Tuning the crystalline electric field and magnetic anisotropy along the CeCuBi2-xSbx series

Quantum oscillations of the quasiparticle lifetime in a metal

Following nearly a century of research, it remains a puzzle that the low-lying excitations of metals are remarkably well explained by effective single-particle theories of non-interacting bands1-4. The abundance of interactions in real materials raises the question of direct spectroscopic signatures of phenomena beyond effective single-particle, single-band behaviour. Here we report the identification of quantum oscillations (QOs) in the three-dimensional topological semimetal CoSi, which defy the standard description in two fundamental aspects. First, the oscillation frequency corresponds to the difference of semiclassical quasiparticle (QP) orbits of two bands, which are forbidden as half of the trajectory would oppose the Lorentz force. Second, the oscillations exist up to above 50 K, in strong contrast to all other oscillatory components, which vanish below a few kelvin. Our findings are in excellent agreement with generic model calculations of QOs of the QP lifetime (QPL). Because the only precondition for their existence is a nonlinear coupling of at least two electronic orbits, for example, owing to QP scattering on defects or collective excitations, such QOs of the QPL are generic for any metal featuring Landau quantization with several orbits. They are consistent with certain frequencies in topological semimetals5-9, unconventional superconductors10,11, rare-earth compounds12-14 and Rashba systems15, and permit to identify and gauge correlation phenomena, for example, in two-dimensional materials16,17 and multiband metals18.

B20 Weyl Semimetal CoSi Film Fabricated by Flash-Lamp Annealing

B20-CoSi is a newly discovered Weyl semimetal that crystallizes into a noncentrosymmetric crystal structure. However, the investigation of B20-CoSi has so far been focused on bulk materials, whereas the growth of thin films on technology-relevant substrates is a prerequisite for most practical applications. In this study, we have used millisecond-range flash-lamp annealing, a nonequilibrium solid-state reaction, to grow B20-CoSi thin films. By optimizing the annealing parameters, we were able to obtain thin films with a pure B20-CoSi phase. The magnetic and transport measurements indicate the appearance of the charge density wave and chiral anomaly. Our work presents a promising method for preparing thin films of most binary B20 transition-metal silicides, which are candidates for topological Weyl semimetals.

Shubnikov-de Haas and de Haas-van Alphen oscillations in Czochralski grown CoSi single crystal

Anisotropic transport, Shubnikov-de Haas (SdH), and de Haas-van Alphen (dHvA) quantum oscillations studies are reported on a high-quality CoSi single crystal grown by the Czochralski method. Temperature-dependent resistivities indicate the dominating electron-electron scattering. Magnetoresistance (MR) at 2 K reaches 610% forI ∥ [111]andB ∥ [011-], whereas it is 500% forI ∥ [011-] andB ∥ [111]. A negative slope in field-dependent Hall resistivity suggests electrons are the majority carriers. The carrier concentration extracted from Hall conductivity indicates no electron-hole compensation. In 3D CoSi, the electron transport lifetime is found to be approximately in the same order as the quantum lifetime, whereas in 2Delectron gas the long-range scattering drives the transport life much larger than the quantum lifetime. From MR and Hall SdH oscillations, the effective masses and Dingle temperatures have been calculated. The dHvA oscillation reveals three frequencies at 18 T (γ), 558 T (α) and 663 T (β), whereas, SdH oscillation results in only two frequenciesαandβ. Theγfrequency observed in dHvA oscillation is a tiny hole pocket at the Γ point.

Network of Topological Nodal Planes, Multifold Degeneracies, and Weyl Points in CoSi

We showcase the importance of global band topology in a study of the Weyl semimetal CoSi as a representative of chiral space group (SG) 198. We identify a network of band crossings comprising topological nodal planes, multifold degeneracies, and Weyl points consistent with the fermion doubling theorem. To confirm these findings, we combined the general analysis of the band topology of SG 198 with Shubnikov-de Haas oscillations and material-specific calculations of the electronic structure and Berry curvature. The observation of two nearly dispersionless Shubnikov-de Haas frequency branches provides unambiguous evidence of four Fermi surface sheets at the R point that reflect the symmetry-enforced orthogonality of the underlying wave functions at the intersections with the nodal planes. Hence, irrespective of the spin-orbit coupling strength, SG 198 features always six- and fourfold degenerate crossings at R and Γ that are intimately connected to the topological charges distributed across the network.

Quasi-symmetry protected topology in a semi-metal

The crystal symmetry of a material dictates the type of topological band structures it may host, and therefore symmetry is the guiding principle to find topological materials. Here we introduce an alternative guiding principle, which we call 'quasi-symmetry'. This is the situation where a Hamiltonian has an exact symmetry at lower-order that is broken by higher-order perturbation terms. This enforces finite but parametrically small gaps at some low-symmetry points in momentum space. Untethered from the restraints of symmetry, quasi-symmetries eliminate the need for fine-tuning as they enforce that sources of large Berry curvature will occur at arbitrary chemical potentials. We demonstrate that a quasi-symmetry in the semi-metal CoSi stabilizes gaps below 2 meV over a large near-degenerate plane that can be measured in the quantum oscillation spectrum. The application of in-plane strain breaks the crystal symmetry and gaps the degenerate point, observable by new magnetic breakdown orbits. The quasi-symmetry, however, does not depend on spatial symmetries and hence transmission remains fully coherent. These results demonstrate a class of topological materials with increased resilience to perturbations such as strain-induced crystalline symmetry breaking, which may lead to robust topological applications as well as unexpected topology beyond the usual space group classifications.

Chirality locking charge density waves in a chiral crystal

In Weyl semimetals, charge density wave (CDW) order can spontaneously break the chiral symmetry, gap out the Weyl nodes, and drive the material into the axion insulating phase. Investigations have however been limited since CDWs are rarely seen in Weyl semimetals. Here, using scanning tunneling microscopy/spectroscopy (STM/S), we report the discovery of a novel unidirectional CDW order on the (001) surface of chiral crystal CoSi – a unique Weyl semimetal with unconventional chiral fermions. The CDW is incommensurate with both lattice momentum and crystalline symmetry directions, and exhibits an intra unit cell π phase shift in the layer stacking direction. The tunneling spectrum shows a particle-hole asymmetric V-shaped energy gap around the Fermi level that modulates spatially with the CDW wave vector. Combined with first-principle calculations, we identify that the CDW is locked to the crystal chirality and is related by a mirror reflection between the two enantiomers of the chiral crystal. Our findings reveal a novel correlated topological quantum state in chiral CoSi crystals and raise the potential for exploring the unprecedented physical behaviors of unconventional chiral fermions.

The interplay between electron correlation and topological properties remains less understood. Here, the authors report a charge density wave (CDW) order on the (001) surface of a Weyl semimetal CoSi, where an energy gap modulates spatially with the CDW wave vector.