Charge instability of topological Fermi arcs in chiral crystal CoSi.

Topological boundary states emerged at the spatial boundary between topological non-trivial and trivial phases, are usually gapless, or commonly referred as metallic states. For example, the surface state of a topological insulator is a gapless Dirac state. These metallic topological boundary states are typically well described by non-interacting fermions. However, the behavior of topological boundary states with significant electron-electron interactions, which could turn the gapless boundary states into gapped ordered states, e.g., density wave states or superconducting states, is of great interest theoretically, but is still lacking evidence experimentally. Here, we report the observation of incommensurable charge density wave (CDW) formed on the topological boundary states driven by the electron-electron interactions on the (001) surface of CoSi. The wavevector of CDW varies as the temperature changes, which coincides with the evolution of topological surface Fermi arcs with temperature. The orientation of the CDW phase is determined by the chirality of the Fermi arcs, which indicates a direct association between CDW and Fermi arcs. Our finding will stimulate the search of more interactions-driven ordered states, such as superconductivity and magnetism, on the boundaries of topological materials.

Discovery of [Formula: see text] rotation anomaly in topological crystalline insulator SrPb.

Topological crystalline insulators (TCIs) are insulating electronic states with nontrivial topology protected by crystalline symmetries. Recently, theory has proposed new classes of TCIs protected by rotation symmetries [Formula: see text], which have surface rotation anomaly evading the fermion doubling theorem, i.e., n instead of 2n Dirac cones on the surface preserving the rotation symmetry. Here, we report the first realization of the [Formula: see text] rotation anomaly in a binary compound SrPb. Our first-principles calculations reveal two massless Dirac fermions protected by the combination of time-reversal symmetry [Formula: see text] and [Formula: see text] on the (010) surface. Using angle-resolved photoemission spectroscopy, we identify two Dirac surface states inside the bulk band gap of SrPb, confirming the [Formula: see text] rotation anomaly in the new classes of TCIs. The findings enrich the classification of topological phases, which pave the way for exploring exotic behavior of the new classes of TCIs.

Chiral fermion reversal in chiral crystals.

In materials chiral fermions such as Weyl fermions are characterized by nonzero chiral charges, which are singular points of Berry curvature in momentum space. Recently, new types of chiral fermions beyond Weyl fermions have been discovered in structurally chiral crystals CoSi, RhSi and PtAl. Here, we have synthesized RhSn single crystals, which have opposite structural chirality to the CoSi crystals we previously studied. Using angle-resolved photoemission spectroscopy, we show that the bulk electronic structures of RhSn are consistent with the band calculations and observe evident surface Fermi arcs and helical surface bands, confirming the existence of chiral fermions in RhSn. It is noteworthy that the helical surface bands of the RhSn and CoSi crystals have opposite handedness, meaning that the chiral fermions are reversed in the crystals of opposite structural chirality. Our discovery establishes a direct connection between chiral fermions in momentum space and chiral lattices in real space.

Observation of unconventional chiral fermions with long Fermi arcs in CoSi.

Chirality-the geometric property of objects that do not coincide with their mirror image-is found in nature, for example, in molecules, crystals, galaxies and life forms. In quantum field theory, the chirality of a massless particle is defined by whether the directions of its spin and motion are parallel or antiparallel. Although massless chiral fermions-Weyl fermions-were predicted 90 years ago, their existence as fundamental particles has not been experimentally confirmed. However, their analogues have been observed as quasiparticles in condensed matter systems. In addition to Weyl fermions1-4, theorists have proposed a number of unconventional (that is, beyond the standard model) chiral fermions in condensed matter systems5-8, but direct experimental evidence of their existence is still lacking. Here, by using angle-resolved photoemission spectroscopy, we reveal two types of unconventional chiral fermion-spin-1 and charge-2 fermions-at the band-crossing points near the Fermi level in CoSi. The projections of these chiral fermions on the (001) surface are connected by giant Fermi arcs traversing the entire surface Brillouin zone. These chiral fermions are enforced at the centre or corner of the bulk Brillouin zone by the crystal symmetries, making CoSi a system with only one pair of chiral nodes with large separation in momentum space and extremely long surface Fermi arcs, in sharp contrast to Weyl semimetals, which have multiple pairs of Weyl nodes with small separation. Our results confirm the existence of unconventional chiral fermions and provide a platform for exploring the physical properties associated with chiral fermions.

Quasiparticle interference evidence of the topological Fermi arc states in chiral fermionic semimetal CoSi.

Chiral fermions in solid state feature "Fermi arc" states, connecting the surface projections of the bulk chiral nodes. The surface Fermi arc is a signature of nontrivial bulk topology. Unconventional chiral fermions with an extensive Fermi arc traversing the whole Brillouin zone have been theoretically proposed in CoSi. Here, we use scanning tunneling microscopy/spectroscopy to investigate quasiparticle interference at various terminations of a CoSi single crystal. The observed surface states exhibit chiral fermion-originated characteristics. These reside on (001) and (011) but not (111) surfaces with p-rotation symmetry, spiral with energy, and disperse in a wide energy range from ~-200 to ~+400 mV. Owing to the high-energy and high-space resolution, a spin-orbit coupling-induced splitting of up to ~80 mV is identified. Our observations are corroborated by density functional theory and provide strong evidence that CoSi hosts the unconventional chiral fermions and the extensive Fermi arc states.