A6: Global band topology: from point crossings and nodal planes to KondoWeyl fermions
Marc Wilde, Andreas Schnyder, Laura Classen
Topological materials are of interest both for fundamental research and applications in spintronics and quantum technology. These materials exhibit a diverse set of different band topologies, including Weyl points, multifold band crossings, and nodal planes. In this project we combine theoretical band topology calculations with quantum oscillation experiments to (i) study the interdependence among multiple band topologies, (ii) devise generic means to place the band topologies at the Fermi level, and (iii) work out methods to efficiently control the band topology by external tuning parameters.
Publications
2024 

Wu, X.; Chakraborty, D.; Schnyder, A. P.; Greco, A. Crossover between electronelectron and electronphonon mediated pairing on the Kagome lattice Journal Article Phys. Rev. B 109, 014517, 2024. @article{wu_crossover_2024,  
Huber, N.; Mishra, S.; Sheikin, I.; Alpin, K.; Schnyder, A. P.; Benka, G.; Bauer, A.; Pfleiderer, C.; Wilde, M. A. Fermi surface of the chiral topological semimetal CoSi Journal Article Phys. Rev. B 109, 205115, 2024. @article{huber_fermi_2024, We report a study of the Fermi surface of the chiral semimetal CoSi and its relationship to a network of multifold topological crossing points, Weyl points, and topological nodal planes in the electronic band structure. Combining quantum oscillations in the Hall resistivity, magnetization, and torque magnetization with ab initio electronic structure calculations, we identify two groups of Fermisurface sheets, one centered at the 𝑅 point and the other centered at the Γ point. The presence of topological nodal planes at the Brillouin zone boundary enforces topological protectorates on the Fermisurface sheets centered at the 𝑅 point. In addition, Weyl points exist close to the Fermisurface sheets centered at the 𝑅 and the Γ points. In contrast, topological crossing points at the 𝑅 point and the Γ point, which have been advertised to feature exceptionally large Chern numbers, are located at a larger distance to the Fermi level. Representing a unique example in which the multitude of topological band crossings has been shown to form a complex network, our observations in CoSi highlight the need for detailed numerical calculations of the Berry curvature at the Fermi level, regardless of the putative existence and the possible character of topological band crossings in the band structure.  
Hu, Y.; Ma, J.; Li, Y.; Jiang, Y.; Gawryluk, D. J.; Hu, T.; Teyssier, J.; Multian, V.; Yin, Z.; Xu, S.; others, Phonon promoted charge density wave in topological kagome metal ScV_{6}Sn_{6} Journal Article Nat. Commun. 15, 1658, 2024. @article{hu_phonon_2024,  
Parshukov, K.; Wiedmann, R.; Schnyder, A. P. Topological responses from gapped Weyl points in 2D altermagnets Unpublished 2024, arXiv.2403.09520. @unpublished{parshukov_topological_2024, Altermagnetism combines aspects of both ferromagnetism and antiferromagnetism, breaking spin degeneracy while possessing no net magnetization. In this work, we study the symmetry requirements for topologically protected Weyl points in 2D altermagnets, involving bands with the same spin quantum number. We classify all spinwallpaper groups whose symmetries protect 2D Weyl points and show that their nontrivial topology is charactrized by a quantized $textbackslashpi$Berry phase. Representative electronic tightbinding and magnonic linear spinwave models are constructed to investigate the unusual transport characteristics of these 2D Weyl points. Different mass terms, induced for example through strain or via coupling to light or a substrate, gap out the Weyl points leading to emerging gapped topological phases. Depending on the mass terms, these phases carry finite Chern and/or spin Chern numbers and exhibit protected edge states as well as anomalous electronic and thermal Hall responses. We calculate these Hall currents for the different topological phases.  
