Direct observation of sixfold exotic fermions in the pyrite-structured topological semimetal PdSb2

Abstract

Pyrite-type PdSb 2 with a nonsymmorphic cubic structure has been predicted to host six-fold-degenerate exotic fermions beyond the Dirac and Weyl fermions. Though magnetotransport measurements on PdSb 2 suggest its topologically nontrivial character, direct spectroscpic study of its band structure remains absent. Here, by utilizing high-resolution angle-resolved photoemission spectroscopy, we present a systematic study on its bulk and surface electronic structure. Through careful comparison with first-principles calculations, we verify the existence of six-fold fermions in PdSb 2 , which are formed by three doubly degenerate bands centered at the R point in the Brillouin zone. These bands exhibit parabolic dispersion close to six-fold fermion nodes, in sharp contrast to previously reported ones in chiral fermion materials. Furthermore, our data reveal no protected Fermi arcs in PdSb 2 , which is compatible with its achiral structure. Our findings provide a remarkable platform for study of new topological fermions and indicate their potential applications.In high-energy physics, three types of fermions have been predicated to exist in our universe according to the Lanrence invarience, i.e. the Dirac, Weyl and Majorana fermions. Although the existence of Weyl and Majorana fermions as elementary particles is still under hot debate, some quasiparticles constructed out of excitations were theoretically proposed to be able to mimic all three fermions in solids. Very soon after these predictions, Dirac [1-4], Weyl [5-10] and Majorana fermions [11][12][13] were experimentally confirmed to actually exist in topological non-trivial materials. Moreover, rather than the Poincarè symmetry, it is the invariance under crystal symmetry of one of 230 space groups that constrains fermions in solids [14][15][16][17], and thus there might exist some novel fermions beyond elementary particles discussed in highenergy physics. In solids, it is well known that the topological non-trivial four-and two-fold degenerate band crossings correspond to Dirac and Wely fermions, respectively. While, allowed by crystal symmetries, some new exotic fermions showing three-, six-, or eight-fold degeneracy of band crossings have been proposed, which are particularly intriguing since there are no counterparts in high-energy physics due to Poincarè symmetry constrains [14].To date, angle-resolved photoemission spectroscopy (ARPES) experiments have verified several types of exotic fermions beyond the Dirac and Weyl ones. Unique triply degenerate points in the electronic structure of molybdenum phosphide were reported [18]. Moreover, four-, six-(double * Equal contributions † spin-1) and eight-fold (charge-2) degenerate chiral fermions were as well observed in AlPt [19] and CoSi [20-23] families with extremely long surface Fermi arcs, in sharp contrast to Weyl semimetals which have multiple pairs of Weyl nodes with only small separation. In addition, four types of symmetry-stabilized topological fermions have been observed in PdBiSe [24]. The pyrite PdSb 2 ...

Charge density wave and weak Kondo effect in a Dirac semimetal CeSbTe

“…Topological semimetals are special types of semimetals, exhibiting low-energy excitations that are analogous to high-energy elementary particles [17]. They can be classified into Dirac semimetals [18,19], Weyl semimetals [20][21][22][23][24], nodal-line semimetals [25] and semimetals with exotic degeneracies [26,27]. Dirac semimetals host fourfold degenerate Dirac points with linear dispersion along three momentum directions, which are protected by crystal symmetries.…”

Topological Materials Discovery from Crystal Symmetry

“…6(a,b)]. Examples include the band-inversion, partially dispers-ing threefold points predicted in θ-TaN [ICSD 76455, SG 187 (P 6m2)] [282] and the WC family [ICSD 672362, SG 187 (P 6m2)] [283,284] and confirmed through ARPES in MoP [ICSD 644091, SG 187 (P 6m2)] [285] and WC [286], the coexisting Dirac and Weyl points predicted in the SrHgPb family [ICSD 602710, SG 186 (P 6 3 mc)] [287], and the achiral sixfold fermions observed in PdSb 2 [ICSD 77109, SG 205 (P a 3)] through ARPES experiments [288]. In the aforementioned band-inversion threefold point and mixed Dirac-Weyl TSMs, the nontrivial bulk stable topology and topological surface states originate from a combination of band inversion and chiral-fermion (Weylpoint) descent relations, but are not directly related to the bulk threefold and Dirac points themselves [289].…”

Sixfold fermion near the Fermi level in cubic PtBi2

“…Indeed, despite the relatively large number of confirmed Weyl and Dirac systems , few show band crossings in close proximity to the Fermi level. For semimetals hosting unconventional fermions the list is smaller still, especially given that to date, few such materials have actually been synthesized and checked experimentally for the presence of nodal fermions [42][43][44][45][46][47][48][49][50].…”