Weyl semimetals host topologically protected Fermi arcs on their surfaces, originating from the Chern number of the bulk Weyl nodes. In trigonal PtBi_2, superconducting signatures have been associated with the Fermi arcs. Theoretical descriptions of this surface superconductivity have so far relied on effective models that are not directly tied to the microscopic electronic structure of the material. In this work we develop a minimal description of the low-energy bands guided by density functional theory calculations and fully constrained by the relevant crystalline and time-reversal symmetries. The model captures the evolution of the Weyl nodes with spin-orbit coupling, including node annihilations, and is able to describe the spin-momentum locking of the surface Fermi arcs. It reproduces the orbital content and the band topology of PtBi_2 and provides a starting point for further studies.

Recent reports of surface-localized topological superconductivity in trigonal PtBi_2 highlight the importance of understanding its surface electronic structure. We investigate the bulk and surface band structure of PtBi_2 using angle-resolved photoemission spectroscopy (ARPES) and first-principles calculations. Through photon-energy- and polarization-dependent measurements, we disentangle bulk dispersions from surface states on the two distinct surface terminations of PtBi_2(0001). For both terminations, we assign several different surface states and find good agreement between experiment and calculations. Based on our calculations, we analyze the orbital composition in the surface and bulk bands and compare the results to polarization-dependent ARPES measurements. Together, our results provide a coherent picture of the surface electronic structure of PtBi_2 across both surface terminations.

We report a study of Shubnikov–de Haas oscillations in high-quality single crystals of ferromagnetic Weyl semimetal Co3Sn2S2. The Fermi surfaces resolved in our experiments are three-dimensional and reflect an underlying trigonal crystallographic symmetry. Combined with density functional calculations, we identify that multiple Fermi surfaces in the system—of both electron and hole nature—arise from the energy dispersion of the (spin-orbit gapped) mirror-protected nodal rings. We observe an evolution of the Fermi surfaces with in-plane magnetic fields, in contrast to field perpendicular to the kagome lattice planes, which has little effect. Viewed alongside the easy-axis anisotropy of the system, our observation reveals an evolution of the electronic structure of Co3Sn2S2—including the Weyl points—with the ferromagnetic moment orientation. Through the case study of Co3Sn2S2, our results provide concrete experimental evidence of an anisotropic interplay via spin-orbit coupling between the magnetic degrees of freedom and electronic band singularities, which has long been expected in semimetallic and metallic magnetic systems.

Altermagnets are a novel class of fully spin-compensated magnetic materials that nevertheless have spin-split electronic bands, offering novel perspectives for spintronics applications. Based on a rigorous analysis of altermagnetic many-body models and their symmetry we establish the important role of two fundamental types of polarizations in altermagnetic insulators: the charge and the spinetic one, where the latter corresponds to a macroscopic spin-displacement field. First principles calculations confirm and quantify their presence in real materials. The two polarizations are directly coupled and emerge in orthogonal directions when inversion symmetry is broken, either by the system developing a spontaneously ferroelectric polarization (in ferroelectric altermagnets), or by a charge displacement induced by an external electric field (for inversion invariant altermagnetic insulators). This presence of large and switchable spin accumulations constitute an attractive fundamental feature of altermagnetic insulators.

Altermagnets (AMs) constitute a novel class of spin-compensated materials in which opposite-spin sublattices are connected by a crystal rotation, causing their electronic iso-energy surfaces to be spin-split. While cubic and tetragonal crystal symmetries tend to produce AMs in which the splitting of electronic iso-energy surfaces has d-wave symmetry, hexagonal AMs, such as CrSb and MnTe, are g-wave AMs. Here we investigate the purely magnetic modes and spin-textures of g-wave AMs and show that they are drastically different for easy-axial (CrSb) and easy-planar (MnTe) materials. We show that in CrSb the splitting of the chiral magnon branches possesses g-wave symmetry, with each branch carrying a fixed momentum-independent magnetic moment. The altermagnetic splitting is not affected by the easy-axial anisotropy and is the same as that in the nonrelativistic limit. The magnon splitting of MnTe, however, does not strictly possess g-wave symmetry due to its easy-planar anisotropy. Instead, the magnetic moment of each branch becomes momentum-dependent, with a distribution that is of g-wave symmetry. To generalize the concept of the altermagnetic splitting beyond the nonrelativistic limit, we introduce alternative, directly observable splitting parameter which comprises both the magnon eigenenergy and its magnetic moment and possesses the g-wave symmetry in both easy-axial and easy-planar cases. The associated altermagnetic domain walls in easy-axial CrSb possess a net magnetization with an amplitude that depends on their orientation.

