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Studies of moiré systems have explained the effect of superlattice modulations on their properties, demonstrating new correlated phases. However, most experimental studies have focused on a few layers in two-dimensional systems. Extending twistronics to three dimensions, in which the twist extends into the third dimension, remains underexplored because of the challenges associated with the manual stacking of layers. Here we study three-dimensional twistronics using a self-assembled twisted spiral superlattice of multilayered WS2. Our findings show an opto-twistronic Hall effect driven by structural chirality and coherence length, modulated by the moiré potential of the spiral superlattice. This is an experimental manifestation of the noncommutative geometry of the system. We observe enhanced light–matter interactions and an altered dependence of the Hall coefficient on photon momentum. Our model suggests contributions from higher-order quantum geometric quantities to this observation, providing opportunities for designing quantum-materials-based optoelectronic lattices with large nonlinearities. 

Abstract Surface plasmons, which allow tight confinement of light, suffer from high intrinsic electronic losses. It has been shown that stimulated emission from excited electrons can transfer energy to plasmons and compensate for the high intrinsic losses. To-date, these realizations have relied on introducing an external gain media coupled to the surface plasmon. Here, we propose that plasmons in two-dimensional materials with closely located electron and hole Fermi pockets can be amplified, when an electrical current bias is applied along the displaced electron-hole pockets, without the need for an external gain media. As a prototypical example, we consider WTe₂from the family of 1T$${}^{{\prime} }$$ ${}^{\prime }$-MX₂materials, whose electronic structure can be described within a type-II tilted massive Dirac model. We find that the nonlocal plasmonic response experiences prominent gain for experimentally accessible currents on the order of mAμm⁻¹. Furthermore, the group velocity of the plasmon found from the isofrequency curves imply that the amplified plasmons are highly collimated along a direction perpendicular to the Dirac node tilt when the electrical current is applied along it. 

Abstract Integrated phononics plays an important role in both fundamental physics and technology. Despite great efforts, it remains a challenge to break time-reversal symmetry to achieve topological phases and non-reciprocal devices. Piezomagnetic materials offer an intriguing opportunity as they break time-reversal symmetry intrinsically, without the need for an external magnetic field or an active driving field. Moreover, they are antiferromagnetic, and possibly compatible with superconducting components. Here, we develop a theoretical framework that combines linear elasticity with Maxwell’s equations via piezoelectricity and/or piezomagnetism beyond the commonly adopted quasi-static approximation. Our theory predicts and numerically demonstrates phononic Chern insulators based on piezomagnetism. We further show that the topological phase and chiral edge states in this system can be controlled by the charge doping. Our results exploit a general duality relation between piezoelectric and piezomagnetic systems, which can potentially be generalized to other composite metamaterial systems.