Multiple Types of Topological Fermions in Transition Metal Silicides

Abstract

Exotic massless fermionic excitations with non-zero Berry flux, other than Dirac and Weyl fermions, could exist in condensed matter systems under the protection of crystalline symmetries, such as spin-1 excitations with 3-fold degeneracy and spin-3/2 Rarita-Schwinger-Weyl fermions. Herein, by using ab initio density functional theory, we show that these unconventional quasiparticles coexist with type-I and type-II Weyl fermions in a family of transition metal silicides, including CoSi, RhSi, RhGe and CoGe, when the spin-orbit coupling (SOC) is considered. Their non-trivial topology results in a series of extensive Fermi arcs connecting projections of these bulk excitations on side surface, which is confirmed by (010) surface electronic spectra of CoSi. In addition, these stable arc states exist within a wide energy window around the Fermi level, which makes them readily accessible in angle-resolved photoemission spectroscopy measurements.Introduction.-Three types of fermions play fundamental roles in our understanding of nature: Majorana, Dirac and Weyl [1]. Much attention has been paid to looking for these fundamental particles in high energy physics during past few decades, whereas only signature of Dirac fermions is captured. Interestingly, the same movement comes up in the field of condensed matter physics [2], and great achievements have been made in last few years. For example, the Majorana-like excitations are detected in superconducting heterostructures [3][4][5][6]; the Dirac [7][8][9][10][11][12] and Weyl [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] fermions are observed in some compounds. These quasiparticles in solid states are not only important for basic science, but also show great potential for practical applications on new devices [30,31].Because symmetries in condensed matter physics are usually much lower than the Poincaré symmetry in high energy physics, quasiparticles in solid states are less constrained such that various new types of fermionic excitations are predicted to exist in 3D lattices [32]. Among these allowed by space group (SG) symmetries are spin-1 and spin-3/2 massless fermionic excitations, besides the well-known spin-1/2 case, namely the Weyl fermion. All of these massless quasiparticles can be described by the low energy Hamiltonian in a unified manner to the linear order of momentum

Three-component fermions with surface Fermi arcs in tungsten carbide

“…Finally, we mention that the three-component fermions observed in WC are essentially distinct from the chiral fermions enforced by filling and symmetry in the non-symmorphic systems 4,10,11,18 , in which the non-zero topological charges protect the Weyl-type Fermi arcs. In the latter case, the bulk nodes with opposite topological charges are pinned at either the centre or the corner of the bulk BZ, and thus the surface Fermi arcs connecting their projections can span over a wider segment of the surface BZ.…”

“…In addition to four-and two-fold degeneracy, it has been shown that space-group symmetries in crystals may protect other types of degenerate point, near which the quasiparticle excitations are not the analogues of any elementary fermions described in the standard model. Theory has proposed three-, six-and eight-fold degenerate points at high-symmetry momenta in the BZ in several specific non-symmorphic space groups 3,4,10,11 , where the combination of nonsymmorphic symmetries and other point symmetries leads to three-, six-and eight-dimensional irreducible representations. Theory has also proposed that in a symmorphic space group P m 6 2 (no.…”

“…Recent advances suggest new types of topological semimetal, in which spatial symmetries protect gapless electronic excitations without high-energy analogues [3][4][5][6][7][8][9][10][11] . Here, using angle-resolved photoemission spectroscopy, we observe triply degenerate nodal points near the Fermi level of tungsten carbide with space group P m 6 2 (no.…”

Weyl and Dirac semimetals in three-dimensional solids

“…In principle the inclusion of broken T makes the possibilities even richer. A particularly promising family of materials that is expected to combine multiple types of band touching and long Fermi-arcs on certain surfaces may be found in the AB material class (A = Co, Rh and B=Si, Ge) (Chang et al, 2017;Tang et al, 2017).…”

Threes company

“…Exploiting these advances in symmetry and electronic structure, researchers have just recently proposed the presence of closely related topological surface states and doubled threefold fermions in readily synthesizable crystals in the RhSi family [10,11]. Given the immense number of known crystalline compounds still uninvestigated for nodal fermions, other ideal materials candidates will surely follow.…”