A periodic lattice distortion that reduces the translational symmetry folds electron bands into a reduced Brillouin zone, leading to band mixing and a tendency to gap formation, as in the Peierls transition in one-dimensional systems. However, in higher dimensions, the resulting phase can present topological obstructions preventing a complete gap opening. We discuss two different mechanisms for such obstructions, emergent Weyl nodes and symmetry protected band crossings. Based on density-functional calculations, we show these mechanisms are at play in trigonal PtBi_2.

The trigonal Weyl semimetal PtBi2 presents an intriguing superconducting phase, previously reported to be confined to its topological Fermi arcs within a certain temperature range. This observation highlights the importance of a thorough understanding of its normal phase, particularly the roles that spin-orbit coupling (SOC) and inversion-symmetry breaking play in shaping its band structure. Our density-functional theory calculations reveal that the semimetallic nature of trigonal PtBi2 can be interpreted as stemming from a noncentrosymmetric crystal distortion of a parent structure that drives a metal-to-semimetal transition. This distortion breaks inversion symmetry and, crucially, reduces translational symmetry. Due to its interplay with translational symmetry, inversion-symmetry breaking emerges as the dominant energy scale producing substantial asymmetries (similar to 0.6 eV) in certain short-range hopping amplitudes, superseding the effects of SOC, whose primary role is to define the characteristics of the low-energy nodal structure and of the topological Fermi arcs. This also applies to the formation of the Weyl nodes closest to the Fermi energy, which are found to exist even in the absence of SOC as a result of the orbital physics associated with the reduced translational symmetry.

Altermagnets (AMs) constitute a novel class of spin-compensated materials in which the symmetry connecting opposite-spin sublattices involves a spatial rotation. Here, we uncover a set of unique non-linear, light-driven properties that set AMs apart from traditional ferro- and antiferromagnets. We demonstrate theoretically that the polarization of an electromagnetic pulse that photo-excites electrons and holes in an AM, controls the spin orientation of these non-equilibrium charge carriers. For a d-wave AM model and a prototype material, we show that very large post-pump spin polarizations may be attained by exploiting resonances. We show that this protocol also allows, in an AM, to directly probe the spin splitting of the electronic states in energy and momentum space. Thus, it can be used to identify and characterize altermagnetic materials via ultrafast pump-probe Kerr/Faraday spectroscopy or spin- and time-resolved ARPES. This opens up the possibility of devising ultrafast optical switches of non-equilibrium spin-polarization, finely tunable by adjusting the pump-pulse characteristics.

In altermagnets, time-reversal symmetry breaking spin polarizes electronic states, while total magnetization remains zero. In addition, at altermagnetic surfaces Rashba-spin orbit coupling is activated due to broken inversion symmetry, introducing a competing spin-momentum locking interaction. Here we show that their interplay leads to the formation of complex, chiral spin textures that offer nonlinear spin-to-charge conversion properties. Whereas altermagnetic order suppresses the canonical linear in-plane Rashba-Edelstein response, we establish the presence of an anomalous transversal Edelstein effect for planar applied electric and magnetic field or, alternatively, an in-plane magnetization. Additionally, we predict a purely electric-field-driven nonlinear out-of-plane magnetization. We compute the anomalous response within a general altermagnet d-wave model, with parameters extracted from the ab initio electronic structure of an altermagnetic bilayer. Our results suggest altermagnetic surfaces as a promising platform for unconventional spintronic functionalities.

Nodal-line semimetals are a class of topological materials hosting one dimensional lines of band degeneracy. Kramers nodal-line (KNL) metals/semimetals have recently been theoretically recognized as a class of topological states inherent to all non-centrosymmetric achiral crystal lattices. The electronic structure of candidate KNL semimetal YAuGe is investigated by angle-resolved photoemission spectroscopy (ARPES) and quantum oscillations as well as by density functional theory (DFT) calculations. DFT has revealed that YAuGe hosts KNLs on the Γ-A-L-M plane of the Brillouin zone, that are protected by the time reversal and mirror-inversion symmetries. Through ARPES and quantum oscillations, signatures of hole bands enclosing the Γ point are identified, and the observed splitting of quantum oscillation frequency with angle is attributed to spin-orbit-coupling-induced band splitting away from the KNLs. Furthermore, it is shown that the degeneracy of the nodal lines along the Γ-A line is lifted by the time-reversal-symmetry breaking when the Y is substituted by magnetic R ions (R = rare earth). This becomes a source of Berry curvature and contributes to the anomalous Hall effect in magnetic RAuGe. These findings establish RAuGe as a new class of KNL semimetals offering significant potential for engineering of anomalous magnetotransport properties via magnetic rare-earth substitution.

