Twist-Optics: Controlling the Propagation of Phonon Polaritons with Twisted van der Waals Stacks

The discovery of flat-band unconventional superconductivity and Mott insulating behavior in twisted graphene bilayers in 2018 was a groundbreaking and highly impactful development in condensed matter physics. It generated significant attention and excitement, sparking intense research into emergent quantum phenomena, challenging theoretical frameworks, and potentially revolutionizing superconducting materials. This finding spurred intense research on aiming to uncover novel physical phenomena by twisting layers of vdW materials, initially in the realm of electronics, thereby initiating a field that received the name of twistronics. The first section of this chapter extends the concepts of twistronics to the world of nano-optics and polaritonics. Namely, we show that the superposition of two twisted thin slabs of highly anisotropic materials provides a neat platform for controlling and steering polariton propagation. Through near-field nanoimaging on twisted bilayers of \(\alpha \text{-MoO}_{3}\) , the in-plane polaritonic dispersion is shown to undergo a transition from elliptic to hyperbolic as a function of both frequency and twist angle. Interestingly, at the critical twist angle between the two regimes, the so-called magic angle, the two arms of the polaritonic dispersion become flat and parallel, thereby allowing a single direction for propagation that is free of geometrical spreading. This leads to a guiding, collimation effect achievable across the entire Reststrahlen band by tuning the twist angle that has received the name of canalization. The twisting of layers to tailor the transition frequency at which the phonon polaritons become canalized provides an innovative avenue to steer and guide light-matter interactions that has since been coined as twist-optics. Building on this discovery, the effect of a third layer is studied in the second section of the chapter, to explore novel capabilities for controlling the propagation of PhPs. Repeatedly reassembling a third layer offers a novel strategy for re-configuring the twist angle in stacked structures. In fact, the addition of a third layer gives rise to unique features that are not present in twisted bilayers and single layers, and provides a major difference with respect to polariton canalization, such as all-angle tunable, robust and broadband canalization. Moreover, IFCs in trilayers can have highly non-intuitive asymmetric shapes due to the breaking of mirror symmetries, similar to those found in crystals with lower symmetry than orthorhombic, such as monoclinic. The near-field experiments reported in this chapter were carried out by Dr. Jiahua Duan (University of Oviedo, Spain). Sample fabrication was performed by Dr. Jiahua Duan (University of Oviedo, Spain). Dr. Iván Prieto (Institute of Science and Technology, Austria) contributed to sample fabrication in the first section of this chapter, while Ana Isabel Fernández-Tresguerres Mata (University of Oviedo, Spain) contributed to sample fabrication in the second section. The derivations in the first section were performed together with Nathaniel Capote-Robayna (Donostia International Physics Center, Spain), while the calculations in the second section were performed in collaboration with Christian Lanza (University of Oviedo, Spain), Kirill Voronin and Nathaniel Capote-Robayna (Donostia International Physics Center, Spain). The results reported in the first section of this chapter were published in “Twisted Nano-Optics: Manipulating Light at the Nanoscale with Twisted Phonon Polaritonic Slabs” by Jiahua Duan et al. Nano Letters 2020, 20, 5323–5329 (2020). The results reported in the second section of the chapter were published in “Multiple and spectrally robust photonic magic angles in reconfigurable \(\alpha \text{-MoO}_{3}\) trilayers” by Jiahua Duan, Gonzalo Álvarez-Pérez, Christian Lanza, Kirill Voronin et al. Nature Materials 22, 867–872 (2023).