The anomalous Hall effect (AHE) is one of the most fundamental phenomena in physics. In the highly conductive regime, ferromagnetic metals have been the focus of past research. Here, we report a giant extrinsic AHE in KV3Sb5, an exfoliable, highly conductive semimetal with Dirac quasiparticles and a vanadium Kagome net. Even without report of long range magnetic order, the anomalous Hall conductivity reaches 15,507 Ω−1 cm−1 with an anomalous Hall ratio of ≈ 1.8%; an order of magnitude larger than Fe. Defying theoretical expectations, KV3Sb5 shows enhanced skew scattering that scales quadratically, not linearly, with the longitudinal conductivity, possibly arising from the combination of highly conductive Dirac quasiparticles with a frustrated magnetic sublattice. This allows the possibility of reaching an anomalous Hall angle of 90° in metals. This observation raises fundamental questions about AHEs and opens new frontiers for AHE and spin Hall effect exploration, particularly in metallic frustrated magnets.

The realization of Dirac and Weyl physics in solids has made topological materials one of the main focuses of condensed matter physics. Recently, the topic of topological nodal line semimetals, materials in which Dirac or Weyl-like crossings along special lines in momentum space create either a closed ring or line of degeneracies, rather than discrete points, has become a hot topic in topological quantum matter. Here, we review the experimentally confirmed and theoretically predicted topological nodal line semimetals, focusing in particular on the symmetry protection mechanisms of the nodal lines in various materials. Three different mechanisms: a combination of inversion and time-reversal symmetry, mirror reflection symmetry, and nonsymmorphic symmetry and their robustness under the effect of spin orbit coupling are discussed. We also present a new Weyl nodal line material, the Te-square net compound KCu 2 EuTe 4 , which has several Weyl nodal lines including one extremely close to the Fermi level (<30 meV below E F ). Finally, we discuss potential experimental signatures for observing exotic properties of nodal line physics. ARTICLE HISTORY

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Time-reversal-symmetry-breaking Weyl semimetals (WSMs) have attracted great attention recently because of the interplay between intrinsic magnetism and topologically nontrivial electrons. Here, we present anomalous Hall and planar Hall effect studies on Co 3 Sn 2 S 2 nanoflakes, a magnetic WSM hosting stacked Kagome lattice. The reduced thickness modifies the magnetic properties of the nanoflake, resulting in a 15-time larger coercive field compared with the bulk, and correspondingly modifies the transport properties. A 22% enhancement of the intrinsic anomalous Hall conductivity (AHC), as compared to bulk material, was observed. A magnetic field-modulated AHC, which may be related to the changing Weyl point separation with magnetic field, was also found. Furthermore, we showed that the PHE in a hard magnetic WSM is a complex interplay between ferromagnetism, orbital magnetoresistance, and chiral anomaly. Our findings pave the way for a further understanding of exotic transport features in the burgeoning field of magnetic topological phases.

The coexistence of gate-tunable superconducting, magnetic and topological orders in magic-angle twisted bilayer graphene provides opportunities for the creation of hybrid Josephson junctions. Here we report the fabrication of gate-defined symmetry-broken Josephson junctions in magic-angle twisted bilayer graphene, where the weak link is gate-tuned close to the correlated insulator state with a moiré filling factor of υ = −2. We observe a phase-shifted and asymmetric Fraunhofer pattern with a pronounced magnetic hysteresis. Our theoretical calculations of the junction weak link—with valley polarization and orbital magnetization—explain most of these unconventional features. The effects persist up to the critical temperature of 3.5 K, with magnetic hysteresis observed below 800 mK. We show how the combination of magnetization and its current-induced magnetization switching allows us to realise a programmable zero-field superconducting diode. Our results represent a major advance towards the creation of future superconducting quantum electronic devices.

The simultaneous co-existence and gate-tuneability of the superconducting (SC), magnetic and topological orders in magic angle twisted bilayer graphene (MATBG) open up entirely new possibilities for the creation of complex hybrid Josephson junctions (JJ). Here we report on the creation of gate-defined, symmetry broken Josephson junctions in MATBG, where the weak link is gate-tuned close to the correlated state at a moiré filling factor of 𝛖 = -2. A highly unconventional Fraunhofer pattern emerges, in which supercurrent is carried by edge states, it is phase-shifted and asymmetric with respect to the current and magnetic field directions, and shows a pronounced magnetic hysteresis. Interestingly, our theoretical calculations of the JJ with a valley polarized υ = -2 with orbital magnetization as the weak link explain most of these unconventional features without fine tuning the parameters. While these unconventional Josephson effects persist up to the critical temperature Tc ~ 3.5 K of the superconducting state, at temperatures below T < 800 mK, we observed a pronounced magnetic hysteresis. We demonstrate how the combination of magnetization and its current induced magnetization switching in the MATBG JJ allows us to realize a programmable zero field superconducting diode, which represents a major building block for a new generation of superconducting quantum electronics.