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1. Photonic Band Gaps and Resonance Modes in 2D Twisted Moiré Photonic Crystal

   https://doi.org/10.3390/photonics8100408  

   Alnasser, Khadijah; Kamau, Steve; Hurley, Noah; Cui, Jingbiao; Lin, Yuankun (October 2021, Photonics)

   The study of twisted bilayer 2D materials has revealed many interesting physics properties. A twisted moiré photonic crystal is an optical analog of twisted bilayer 2D materials. The optical properties in twisted photonic crystals have not yet been fully elucidated. In this paper, we generate 2D twisted moiré photonic crystals without physical rotation and simulate their photonic band gaps in photonic crystals formed at different twisted angles, different gradient levels, and different dielectric filling factors. At certain gradient levels, interface modes appear within the photonic band gap. The simulation reveals “tic tac toe”-like and “traffic circle”-like modes as well as ring resonance modes. These interesting discoveries in 2D twisted moiré photonic crystal may lead toward its application in integrated photonics. 

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2. Lifts of Twisted K3 Surfaces to Characteristic 0

   https://doi.org/10.1093/imrn/rnab334  

   Bragg, Daniel (January 2022, International Mathematics Research Notices)

   Abstract Deligne [9] showed that every K3 surface over an algebraically closed field of positive characteristic admits a lift to characteristic 0. We show the same is true for a twisted K3 surface. To do this, we study the versal deformation spaces of twisted K3 surfaces, which are particularly interesting when the characteristic divides the order of the Brauer class. We also give an algebraic construction of certain moduli spaces of twisted K3 surfaces over $${\operatorname {Spec}}\ \textbf {Z}$$ and apply our deformation theory to study their geometry. As an application of our results, we show that every derived equivalence between twisted K3 surfaces in positive characteristic is orientation preserving. 

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3. Torsional periodic lattice distortions and diffraction of twisted 2D materials

   https://doi.org/10.1038/s41467-022-35477-x  

   Sung, Suk Hyun; Goh, Yin Min; Yoo, Hyobin; Engelke, Rebecca; Xie, Hongchao; Zhang, Kuan; Li, Zidong; Ye, Andrew; Deotare, Parag B.; Tadmor, Ellad B.; et al (December 2022, Nature Communications)

   Abstract Twisted 2D materials form complex moiré structures that spontaneously reduce symmetry through picoscale deformation within a mesoscale lattice. We show twisted 2D materials contain a torsional displacement field comprised of three transverse periodic lattice distortions (PLD). The torsional PLD amplitude provides a single order parameter that concisely describes the structural complexity of twisted bilayer moirés. Moreover, the structure and amplitude of a torsional periodic lattice distortion is quantifiable using rudimentary electron diffraction methods sensitive to reciprocal space. In twisted bilayer graphene, the torsional PLD begins to form at angles below 3.89° and the amplitude reaches 8 pm around the magic angle of 1. 1°. At extremely low twist angles (e.g. below 0.25°) the amplitude increases and additional PLD harmonics arise to expand Bernal stacked domains separated by well defined solitonic boundaries. The torsional distortion field in twisted bilayer graphene is analytically described and has an upper bound of 22.6 pm. Similar torsional distortions are observed in twisted WS 2 , CrI 3 , and WSe 2 /MoSe 2 . 

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4. Fabrications of twisted moiré photonic crystal and random moiré photonic crystal and their potential applications in light extraction

   https://doi.org/10.1088/1361-6528/ad024a  

   Alnasser, Khadijah; Li, Shan; Sidhik, Siraj; Kamau, Steve; Hou, Jin; Hurley, Noah; Alzaid, Ayman; Wang, Sicheng; Yan, Hao; Deng, Jiangdong; et al (October 2023, Nanotechnology)

   Abstract Twisted moiré photonic crystal is an optical analog of twisted graphene or twisted transition metal dichalcogenide bilayers. In this paper, we report the fabrication of twisted moiré photonic crystals and randomized moiré photonic crystals and their use in enhanced extraction of light in light-emitting diodes (LEDs). Fractional diffraction orders from randomized moiré photonic crystals are more uniform than those from moiré photonic crystals. Extraction efficiencies of 76.5%, 77.8% and 79.5% into glass substrate are predicted in simulations of LED patterned with twisted moiré photonic crystals, defect-containing photonic crystals and random moiré photonic crystals, respectively, at 584 nm. Extraction efficiencies of optically pumped LEDs with 2D perovskite (BA)₂(MA)_n−1Pb_nI_3n+1ofn= 3 and (5-(2′-pyridyl)-tetrazolato)(3-CF₃−5-(2′-pyridyl)pyrazolato) platinum(II) (PtD) have been measured. 

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5. Enhanced Modeling of Twisted String Actuators with Low-Torque Motors Accounting for Strings’ Friction and Opposing Torque

   Konda, Revanth; Zhang, Jun (July 2025, Proceedings of the 2025 American Control Conference (ACC))

   Twisted string actuators (TSAs) have shown strong promise in emerging applications, such as soft robotics and assistive robotics. To construct compact and lightweight TSAs, it is often inevitable to use low-torque and low-speed motors. An accurate TSA model can facilitate the appropriate design of motor-string components and enable TSA’s reliable operation. However, existing models often neglect the twisted strings’ friction and the exerted opposing torque on the motor, which would result in significant discrepancies in predicting the dynamic behaviors of TSAs with low-torque and low-speed motors. This work presents an enhanced model to accurately capture TSA’s dynamics by accounting for the aforementioned phenomena. The theory of torsional closed-wrapped helical springs is used to capture the friction between the twisted strings. The total elastic potential energy of the strings considering string curvature is used to derive the total opposing torque exerted by the twisted strings. The proposed model is experimentally identified, validated, and compared with an existing TSA model to confirm its superior accuracy. 

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