Observation of three-component fermions in the topological semimetal molybdenum phosphide

Abstract

Condensed matter systems can host quasiparticle excitations that are analogues to elementary particles such as Majorana, Weyl, and Dirac fermions. Recent advances in band theory have expanded the classification of fermions in crystals, and revealed crystal symmetry-protected electron excitations that have no high-energy counterparts.Here, using angle-resolved photoemission spectroscopy, we demonstrate the existence of a triply degenerate point in the electronic structure of MoP crystal, where the quasiparticle excitations are beyond the Majorana-Weyl-Dirac classification.Furthermore, we observe pairs of Weyl points in the bulk electronic structure coexisting with the 'new fermions', thus introducing a platform for studying the interplay between different types of fermions.In quantum field theory, Lorentz invariance gives three types of fermions, namely, the Dirac, Weyl and Majorana fermions (1,2). While it is still under debate whether any elementary particle of Weyl or Majorana types exists, all three types of fermions have been proposed to exist as low-energy and long-wavelength quasiparticle excitations in condensed matter systems (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14). The existence of Dirac and Weyl fermions has been experimentally confirmed (15)(16)(17)(18)(19)(20) and that of Majorana fermions has been supported by various experiments (21,22). Recently, it has been shown theoretically that as the Poincare group (Lorentz group plus 4-translation) in the continuum space-time is reduced to the 230 space groups in lattices, more types of fermions (dubbed 'new fermions') are allowed to appear as quasiparticle excitations near certain band crossing points (23-29).Specially, it is well known that fermion statistics is incompatible with three-fold degeneracy in the continuum due to the half-integer spin; yet, three-fold degeneracy (triply degenerate point (TP)) can be protected in a lattice either by rotation symmetries (25-29) or nonsymmorphic symmetries (23,24). In either case, the three-component fermions conceptually lie between Weyl fermions (two-component) and Dirac fermions (four-component) (Fig. 1A), and carry characteristic properties distinct from the other two, including unique surface states and transport features. The crossing point is triply degenerate and protected by the C 3 symmetry along Γ-A, which is similar to the case of the Dirac semimetals Na 3 Bi (7) and Cd 3 As 2 (9). With SOC considered, the bands along Γ-A are reconstructed into two doubly-degenerate |J z | = 1/2 bands and two non-degenerate |J z | = 3/2 bands due to the M z mirror symmetry. The crossing points of the bands with different |J z | are protected by the C 3 symmetry, forming four TPs along the Γ-A line (Fig. 1F).We first perform core level photoemission measurements, which confirms the chemical composition of MoP ( Fig. 2A). respectively. We observe one hexagonal hole pocket around Γ and one small hole pocket at K at k z = 0, as well as one almost circular electron pocket around Α at k z = π.These experimental...

Pressure-induced superconductivity in MoP

“…One such material hosting triply degenerate fermion, which has been experimentally identified via angleresolved photoemission spectroscopy (ARPES) is WC (tungsten carbide) structured MoP. 19 The crystal structure of MoP belongs to the symmorphic space group P-6m2 (number 187). Within the crystal lattice, the P atom and Mo atoms are located at the 1d (1/3, 2/3, 1/2) and 1a (0, 0, 0) Wyckoff positions, respectively.…”

“…The recent breakthrough in predicting and identifying unconventional "new fermion" beyond conventional Dirac and Weyl fermion sparked new research interest in the field of topological semimetal. [15][16][17][18][19][20] Among the symmetries of 230 crystal space groups in condensed-matter physics, the threefold, sixfold, and eightfold degenerate quasiparticle excitation emanating from the multiply degenerate points of band crossing near the Fermi level can be protected in a crystal lattice either by symmorphic rotation combined with mirror symmetries or by non-symmorphic …”

Unconventional quantum Hall effects in two-dimensional massive spin-1 fermion systems

“…Beyond these fermions permitted in particle physics, a new fermion violating Lorentz invariance 17,18 , which is called type-II Weyl fermions 18 (also called structured Weyl fermions 17 ), has been discovered in superfluids 17 and condensed matter materials [18][19][20][21] . Recently, another type of new fermions in three dimensions beyond conventional fermions in particle physics were predicted in solid-state materials [22][23][24][25][26][27][28] ; they are named unconventional fermions with highly degenerate points that are described by an effective Hamiltonian H = k ·Ŝ with k being the momenta andŜ being the angular momentum matrices. These highly degenerate fermions have also been studied in 2D systems [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] , especially for spin-1 fermions, which can be realized in the dice model [29][30][31][32][33][34][35][36]…”

Magnetic and noncentrosymmetric Weyl fermion semimetals in the RAlGe family of compounds ( R=rareearthChang1, Singh2, Xu3 et al. 2018Phys. Rev. B17231020View full textAdd to dashboardCite

“…Further transport measurements have revealed unconventional magnetic and optical responses of TaAs family [26][27][28][29]. Despite recent advances of topological semimetals in both theory [30][31][32][33][34][35][36][37][38][39][40][41][42][43] and experiment [26][27][28][29][44][45][46][47][48][49][50][51] , the ferromagnetic Weyl semimetal [8,9,[52][53][54][55][56][57] has not been realised in experiments. A key issue is that first-principles band structure calculations on these magnetic materials (e.g.…”