2023 

Alpin, K.; Hirschmann, M. M.; Heinsdorf, N.; Leonhardt, A.; Yau, W. Y.; Wu, X.; Schnyder, A. P. Fundamental laws of chiral band crossings: Local constraints, global constraints, and topological phase diagrams Journal Article Phys. Rev. Research 5, 043165, 2023. @article{alpin_fundamental_2023, We derive two fundamental laws of chiral band crossings: (i) a local constraint relating the Chern number to phase jumps of rotation eigenvalues and (ii) a global constraint determining the number of chiral crossings on rotation axes. Together with the fermion doubling theorem, these laws describe all conditions that a network of chiral band crossing must satisfy. We apply the fundamental laws to prove the existence of enforced double Weyl points, nodal planes, and generic Weyl points, among others. In addition, we show that chiral space group symmetries can not stabilize nodal lines with finite Chern numbers. Combining the local constraint with explicit lowenergy models, we determine the generic topological phase diagrams of all multifold crossings. Remarkably, we find a fourfold crossing with Chern number 5, which exceeds the previously conceived maximum Chern number of 4. We identify materials crystallizing in space group 198, such as B20 materials and BaAsPt, as suitable compounds with this Chern number 5 crossing.  
Kumar, V.; Bauer, A.; Franz, C.; Spallek, J.; Schönmann, R.; Stekiel, M.; Schneidewind, A.; Wilde, M. A.; Pfleiderer, C. Lowtemperature antiferromagnetic order in orthorhombic CePdAl_{3} Journal Article Phys. Rev. Research 5, 023157, 2023. @article{kumar_lowtemperature_2023, We report the magnetization, ac susceptibility, and specific heat of optically floatzoned single crystals of CePdAl3. In comparison to the properties of polycrystalline CePdAl3 reported in the literature, which displays a tetragonal crystal structure and no longrange magnetic order, our single crystals exhibit an orthorhombic structure (𝐶𝑚𝑐𝑚) and antiferromagnetic order below a Néel temperature 𝑇1=5.6 K. The specific heat at zero field shows two anomalies, namely, a broad transition at 𝑇1=5.6 K followed by a 𝜆anomaly at 𝑇2=5.4 K. A conservative estimate of the Sommerfeld coefficient of the electronic specific heat, 𝛾=121mJK−2mol−1, indicates a moderately enhanced heavyfermion ground state. A twin microstructure evolves in the family of planes spanned by the basal plane lattice vectors 𝐚o and 𝐜o , with the magnetic hard axis 𝐛o common to all twins. The antiferromagnetic state is characterized by a strong ao, co easyplane magnetic anisotropy where the ao direction is the easy axis in the easy plane. A spinflop transition induced under magnetic field along the easy directions, results in complex magnetic phase diagrams. Taken together, our results reveal a high sensitivity of the magnetic and electronic properties of CePdAl3 to its structural modifications.  
Huber, N.; Leeb, V.; Bauer, A.; Benka, G.; Knolle, J.; Pfleiderer, C.; Wilde, M. A. Quantum oscillations of the quasiparticle lifetime in a metal Journal Article Nature 621, 276, 2023. @article{huber_quantum_2023, Following nearly a century of research, it remains a puzzle that the lowlying excitations of metals are remarkably well explained by effective singleparticle theories of noninteracting bands(14). The abundance of interactions in real materials raises the question of direct spectroscopic signatures of phenomena beyond effective singleparticle, singleband behaviour. Here we report the identification of quantum oscillations (QOs) in the threedimensional 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 semimetals(59), unconventional superconductors(10,11), rareearth compounds(1214) and Rashba systems(15), and permit to identify and gauge correlation phenomena, for example, in twodimensional materials(16,17) and multiband metals(18).  
Heinsdorf, N.; Joshi, D. G.; Katsura, H.; Schnyder, A. P. Stable Bosonic Topological Edge Modes in the Presence of ManyBody Interactions Unpublished 2023, arXiv:2309.15113. @unpublished{heinsdorf_stable_2023, 