In this review paper, we stress the importance of the higher transcendental Wright functions of the second kind in the framework of Mathematical Physics. We first start with the analytical properties of the classical Wright functions of which we distinguish two kinds. We then justify the relevance of the Wright functions of the second kind as fundamental solutions of the time-fractional diffusion-wave equations. Indeed, we think that this approach is the most accessible point of view for describing non-Gaussian stochastic processes and the transition from sub-diffusion processes to wave propagation. Through the sections of the text and suitable appendices, we plan to address the reader in this pathway towards the applications of the Wright functions of the second kind.
Kagome materials have emerged as a setting for emergent electronic phenomena that encompass different aspects of symmetry and topology. It is debated whether the XV6Sn6 kagome family (where X is a rare-earth element), a recently discovered family of bilayer kagome metals, hosts a topologically non-trivial ground state resulting from the opening of spin–orbit coupling gaps. These states would carry a finite spin Berry curvature, and topological surface states. Here we investigate the spin and electronic structure of the XV6Sn6 kagome family. We obtain evidence for a finite spin Berry curvature contribution at the centre of the Brillouin zone, where the nearly flat band detaches from the dispersing Dirac band because of spin–orbit coupling. In addition, the spin Berry curvature is further investigated in the charge density wave regime of ScV6Sn6 and it is found to be robust against the onset of the temperature-driven ordered phase. Utilizing the sensitivity of angle-resolved photoemission spectroscopy to the spin and orbital angular momentum, our work unveils the spin Berry curvature of topological kagome metals and helps to define its spectroscopic fingerprint.
The active (110) surface of the benchmark oxygen evolution catalyst RuO 2 spans a flat-band surface state (FBSS) between the surface projections of its Dirac nodal lines (DNLs) that define the electronic properties of this functional semimetal. Monitoring well-known surface adsorption processes of H 2 , O 2 , NO, and CO by in operando angle-resolved photoemission spectroscopy, we selectively modify the oxidation state of individual Ru surface sites and identify the electronic nature of the FBSS: stabilized by bridging oxygen O br p z , the FBSS disperses along ⟨001⟩ oriented chains of bridging Ru br 4d z 2 orbitals, collapses upon O br removal, yet remains surprisingly unaffected by the oxidation state of the undercoordinated 1f-cus-Ru species. This directly reflects in the ability of RuO 2 (110) to oxidize CO and H 2 along with its inability to oxidize NO, demonstrating the FBSS's active role in catalytic charge transfer processes at the oxygen bridge sites. Our synergetic approach provides momentum-resolved insights to the interplay of a catalyst's delocalized electronic band structure and the localized orbitals of its surface reactantsa route toward a microscopic understanding of heterogeneous catalysis.
From first-principles calculations, we investigate the structural and electronic properties of the kagome metals AV3Sb5 (A=Cs, K, Rb) under isotropic and anisotropic pressure. Charge-ordering patterns are found to be unanimously suppressed, while there is a significant rearrangement of p-type and m-type Van Hove point energies with respect to the Fermi level. Already for moderate tensile strain along the V plane and compressive strain normal to the V layer, we find that a Van Hove point can be shifted to the Fermi energy. Such a mechanism provides an invaluable tuning knob to alter the correlation profile in the kagome metal, and suggests itself for further experimental investigation. It might allow us to reconcile possible multidome superconductivity in kagome metals not only from phonons but also from the viewpoint of unconventional pairing.
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