting 100$\%$ spin polarization. Our findings reveal the coexistence offlat bands, diverse topological semimetal states and ferromagnetism within inPb$_{10}$(PO$_{4}$)$_{6}$O$_{4}$, which may provide valuable insights forfurther exploring intriguing interplay between superconductivity and exoticelectronic states.

Flat-band and multi-dimensional fermions in Pb10(PO4)6O4