Kagome-nets, appearing in electronic, photonic and cold-atom systems, host frustrated fermionic and bosonic excitations. However, it is rare to find a system to study their fermion–boson many-body interplay. Here we use state-of-the-art scanning tunneling microscopy/spectroscopy to discover unusual electronic coupling to flat-band phonons in a layered kagome paramagnet, CoSn. We image the kagome structure with unprecedented atomic resolution and observe the striking bosonic mode interacting with dispersive kagome electrons near the Fermi surface. At this mode energy, the fermionic quasi-particle dispersion exhibits a pronounced renormalization, signaling a giant coupling to bosons. Through the self-energy analysis, first-principles calculation, and a lattice vibration model, we present evidence that this mode arises from the geometrically frustrated phonon flat-band, which is the lattice bosonic analog of the kagome electron flat-band. Our findings provide the first example of kagome bosonic mode (flat-band phonon) in electronic excitations and its strong interaction with fermionic degrees of freedom in kagome-net materials.

The nontrivial magnetic texture in real space gives rise to the intriguing phenomenon of the topological Hall effect (THE), which is relatively less explored in topological semimetals. Here, we report a large THE in the antiferromagnetic (AFM) state in single crystals of EuAgAs, an AFM Dirac semimetal. EuAgAs hosts an AFM ground state below $T_N=12$ K with a weak ferromagnetic component. The in-plane isothermal magnetization below $T_N$ exhibits a weak metamagnetic transition. We also observe chiral anomaly induced positive longitudinal magnetoconductivity, which indicates a Weyl fermion state under an applied magnetic field. The first-principles calculations reveal that EuAgAs is an AFM Dirac semimetal with a pair of Dirac cones, and therefore a Weyl semimetallic state can be realized under time-reversal symmetry breaking via an applied magnetic field. Our study establishes that EuAgAs is a system for exploiting the interplay of band topology and the topology of the magnetic texture.

Saddle-point Van Hove singularities in the topological surface states are interesting because they can provide a new pathway for accessing exotic correlated phenomena in topological materials. Here, based on first-principles calculations combined with a $\mathbf{k}·\mathbf{p}$ model Hamiltonian analysis, we show that the layered platinum mineral jacutingaite (${\mathrm{Pt}}_2{\mathrm{HgSe}}_3$) harbors saddlelike topological surface states with associated Van Hove singularities. ${\mathrm{Pt}}_2{\mathrm{HgSe}}_3$ is shown to host two distinct types of nodal lines without spin-orbit coupling (SOC), which are protected by combined inversion ($\mathcal{I}$) and time-reversal ($\mathcal{T}$) symmetries. Switching on the SOC gaps out the nodal lines and drives the system into a topological state with nonzero weak topological invariant $Z_2=(0;001)$ and mirror Chern number $n_M=-2$. Surface states on the naturally cleaved (001) surface are found to be nontrivial with a unique saddlelike energy dispersion with type II Van Hove singularities. We also discuss how modulating the crystal structure can drive ${\mathrm{Pt}}_2{\mathrm{HgSe}}_3$ into a Dirac semimetal state with a pair of Dirac points. Our results indicate that ${\mathrm{Pt}}_2{\mathrm{HgSe}}_3$ is an ideal candidate material for exploring the properties of topological insulators with saddlelike surface states.

Recent classification efforts encompassing crystalline symmetries have revealed rich possibilities for solid-state systems to support a tapestry of exotic topological states. However, finding materials that realize such states remains a daunting challenge. Here, we show how the interplay of topology, symmetry, and magnetism combined with doping and external electric and magnetic field controls can be used to drive the ${\mathrm{SrIn}}_2{\mathrm{As}}_2$ materials family into a variety of topological phases. Our first-principles calculations and symmetry analysis reveal that ${\mathrm{SrIn}}_2{\mathrm{As}}_2$ is a dual topological insulator with $Z_2=(1;000)$ and mirror Chern number $C_M=-1$. Its isostructural and isovalent antiferromagnetic cousin ${\mathrm{EuIn}}_2{\mathrm{As}}_2$ is found to be an axion insulator with $Z_4=2$. The broken time-reversal symmetry via Eu doping in ${\mathrm{Sr}}_{1-x}{\mathrm{Eu}}_x{\mathrm{In}}_2{\mathrm{As}}_2$ results in a higher-order or topological crystalline insulator state depending on the orientation of the magnetic easy axis. We also find that antiferromagnetic ${\mathrm{EuIn}}_2{\mathrm{P}}_2$ is a trivial insulator with $Z_4=0$, and that it undergoes a magnetic-field-driven transition to an ideal Weyl fermion or nodal fermion state with $Z_4=1$ with applied magnetic field. Our study identifies ${\mathrm{Sr}}_{1-x}{\mathrm{Eu}}_x{\mathrm{In}}_2{(\text{As},\mathrm{P})}_2$ as a tunable materials platform for investigating the physics and applications of Weyl and nodal fermions in the scaffolding of crystalline and axion insulator states.

Topological superconductors present an ideal platform for exploring nontrivial superconductivity and realizing the Majorana boundary modes. However, finding a single-phase topological material with nontrivial superconducting states has been a challenge. Here, we predict nontrivial superconductivity in the pristine chiral metal RhGe with a transition temperature of 5.8 K. Chiral symmetries in RhGe enforce multifold Weyl fermions at high-symmetry momentum points and spin-polarized Fermi arc states that span the entire surface Brillouin zone. These bulk and surface chiral states support multiple type-II van Hove singularities that enhance superconductivity in RhGe. Our analysis of superconducting pairing symmetries involving Chiral Fermi pockets in RhGe indicates the presence of nontrivial superconducting pairing. Our study establishes RhGe as a promising candidate material for hosting mixed-parity pairing and topological superconductivity.