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In ordinary materials, electrons conduct both electricity and heat, where their charge-entropy relations observe the Mott formula and the Wiedemann-Franz law. In topological quantum materials, the transverse motion of relativistic electrons can be strongly affected by the quantum field arising around the topological fermions, where a simple model description of their charge-entropy relations remains elusive. Here we report the topological charge-entropy scaling in the kagome Chern magnet TbMn 6 Sn 6 , featuring pristine Mn kagome lattices with strong out-of-plane magnetization. Through both electric and thermoelectric transports, we observe quantum oscillations with a nontrivial Berry phase, a large Fermi velocity and two-dimensionality, supporting the existence of Dirac fermions in the magnetic kagome lattice. This quantum magnet further exhibits large anomalous Hall, anomalous Nernst, and anomalous thermal Hall effects, all of which persist to above room temperature. Remarkably, we show that the charge-entropy scaling relations of these anomalous transverse transports can be ubiquitously described by the Berry curvature field effects in a Chern-gapped Dirac model. Our work points to a model kagome Chern magnet for the proof-of-principle elaboration of the topological charge-entropy scaling. Elucidating the nature of topological magnets is at quantum frontier. Here the authors report a topological charge-entropy relation in TbMn 6 Sn 6 that goes beyond conventional electron behavior and points to a transport visualization of Chern gapped Dirac fermions.

A two-dimensional (2D) Weyl semimetal, akin to a spinful variant of graphene, represents a topological matter characterized by Weyl fermion-like quasiparticles in low dimensions. The spinful linear band structure in two dimensions gives rise to distinctive topological properties, accompanied by the emergence of Fermi string edge states. We report the experimental realization of a 2D Weyl semimetal, bismuthene monolayer grown on SnS(Se) substrates. Using spin and angle-resolved photoemission and scanning tunneling spectroscopies, we directly observe spin-polarized Weyl cones, Weyl nodes, and Fermi strings, providing consistent evidence of their inherent topological characteristics. Our work opens the door for the experimental study of Weyl fermions in low-dimensional materials. 2D Weyl semimetals are spin-polarized analogues of graphene that promise access to various topological properties of matter. Here, the authors evidence spin-polarized Weyl cones, Weyl nodes, and Fermi strings in monolayer bismuthene.

Weyl semimetals are a unique class of topological materials, possessing Fermi-arc surface states and exhibiting the chiral anomaly effect. The chiral anomaly refers to non-equilibrium charge transfer within a Weyl-node pair of opposite chirality under the condition of aligned electric and magnetic fields ( E ∥ B ), leading to non-conserved chiral charges and thus enhanced electrical conductivity. In experiments, such an enhanced conductivity due to the chiral anomaly manifests as a negative longitudinal magnetoresistance (MR) when the external field H is applied along the bias current direction I . In this work, we present rigorous ϕ - and α -dependent magnetotransport measurements to investigate such a negative longitudinal MR due to the chiral anomaly in a sunbeam-shaped device fabricated from an untwinned Weyl metal SrRuO 3 (SRO) thin film. Here, ϕ ( α ) represents the angle between I and the in-plane H (SRO monoclinic [001] o ). Unusual ϕ dependences of in-plane MR and Hall effects were uncovered at low temperatures, accompanied by the emergence of the fourfold-symmetric component in the in-plane MR. These results indicate that the chiral anomaly and resistivity anisotropy in SRO play important roles. In particular, the dramatic variation of Weyl nodes near the Fermi level through magnetic field manipulation of the magnetization orientation, as revealed by band structure calculations, is consistent with the observed in-plane MR and Hall effect.

