Theoretical design of ellipsoidal nodal surface semimetals via hypervalent hydrides at high pressure

Topological band theory has emerged as a powerful framework to classify and understand the electronic properties of materials. Topological semimetals, which have protected band crossings near the Fermi level and include Dirac and Weyl points, lines, or surfaces, generally remain uncommon. Hypervalent compounds exhibit tunable highly degenerate nonbonding states driving band crossings, so they could provide an effective platform to explore topological semimetallic phases. Here, we identify the topology of the electronic structure of hypervalent hydrides ${A}_{2}B{\mathrm{H}}_{6}$ at ambient pressure and high pressure, and describe the microscopic origin of topological states via hydrogen nonbonding states. Importantly, we discover an ellipsoidal nodal surface, a hitherto unrecognized type of fermionic excitation, in ${\mathrm{Mg}}_{2}\mathrm{Be}{\mathrm{H}}_{6}$ with space group $\mathit{Fm}\overline{3}$$m$. The nodal surface electrons couple strongly to phonons, causing a lattice instability that drives the system towards a charge density wave phase that competes with the topological nodal surface phase, with pressure providing a control parameter. Additionally, in the nodal surface phase we predict superconductivity with a critical temperature of 20 K. We anticipate our work will encourage materials realizations of topological phases and help rationalize high pressure experiments using ideas from topological theory.