Topological matter articles from across Nature Portfolio

Quantum geometry gives rise to many fascinating phenomena in solids that go beyond Landau theory. A general framework is now introduced to measure the quantum geometric tensor in solids — a fundamental physical quantity that encodes the complete geometric information of the Bloch state.

Flat bands states can be written, in general, as localized states that can couple by placing impurities at the overlapping regions, when present. The authors develop an analytic framework to derive impurity states in a diamond chain with magnetic flux and find an exotic behavior of these states characterized by a half-integer winding number.

Oxygen evolution is a key reaction in electrolysers and involves a spin-dependent, multi-electron transfer process. Here the authors use topological semimetals with intrinsic chirality as a means to control spin in oxygen evolution catalysts, and explore the role of spin–orbit coupling in determining activity.

Experiments that directly probe the quantum geometric tensor in solids have not been reported. Now, the quantum metric and spin Berry curvature—dual components of the quantum geometric tensor—have been simultaneously measured in reciprocal space.

The symmetry of free space greatly restricts the properties of quasiparticles that exist in free space. Solid state systems, with the discrete symmetry of the crystal lattice, have far fewer restrictions, and here, Fang et al find a vast array of new quasiparticles, with distinct energy dispersions or external field couplings that can only be realised in the spin-space group.

Quantum geometry gives rise to many fascinating phenomena in solids that go beyond Landau theory. A general framework is now introduced to measure the quantum geometric tensor in solids — a fundamental physical quantity that encodes the complete geometric information of the Bloch state.

Scanning tunnelling microscopy experiments enable the realization of artificially built topological quantum magnets with titanium atoms and graphene goblets.

Electrons in a chiral topological material exhibit a unique orbital angular momentum profile in momentum space that resembles magnetic monopoles. It gives an opportunity to utilize the orbital motion of electrons for information processing — so-called orbitronics.

Topological insulators exhibit unidirectional flow of robust electric charge at the edge of the system. Two recent experiments have observed these chiral edge modes in exceptionally controllable settings of ultracold atoms.

Angle-resolved photoemission spectroscopy measurements identify dark electron states in palladium diselenide, cuprate superconductors, and lead halide perovskites. These dark states are attributed to the two pairs of sublattices in each of the solids, which leads to a double two-level quantum system in which double destructive interference can occur.

Thanks to improved control of device fabrication and an expanding characterization toolbox, moiré materials stay in the spotlight as we discover more about the unique phenomena they realize.