Half-Heusler compounds are a class of materials with great potential for the study of distinct electronic states. In this work, we investigate, from first-principles, the possibility of hinge modes in closely related topological phases that are tunable by moderate uni-axial strain. We consider two compounds: LiSbZn and LiBiZn. While LiSbZn has a topologically trivial band structure, the larger spin-orbit coupling of Bi causes a band inversion in LiBiZn. We predict the existence of topologically trivial hinge states in both cases. The hinge modes are affected by both the crystal termination, and the bulk topological phase transitions, albeit indirectly: When present, topological surface modes hybridize with the hinge states and obscure their visibility. Thus, we find that the most visible hinge modes occur when no band inversions are present in the material. Our work highlights the interplay and competition between surface and hinge modes in half-Heuslers, and may help guide the experimental search for robust boundary signatures in these materials.

High-resolution angle-resolved photoemission spectroscopy (ARPES) performed on the single-layered cuprate (Pb1-y,Biy)2Sr2-xLaxCuO6+delta (Bi2201) reveals a 6-10% difference in the nodal kF vectors along the TY and TX directions. This asymmetry is notably larger than the 2% orthorhombic distortion in the CuO2 plane lattice constants determined using X-ray crystallography from the same samples. First principles calculations indicate that crystal-field splitting of the bands lies at the root of the kF asymmetry. Concomitantly, the nodal Fermi velocities for the TY quadrant exceed those for TX by 4%. Momentum distribution curve widths for the two nodal dispersions are also anisotropic, showing identical energy dependencies, bar a scaling factor of similar to 1.17 +/- 0.05 between TY and TX. Consequently, the imaginary part of the self-energy is found to be 10-20% greater along TY than TX. These results emphasize the need to account for Fermi surface asymmetry in the analysis of ARPES data on Bi-based cuprate high temperature superconductors such as Bi2201. To illustrate this point, an orthorhombic tight-binding model (with twofold in-plane symmetry) was used to fit ARPES Fermi surface maps spanning all four quadrants of the Brillouin zone, and the ARPES-derived hole-doping (Luttinger count) was extracted. Comparison of the Luttinger count with one assuming four-fold in-plane symmetry strongly suggests the marked spread in previously-reported Fermi surface areas from ARPES on Bi2201 results from the differences in kF along TY and TX. Using this analysis, a new, linear relationship emerges between the hole-doping derived from ARPES (pARPES) and that derived using the Presland (pPresland) relation such that pARPES = pPresland + 0.11. The implications for this difference between the ARPES-and Presland-derived estimates for p are discussed and possible future directions to elucidate the origin of this discrepancy are presented.

Materials combining topologically non-trivial behavior and superconductivity offer a potential route for quantum computation. However, the set of available materials intrinsically realizing these properties are scarce. Recently, surface superconductivity has been reported in PtBi2 in its trigonal phase and an inherent Weyl semimetal phase has been predicted. Here, based on scanning tunneling microscopy experiments, the signature of topological Fermi arcs are revealed in the normal state patterns of the quasiparticle interference. It is shown that the scattering between Fermi arcs dominates the interference spectra, providing conclusive evidence for the relevance of Weyl fermiology for the surface electronic properties of trigonal PtBi2.

Below the structural transition occurring at Ts = 90 K, FeSe exhibits positive transverse magnetoresistance when the current is applied parallel to the ab plane. In this study, we show that, in contrast, when both the magnetic field and the current are aligned along the c axis, the magnetotransport changes significantly. In this configuration, FeSe develops a sizable negative longitudinal magnetoresistance (similar to 15% at T = 10 K and mu 0H = 16 T) in the nematic phase. We attribute this finding to the effect of the applied magnetic field on the scattering from spin fluctuations. Our observations reflect the intricate interplay between spin and orbital degrees of freedom in the nematic phase of FeSe.

