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We discover an intrinsic dipole Hall effect in a variety of magnetic insulating states at integer fillings of twisted MoTe 2 moiré superlattice, including topologically trivial and nontrivial ferro-, antiferro-, and ferri-magnetic configurations. The dipole Hall current, in linear response to in-plane electric field, generates an in-plane orbital magnetization M ∥ along the field, through which an AC field can drive magnetization oscillation up to THz range. Upon the continuous topological phase transitions from trivial to quantum anomalous Hall states in both ferromagnetic and antiferromagnetic configurations, the dipole Hall current and M ∥ have an abrupt sign change, enabling contact-free detection of the transitions through the magnetic stray field. In configurations where the linear response is forbidden by symmetry, the dipole Hall current and M ∥ appear as a crossed nonlinear response to both in-plane and out-of-plane electric fields. These magnetoelectric phenomena showcase fascinating functionalities of insulators from the interplay between magnetism, topology, and electrical polarization., (© 2024. The Author(s).)

The crystal symmetry of a material dictates the type of topological band structures it may host, and therefore symmetry is the guiding principle to find topological materials. Here we introduce an alternative guiding principle, which we call 'quasi-symmetry'. This is the situation where a Hamiltonian has an exact symmetry at lower-order that is broken by higher-order perturbation terms. This enforces finite but parametrically small gaps at some low-symmetry points in momentum space. Untethered from the restraints of symmetry, quasi-symmetries eliminate the need for fine-tuning as they enforce that sources of large Berry curvature will occur at arbitrary chemical potentials. We demonstrate that a quasi-symmetry in the semi-metal CoSi stabilizes gaps below 2 meV over a large near-degenerate plane that can be measured in the quantum oscillation spectrum. The application of in-plane strain breaks the crystal symmetry and gaps the degenerate point, observable by new magnetic breakdown orbits. The quasi-symmetry, however, does not depend on spatial symmetries and hence transmission remains fully coherent. These results demonstrate a class of topological materials with increased resilience to perturbations such as strain-induced crystalline symmetry breaking, which may lead to robust topological applications as well as unexpected topology beyond the usual space group classifications., Competing Interests: Competing Interests The authors declare that they have no competing financial interests.

The phase offset of quantum oscillations is commonly used to experimentally diagnose topologically nontrivial Fermi surfaces. This methodology, however, is inconclusive for spin-orbit-coupled metals where π-phase-shifts can also arise from non-topological origins. Here, we show that the linear dispersion in topological metals leads to a T 2 -temperature correction to the oscillation frequency that is absent for parabolic dispersions. We confirm this effect experimentally in the Dirac semi-metal Cd 3 As 2 and the multiband Dirac metal LaRhIn 5 . Both materials match a tuning-parameter-free theoretical prediction, emphasizing their unified origin. For topologically trivial Bi 2 O 2 Se, no frequency shift associated to linear bands is observed as expected. However, the π-phase shift in Bi 2 O 2 Se would lead to a false positive in a Landau-fan plot analysis. Our frequency-focused methodology does not require any input from ab-initio calculations, and hence is promising for identifying correlated topological materials., (© 2021. The Author(s).)

It has recently been proposed that combining chirality with topological band theory results in a totally new class of fermions. Understanding how these unconventional quasiparticles propagate and interact remains largely unexplored so far. Here, we use scanning tunneling microscopy to visualize the electronic properties of the prototypical chiral topological semimetal PdGa. We reveal chiral quantum interference patterns of opposite spiraling directions for the two PdGa enantiomers, a direct manifestation of the change of sign of their Chern number. Additionally, we demonstrate that PdGa remains topologically non-trivial over a large energy range, experimentally detecting Fermi arcs in an energy window of more than 1.6 eV that is symmetrically centered around the Fermi level. These results are a consequence of the deep connection between chirality in real and reciprocal space in this class of materials, and, thereby, establish PdGa as an ideal topological chiral semimetal.