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Abstract The discovery of topological semimetals with multifold band crossings has opened up a new and exciting frontier in the field of topological physics. These materials exhibit large Chern numbers, leading to long double Fermi arcs on their surfaces, which are protected by either crystal symmetries or topological order. The impact of these multifold crossings extends beyond surface science, as they are not constrained by the Poincar classification of quasiparticles and only need to respect the crystal symmetry of one of the 1651 magnetic space groups. Consequently, we observe the emergence of free fermionic excitations in solid-state systems that have no high-energy counterparts, protected by non-symmorphic symmetries. In this work, we review the recent theoretical and experimental progress made in the field of multifold topological semimetals. We begin with the theoretical prediction of the so-called multifold fermions and discuss the subsequent discoveries of chiral and magnetic topological semimetals. Several experiments that have realized chiral semimetals in spectroscopic measurements are described, and we discuss the future prospects of this field. These exciting developments have the potential to deepen our understanding of the fundamental properties of quantum matter and inspire new technological applications in the future. 

Abstract The geometric phase of an electronic wave function, also known as Berry phase, is the fundamental basis of the topological properties in solids. This phase can be tuned by modulating the band structure of a material, providing a way to drive a topological phase transition. However, despite significant efforts in designing and understanding topological materials, it remains still challenging to tune a given material across different topological phases while tracing the impact of the Berry phase on its quantum transport properties. Here, we report these two effects in a magnetotransport study of ZrTe₅. By tuning the band structure with uniaxial strain, we use quantum oscillations to directly map a weak-to-strong topological insulator phase transition through a gapless Dirac semimetal phase. Moreover, we demonstrate the impact of the strain-tunable spin-dependent Berry phase on the Zeeman effect through the amplitude of the quantum oscillations. We show that such a spin-dependent Berry phase, largely neglected in solid-state systems, is critical in modeling quantum oscillations in Dirac bands of topological materials. 

Abstract New developments in the field of topological matter are often driven by materials discovery, including novel topological insulators, Dirac semimetals, and Weyl semimetals. In the last few years, large efforts have been made to classify all known inorganic materials with respect to their topology. Unfortunately, a large number of topological materials suffer from non‐ideal band structures. For example, topological bands are frequently convoluted with trivial ones, and band structure features of interest can appear far below the Fermi level. This leaves just a handful of materials that are intensively studied. Finding strategies to design new topological materials is a solution. Here, a new mechanism is introduced, which is based on charge density waves and non‐symmorphic symmetry, to design an idealized Dirac semimetal. It is then shown experimentally that the antiferromagnetic compound GdSb_0.46Te_1.48is a nearly ideal Dirac semimetal based on the proposed mechanism, meaning that most interfering bands at the Fermi level are suppressed. Its highly unusual transport behavior points to a thus far unknown regime, in which Dirac carriers with Fermi energy very close to the node seem to gradually localize in the presence of lattice and magnetic disorder. 

One of the most striking signatures of Weyl fermions in solid-state systems is their surface Fermi arcs. Fermi arcs can also be localized at internal twin boundaries where two Weyl materials of opposite chirality meet. In this work, we derive constraints on the topology and connectivity of these “internal Fermi arcs.” We show that internal Fermi arcs can exhibit transport signatures, and we propose two probes: quantum oscillations and a quantized chiral magnetic current. We propose merohedrally twinned B20 materials as candidates to host internal Fermi arcs, verified through both model and calculations. Our theoretical investigation sheds light on the topological features and motivates experimental studies on the intriguing physics of internal Fermi arcs. 

Flat electronic bands are expected to show proportionally enhanced electron correlations, which may generate a plethora of novel quantum phases and unusual low-energy excitations. They are increasingly being pursued in d-electron-based systems with crystalline lattices that feature destructive electronic interference, where they are often topological. Such flat bands, though, are generically located far away from the Fermi energy, which limits their capacity to partake in the low-energy physics. Here we show that electron correlations produce emergent flat bands that are pinned to the Fermi energy. We demonstrate this effect within a Hubbard model, in the regime described by Wannier orbitals where an effective Kondo description arises through orbital-selective Mott correlations. Moreover, the correlation effect cooperates with symmetry constraints to produce a topological Kondo semimetal. Our results motivate a novel design principle for Weyl Kondo semimetals in a new setting, viz. d-electron-based materials on suitable crystal lattices, and uncover interconnections among seemingly disparate systems that may inspire fresh understandings and realizations of correlated topological effects in quantum materials and beyond. 

Lattice symmetries are central to the characterization of electronic topology. Recently, it was shown that Green's function eigenvectors form a representation of the space group. This formulation has allowed the identification of gapless topological states even when quasiparticles are absent. Here we demonstrate the profundity of the framework in the extreme case, when interactions lead to a Mott insulator, through a solvable model with long-range interactions. We find that both Mott poles and zeros are subject to the symmetry constraints, and relate the symmetry-enforced spectral crossings to degeneracies of the original noninteracting eigenstates. Our results lead to new understandings of topological quantum materials and highlight the utility of interacting Green's functions toward their symmetry-based design. Published by the American Physical Society2024