PdTe is a superconductor with T c  ~ 4.25 K. Recently, evidence for bulk-nodal and surface-nodeless gap features has been reported in PdTe. Here, we investigate the physical properties of PdTe in both the normal and superconducting states via specific heat and magnetic torque measurements and first-principles calculations. Below T c , the electronic specific heat initially decreases in T 3 behavior (1.5 K <  T  <  T c ) then exponentially decays. Using the two-band model, the superconducting specific heat can be well described with two energy gaps: one is 0.372 meV and another 1.93 meV. The calculated bulk band structure consists of two electron bands (α and β) and two hole bands (γ and η) at the Fermi level. Experimental detection of the de Haas-van Alphen (dHvA) oscillations allows us to identify four frequencies ( F α  = 65 T, F β  = 658 T, F γ  = 1154 T, and F η  = 1867 T for H // a ), consistent with theoretical predictions. Nontrivial α and β bands are further identified via both calculations and the angle dependence of the dHvA oscillations. Our results suggest that PdTe is a candidate for unconventional superconductivity.

Two-dimensional (2D) Dirac states with linear dispersion have been observed in graphene and on the surface of topological insulators. 2D Dirac states discovered so far are exclusively pinned at high-symmetry points of the Brillouin zone, for example, surface Dirac states at Γ ¯ in topological insulators Bi 2 Se(Te) 3 and Dirac cones at K and K ′ points in graphene. The low-energy dispersion of those Dirac states are isotropic due to the constraints of crystal symmetries. In this work, we report the observation of novel 2D Dirac states in antimony atomic layers with phosphorene structure. The Dirac states in the antimony films are located at generic momentum points. This unpinned nature enables versatile ways such as lattice strains to control the locations of the Dirac points in momentum space. In addition, dispersions around the unpinned Dirac points are highly anisotropic due to the reduced symmetry of generic momentum points. The exotic properties of unpinned Dirac states make antimony atomic layers a new type of 2D Dirac semimetals that are distinct from graphene. In graphene and on the surfaces of many topological insulators, the Dirac cones are pinned to high symmetry points in reciprocal space. Here, the authors report that the Dirac cones in atomically-thin Sb layers occur at generic reciprocal-space points which can be tuned by lattice strain.

Abstract PdTe is a superconductor withTc 4.25 K. Recently, evidence for bulk-nodal and surface-nodeless gap features has been reported in PdTe. Here, we investigate the physical properties of PdTe in both the normal and superconducting states via specific heat and magnetic torque measurements and first-principles calculations. BelowTc, the electronic specific heat initially decreases inT3behavior (1.5 K < T < Tc) then exponentially decays. Using the two-band model, the superconducting specific heat can be well described with two energy gaps: one is 0.372 meV and another 1.93 meV. The calculated bulk band structure consists of two electron bands (α and β) and two hole bands (γ and η) at the Fermi level. Experimental detection of the de Haas-van Alphen (dHvA) oscillations allows us to identify four frequencies (Fα = 65 T,Fβ = 658 T,Fγ = 1154 T, andFη = 1867 T forH//a), consistent with theoretical predictions. Nontrivial α and β bands are further identified via both calculations and the angle dependence of the dHvA oscillations. Our results suggest that PdTe is a candidate for unconventional superconductivity.

A detailed study on the inter-metallic alloy, Zr2TiAl, has been carried out using first principle electronic structure calculations. We found that a small value of bi-axial strain/stress cause a phase change from anti-ferromagnetic(AFM) to ferromagnetic(FM) with a structural transition from face center cubic (fcc) to body center tetragonal (bct). Calculated electronic band structures show that all strained structures are metallic in nature with Zr-d and Ti-d orbital dominated energy bands near the Fermi level(EF). The stability of FM phase is confirmed with phonon dispersion calculations by using density functional perturbation theory (DFPT). It has been observed that AFM state with both positive and negative bi-axial stress exhibits unstable modes while corresponding FM state shows no such instability. This clearly indicates the existence of large spin phonon coupling in this material.