Trigonal PtBi2 is a layered semimetal without inversion symmetry, featuring 12 Weyl points in the vicinity of the Fermi energy. Its topological Fermi arcs were recently shown to superconduct at low temperatures where bulk superconductivity is absent. Here, we perform first-principles calculations to investigate in detail the bulk and surface electronic structure of PtBi2, and obtain the spin texture as well as the momentum-dependent localization of the arcs. Motivated by the experimentally observed recovery of inversion symmetry under pressure or upon doping, we interpolate between the two structures and determine the energy and momentum dependence of the Weyl nodes. For deeper insights into the surface superconductivity of PtBi2, we construct a symmetry-adapted effective four-band model that accurately reproduces the Weyl points of PtBi2. We supplement this model with an analysis of the symmetry-allowed pairings between the Fermi arcs, which naturally mix spin-singlet and spin-triplet channels. Moreover, the presence of surface-only superconductivity facilitates an intrinsic superconductor-semimetal-superconductor Josephson junction, with the semimetallic phase sandwiched between the two superconducting surfaces. For a phase difference of pi, zero-energy Andreev bound states develop between the two terminations.

An essential ingredient for the production of Majorana fermions for use in quantum computing is topological superconductivity 1 , 2 . As bulk topological superconductors remain elusive, the most promising approaches exploit proximity-induced superconductivity 3 , making systems fragile and difficult to realize 4 – 7 . Due to their intrinsic topology 8 , Weyl semimetals are also potential candidates 1 , 2 , but have always been connected with bulk superconductivity, leaving the possibility of intrinsic superconductivity of their topological surface states, the Fermi arcs, practically without attention, even from the theory side. Here, by means of angle-resolved photoemission spectroscopy and ab initio calculations, we identify topological Fermi arcs on two opposing surfaces of the non-centrosymmetric Weyl material trigonal PtBi 2 (ref. 9 ). We show these states become superconducting at temperatures around 10 K. Remarkably, the corresponding coherence peaks appear as the strongest and sharpest excitations ever detected by photoemission from solids. Our findings indicate that superconductivity in PtBi 2 can occur exclusively at the surface, rendering it a possible platform to host Majorana modes in intrinsically topological superconductor–normal metal–superconductor Josephson junctions.

The material class of kagome metals has rapidly grown and has been established as a field to explore the interplay between electronic topology and magnetism. In this work, we report a combined theoretical and experimental study of the anomalous Hall effect of the ferromagnetic kagome metal Fe3Sn. The compound orders magnetically at 725 K and presents an easy-plane anisotropy. Hall measurements in single crystals below room temperature yield an anomalous Hall conductivity axy similar to 500 (Q cm)-1, which is found to depend weakly on temperature. This value is in good agreement with the band-intrinsic contribution obtained by density-functional calculations. Our calculations also yield the correct magnetic anisotropy energy and predict the existence of Weyl nodes near the Fermi energy.

An essential ingredient for the production of Majorana fermions that can be used for quantum computing is the presence of topological superconductivity. As bulk topological superconductors remain elusive, the most promising approaches exploit proximity-induced superconductivity making systems fragile and difficult to realize. Weyl semimetals due to their intrinsic topology belong to potential candidates too, but search for Majorana fermions has always been connected with the superconductivity in the bulk, leaving the possibility of intrinsic superconductivity of the Fermi surface arcs themselves practically without attention, even from the theory side.Here, by means of angle-resolved photoemission spectroscopy and ab-initio calculations, we unambiguously identify topological Fermi arcs on two opposing surfaces of the non-centrosymmetric Weyl material PtBi2. We show that these states become superconducting at different temperatures around 10K. Remarkably, the corresponding coherencepeaks appear as the strongest and sharpest excitations ever detected by photoemission from solids, suggesting significant technological relevance. Our findings indicate that topological superconductivity in PtBi2 occurs exclusively at the surface, which not only makes it an ideal platform to host Majorana fermions, but may also lead to a unique quantum phase - an intrinsic topological SNS Josephson junction.

Ferromagnetische topologische Isolatoren versprechen Spintronik‐Bauelemente und energieeffiziente Elektronik. Der Vorteil der intrinsischen, magnetischen topologischen Isolatoren der (MnBi2Te4)(Bi2Te3)n‐Familie liegt in den geordneten Lagen aus magnetischen Mn‐Atomen. Diese tendieren jedoch dazu, antiferromagnetisch zu ordnen. Wenige Prozent Mn‐Substitutionsatome schaffen jedoch einen neuen magnetischen Kopplungspfad zwischen diesen Lagen und stellen eine ferromagnetische Ordnung her. Diese ist für den quantisierten anomalen Hall‐Effekt und die damit einhergehenden spinpolarisierten Ströme essenziell.