The discrete time crystal (DTC) is a nonequilibrium phase of matter that spontaneously breaks timetranslation symmetry. Disorder-induced many-body localization can stabilize the DTC phase by breaking ergodicity and preventing thermalization. Here, we observe the hallmark signatures of the manybody- localized DTC using a quantum simulation platform based on individually controllable carbon-13 nuclear spins in diamond. We demonstrate long-lived period-doubled oscillations and confirm that they are robust for generic initial states, thus showing the characteristic time-crystalline order across the many-body spectrum. Our results are consistent with the realization of an out-of-equilibrium Floquet phase of matter and introduce a programmable quantum simulator based on solid-state spins for exploring many-body physics.

The catalytic performances of TiO₂-supported Ni catalysts for the methanation of CO₂ have been investigated using different crystalline phases of TiO₂ (rutile and anatase). The catalytic activity of Ni depends appreciably on the nature of the support. The rate for CO₂ hydrogenation decreases in the order of 10Ni/TiO_2-rutile ≫ 10Ni/TiO_2-anatase. The use of a mixture of catalysts containing 70% 10Ni/TiO_2-anatase + 30% 10Ni/TiO_2-rutile allows for a significant increase of the reaction rate related to 100% 10Ni/TiO_2-rutile. Importantly, it has been demonstrated that the two catalysts do not need to be in direct contact for the synergetic effect to occur. DRIFTS operando analysis during the methanation reaction shows that adsorbed CO accumulates on Ni/TiO_2-anatase and not on Ni/TiO_2-rutile, and that the role of the Ni/TiO_2-rutile is to assist the hydrogenation of this adsorbed CO on the Ni/TiO_2-anatase. Increased CO₂ methanation is also observed by adding Ni-free TiO_2-anatase to 10Ni/TiO_2-rutile, indicating that CO_x hydrogenation can also occur on bare TiO_2-anatase if activated hydrogen can be supplied by another source. H₂-TPD analyses and catalytic tests performed after dilution of the catalysts have shown that hydrogen spillover (mediated by surface or gas-phase species) is at the origin of the synergy observed between the two catalysts for the Sabatier reaction.