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The spacetime light cone is central to the definition of causality in the theory of relativity. Recently, links between relativistic and condensed matter physics have been uncovered, where relativistic particles can emerge as quasiparticles in the energy-momentum space of matter. Here, we unveil an energy-momentum analogue of the spacetime light cone by mapping time to energy, space to momentum, and the light cone to the Weyl cone. We show that two Weyl quasiparticles can only interact to open a global energy gap if they lie in each other’s energy-momentum dispersion cones–analogous to two events that can only have a causal connection if they lie in each other’s light cones. Moreover, we demonstrate that the causality of surface chiral modes in quantum matter is entangled with the causality of bulk Weyl fermions. Furthermore, we identify a unique quantum horizon region and an associated ‘thick horizon’ in the emergent causal structure.

 

Quantum geometry in condensed-matter physics has two components: the real part quantum metric and the imaginary part Berry curvature. Whereas the effects of Berry curvature have been observed through phenomena such as the quantum Hall effect in two-dimensional electron gases and the anomalous Hall effect (AHE) in ferromagnets, the quantum metric has rarely been explored. Here, we report a nonlinear Hall effect induced by the quantum metric dipole by interfacing even-layered MnBi₂Te₄with black phosphorus. The quantum metric nonlinear Hall effect switches direction upon reversing the antiferromagnetic (AFM) spins and exhibits distinct scaling that is independent of the scattering time. Our results open the door to discovering quantum metric responses predicted theoretically and pave the way for applications that bridge nonlinear electronics with AFM spintronics.

 

Three-dimensional (3D) topological semimetals represent a new class of topological matters. The study of this family of materials has been at the frontiers of condensed matter physics, and many breakthroughs have been made. Several topological semimetal phases, including Dirac semimetals (DSMs), Weyl semimetals (WSMs), nodal-line semimetals (NLSMs), and triple-point semimetals, have been theoretically predicted and experimentally demonstrated. The low-energy excitation around the Dirac/Weyl nodal points, nodal line, or triply degenerated nodal point can be viewed as emergent relativistic fermions. Experimental studies have shown that relativistic fermions can result in a rich variety of exotic transport properties, e.g., extremely large magnetoresistance, the chiral anomaly, and the intrinsic anomalous Hall effect. In this review, we first briefly introduce band structural characteristics of each topological semimetal phase, then review the current studies on quantum oscillations and exotic transport properties of various topological semimetals, and finally provide a perspective of this area.