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Ru₃Sn₇ is experimentally demonstrated as an efficient catalyst, with potential utilization of topological surface states for hydrogen evolution reaction. Despite its promising catalytic performance, the topological nature of Ru₃Sn₇ remains uncertain. Particularly, the bulk-boundary correspondence has not yet been established, hence hindering a rigorous justification of its topologically-protected surface states. In this work, the bulk topology of Ru₃Sn₇ is detailed using first-principles calculations and the topological quantum chemistry formalism. Ru3Sn7 turns out to be an enforced semimetal possessing symmetry-protected crossings within a set of bands near the Fermi level, which are enforced and prescribed by the violations of symmetry-prescribed compatibilitymore » relations. Moreover, the surface states and the associated origin from the same set of entangled bands are identified, thereby establishing the bulk-boundary correspondence. To evaluate the effects of chemical modifications, the response of topological surface states to various surface terminations, stoichiometry, and oxidation is examined. The surface structures are globally optimized, and the phase diagrams for various experimental conditions are built. It is shown that, due to changes in the local chemical environment, the original surface states are significantly altered. Modified surface bands can be observed near the Fermi level on surface terminations that preserve the C_4v symmetry.« less

Semimetal PtSn₄ has been experimentally demonstrated as a promising topological electrocatalyst for the hydrogen evolution reaction (HER) under both acidic and alkaline conditions. While two possible mechanisms have been proposed to explain its activity, the role of its surface states in HER remains unclear. It is indeed in question how the surface states of this alloy evolve as HER proceeds. In this study, we investigate the surface termination that sustains conducting surface states on PtSn₄, and we track their evolution during HER catalysis. We show that a reconstructed surface with a Sn-poor termination reproduces the scanning tunneling microscopy pattern observedmore » in experiments and sustains a conducting surface. Through phase diagram and geometric structure analysis, we outline the HER profile following the Volmer–Heyrovsky mechanism. As hydrogen atoms adsorb onto the surface, the structure undergoes further reconstruction to an equilibrium phase with a coverage of two hydrides per unit cell. Meanwhile, the surface electronic bands evolve in response to interactions with the adsorbed hydrogen atoms. A hybridization diagram is further proposed for understanding the surface state evolution based on wave function and chemical bonding analyses. While the Pt atoms serve as conventional sites for hydrogen binding, the surface states of PtSn₄ are essential for stabilizing the hydrogen antibonding states via in-phase electronic interactions with the Sn components. This stabilization results in frontier surface bands that are responsible for driving the HER catalysis. Here, our findings provide a detailed description for the direct involvement of surface states on PtSn4 when employed as a catalyst for HER.« less

We introduce an approach to treat localized correlated electronic states in the otherwise weakly correlated host medium. Here, the environment is dynamically downfolded on the correlated subspace. It is captured via renormalization of one and two quasiparticle interaction terms which are evaluated using many-body perturbation theory. We outline the strategy on how to take the dynamical effects into account by going beyond the static limit approximation. Further, we introduce an efficient stochastic implementation that enables treating the host environment with a large number of electrons at a minimal computational cost. For a small explicitly correlated subspace, the dynamical effects aremore » critical. We demonstrate the methodology by reproducing optical excitations in the negatively charged NV center defect in diamond, that agree with experimental results.« less