# High-Temperature Superconductivity in the Lanthanide Hydrides at Extreme Pressures  
[PERSON]  
Theory and Simulation of Condensed Matter (TSCM), King's College London, The Strand, London WC2R 2 LS, UK; [EMAIL_ADDRESS] (Y.W. ); [EMAIL_ADDRESS] (F.M. ); [EMAIL_ADDRESS] (Z.Z. ); [EMAIL_ADDRESS] (T.T) Correspondence: [EMAIL_ADDRESS] (E.P. ); [EMAIL_ADDRESS] (N.B. ); [EMAIL_ADDRESS] (C.W.) [PERSON]  
Theory and Simulation of Condensed Matter (TSCM), King's College London, The Strand, London WC2R 2 LS, UK; [EMAIL_ADDRESS] (Y.W. ); [EMAIL_ADDRESS] (F.M. ); [EMAIL_ADDRESS] (Z.Z. ); [EMAIL_ADDRESS] (T.T) Correspondence: [EMAIL_ADDRESS] (E.P. ); [EMAIL_ADDRESS] (N.B. ); [EMAIL_ADDRESS] (C.W.) [PERSON]  
Theory and Simulation of Condensed Matter (TSCM), King's College London, The Strand, London WC2R 2 LS, UK; [EMAIL_ADDRESS] (Y.W. ); [EMAIL_ADDRESS] (F.M. ); [EMAIL_ADDRESS] (Z.Z. ); [EMAIL_ADDRESS] (T.T) Correspondence: [EMAIL_ADDRESS] (E.P. ); [EMAIL_ADDRESS] (N.B. ); [EMAIL_ADDRESS] (C.W.) [PERSON]  
Theory and Simulation of Condensed Matter (TSCM), King's College London, The Strand, London WC2R 2 LS, UK; [EMAIL_ADDRESS] (Y.W. ); [PERSON](F.M. ); [EMAIL_ADDRESS] (Z.Z. ); [PERSON].T) Correspondence: [EMAIL_ADDRESS] (E.P. ); [EMAIL_ADDRESS] (N.B. ); [EMAIL_ADDRESS] (C.W.) Z.-..  
Hydrogen disulphide was previously believed to undergo dissociation under high pressures and was not heavily considered as a potential superconductor. However, recent theoretical work has suggested that dissociation would not occur, but that on the contrary, the material would become superconducting [11]. Inspired by this discovery, [PERSON] et al. compressed sulphur hydride in a diamond anvil cell and showed that hydrogen sulphide would indeed form a superconductor when compressed with a \(T_{c}\) of up to 200 K [12]. Armed with this new knowledge, researchers have expanded their search to include lanthanide hydrides under pressure, with notable examples such as La-H [13] and Y-H [14]. The Fermi density and thus superconductivity in La-H systems are determined not only by the \(d\) orbital La electrons and the \(s\) orbital H electrons, but also by the \(f\) orbital electrons of lanthanum [15]. Using DFT, studies have found that the face-centred cubic (FCC) form of LaH\({}_{10}\) is a good metal, with various bands crossing the Fermi level that form a high electronic density at the Fermi level [16]. In contrast, for the YH\({}_{10}\) system, only the \(d\) orbital Y electrons and the \(s\) orbital H electrons become major contributors to the Fermi density at high pressures [17]. As external pressure destabilises the localised La-4\(f\) more than the other orbitals (La-6s, La-5d), the latter populates when pressure is applied, leading to possible novel emergent quantum states associated with the strong electronic correlations. In particular, it was purported that the La-H system has a unique high \(T_{c}\) with \(f\) electrons at the Fermi level [18]. The effects of electronic localisation and hybridisation apply for all high-density compounds, and this is the hallmark of a wide family of similar materials signified by transition metals, lanthanides, and rare-earth elements. Many-body effects give rise to a number of unique and interesting phenomena in similar systems, such as high-temperature superconductivity in cuprates and the metal-insulator transition in vanadates at ambient temperature [19]. The Zaanen-Sawatzky-Allen theory offers a categorisation of transition metal periodic solids in terms of their correlation' strengths and has provided a good knowledge base, though deep understanding of the hydride's characteristics distant from ambient conditions remains hitherto difficult and incomplete [20]. Therefore, in order to identify new hydrogen-rich high-\(T_{c}\) superconductors at the lowest possible pressure, the use of quantitative theoretical computations is required. Superconductivity in these potential compounds is mediated by the interaction between the highly intense lattice vibrations of hydrogen atoms and the localised electrons.