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We introduce a notion of residual diffeomorphism covariance in quantum Kantowski–Sachs (KS) describing the interior of a Schwarzschild black hole. We solve for the family of Hamiltonian constraint operators satisfying the associated covariance condition, as well as parity invariance, preservation of the Bohr Hilbert space of the Loop Quantum KS and a correct (naïve) classical limit. We further explore the imposition of minimality for the number of terms and compare the solution with those of other Hamiltonian constraints proposed for the Loop Quantum KS in the literature. In particular, we discuss a lapse that was recently commonly chosen due to the resulting decoupling of the evolution of the two degrees of freedom and the exact solubility of the model. We show that such a choice of lapse can indeed be quantized as an operator that is densely defined on the Bohr Hilbert space and that any such operator must include an infinite number of shift operators. 

Metallic hydrogen (MH) has been predicted to be metastable, a high temperature superconductor, and a powerful rocket propellant. If true, MH could have an enormous impact on society. We have produced MH in a diamond anvil cell and studied its metastability. At a temperature of 5 K, the load on the metallic hydrogen was stepwise reduced until the pressure was essentially zero. While turning the load or pressure down, the sample evidently transformed to the molecular phase and escaped; the hole in the gasket containing the MH closed. We were unable to determine this value of the metastability pressure. Metallic hydrogen was not observed to be metastable at zero pressure, with no uncertainty. 

X-ray diffraction indicates that the structure of the recently discovered carbonaceous sulfur hydride (C-S-H) room temperature superconductor is derived from previously established van der Waals compounds found in the H2S-H2 and CH4-H2 systems. Crystals of the superconducting phase were produced by a photochemical synthesis technique leading to the superconducting critical temperature Tc of 288 K at 267 GPa. X-ray diffraction patterns measured from 124 to 178 GPa, within the pressure range of the superconducting phase, are consistent with an orthorhombic structure derived from the Al2Cu-type determined for (H2S)2H2 and (CH4)2H2 that differs from those predicted and observed for the S-H system to these pressures. The formation and stability of the C-S-H compound can be understood in terms of the close similarity in effective volumes of the H2S and CH4 components, and denser carbon-bearing S-H phases may form at higher pressures. The results are crucial for understanding the very high superconducting Tc found in the C-S-H system at megabar pressures. 

Last year, the report of Room-Temperature Superconductivity in high-pressure carbonaceous sulfur hydride marked a major milestone in the history of physics: one of the holy grails of condensed matter research was reached after more than one century of continuing efforts. This long path started with Neil Ashcroft’s and Vitaly Ginzburg’s visionary insights on high-temperature superconductivity in metallic hydrogen in the 60’s and 70’s, and has led to the current hydride fever, following the report of high-Tc high-pressure superconductivity in H3S in 2014. This Roadmap collects selected contributions from many of the main actors in this exciting chapter of condensed matter history. Key for the rapid progress of this field has been a new course for materials discovery, where experimental and theoretical discoveries proceed hand in hand. The aim of this Roadmap is not only to offer a snapshot of the current status of superconductor materials research, but also to define the theoretical and experimental obstacles that must be overcome for us to realize fully exploitable room temperature superconductors, and foresee future strategies and research directions. This means improving synthesis techniques, extending first-principles methods for superconductors and structural search algorithms for crystal structure predictions, but also identifying new approaches to material discovery based on artificial intelligence.