The CoSi-family of materials (CoSi, CoGe, RhSi and RhGe) forms a cubic chiral structure and hosts unconventional multifold chiral fermions, such as spin-1 and spin-3/2 fermions, leading to intriguing phenomena like long Fermi arc surface states and exotic transport properties. Recent interest on the phonon behavior in chiral materials is growing due to their unique characteristics, including topological phonons, protected surface states and the chiral phonons with non-zero angular momentums. In this study, we explore the topological and chiral phonon behavior in RhGe, using first-principles density functional theory calculations as well as the symmetry and topological analysis. In particular, we uncover six spin-1 triply degenerate nodal points at the \\(\\) point and six charge-2 double Weyl points at the R point in the Brillouin zone (BZ). Interestingly, these topological features are identical to that in the electronic band structure without the electron spin-orbit coupling, of the same material. We expect that this finding not only applies to the CoSi family but also is universal. Secondly, we find that chiral crystal RhGe hosts chiral phonon modes with a phonon angular momentum (PAM) and an associated phonon magnetic moment (PMM), everywhere in the BZ except at high symmetry points such as \\(\\), R, X and M. The PAM and PMM are large along the chiral rotation axis and also in the vicinity of the topological nodes. Our study also reveals that all the topological phonon modes are chiral. However, the reverse is not always true. Among other things, our finding of the coexistence of topological and chiral phonon modes in chiral RhGe not only deepens our understanding of the phonon behavior in the CoSi-family but also opens new pathways for developing advanced materials and devices.

PdTe is a superconductor with Tc ~4.25 K. Recently, evidence for bulk-nodal and surface-nodeless gap features has been reported in PdTe [Yang et al., Phys. Rev. Lett. 130, 046402 (2023)]. Here, we investigate the physical properties of PdTe in both the normal and superconducting states via specific heat and magnetic torque measurements and first-principles calculations. Below Tc, the electronic specific heat initially decreases in T3 behavior (1.5 K < T < Tc) then exponentially decays. Using the two-band model, the superconducting specific heat can be well described with two energy gaps: one is 0.372 meV and another 1.93 meV. The calculated bulk band structure consists of two electron bands ( and eta) and two hole bands ( and ) at the Fermi level. Experimental detection of the de Haas-van Alphen (dHvA) oscillations allows us to identify four frequencies (F = 65 T, Feta = 658 T, F = 1154 T, and F = 1867 T for H // a), consistent with theoretical predictions. Nontrivial and eta bands are further identified via both calculations and the angle dependence of the dHvA oscillations. Our results suggest that PdTe is a candidate for unconventional superconductivity.

The identification of distinct charge transport features, deriving from nontrivial bulk band and surface states, has been a challenging subject in the field of topological systems. In topological Dirac and Weyl semimetals, nontrivial conical bands with Fermi-arc surface states give rise to negative longitudinal magnetoresistance due to chiral anomaly effect and unusual thickness dependent quantum oscillation from Weyl-orbit effect, which were demonstrated recently in experiments. In this work, we report the experimental observations of large nonlinear and nonreciprocal transport effects for both longitudinal and transverse channels in an untwinned Weyl metal of SrRuO\\(_3\\) thin film grown on a SrTiO\\(_3\\) substrate. From rigorous measurements with bias current applied along various directions with respect to the crystalline principal axes, the magnitude of nonlinear Hall signals from the transverse channel exhibits a simple sin\\(\\) dependence at low temperatures, where \\(\\) is the angle between bias current direction and orthorhombic [001]\\(_ o\\), reaching a maximum when current is along orthorhombic [1-10]\\(_ o\\). On the contrary, the magnitude of nonlinear and nonreciprocal signals in the longitudinal channel attains a maximum for bias current along [001]\\(_ o\\), and it vanishes for bias current along [1-10]\\(_ o\\). The observed \\(\\)-dependent nonlinear and nonreciprocal signals in longitudinal and transverse channels reveal a magnetic Weyl phase with an effective Berry curvature dipole along [1-10]\\(_ o\\) from surface states, accompanied by 1D chiral edge modes along [001]\\(_ o\\).