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Abstract The spatial Kibble–Zurek mechanism is applied to the Kitaev chain with inhomogeneous pairing interactions that vanish in half of the lattice and result in a quantum critical point separating the superfluid and normal-gas phases in real space. The weakly-interacting BCS theory predicts scaling behavior of the penetration of the pair wavefunction into the normal-gas region different from conventional power-law results due to the non-analytic dependence of the BCS order parameter on the interaction. The Bogoliubov–de Gennes (BdG) equation produces numerical results confirming the scaling behavior and hints complications in the strong-interaction regime. The limiting case of the step-function quench reveals the dominance of the BCS coherence length in absence of additional length scale. Furthermore, the energy spectrum and wavefunctions from the BdG equation show abundant in-gap states from the normal-gas region in addition to the topological edge states. 

The high nuclearity cubane-assembled Mn-oxo clusters serve as effective precursors for the preparation of monodispersed Mn₃O₄nanocrystals through the colloidal chemistry approach. 

The structures of multiply quantized vortices (MQVs) of an equal-population atomic Fermi superfluid in a rotating spherical bubble trap approximated as a thin shell are analyzed by solving the Bogoliubov-de Gennes (BdG) equation throughout the BCS-Bose Einstein condensation (BEC) crossover. Consistent with the Poincare-Hopf theorem, a pair of vortices emerge at the poles of the rotation axis in the presence of azimuthal symmetry, and the compact geometry provides confinement for the MQVs. While the single-vorticity vortex structure is similar to that in a planar geometry, higher-vorticity vortices exhibit interesting phenomena at the vortex center, such as a density peak due to accumulation of a normal Fermi gas and reversed circulation of current due to in-gap states carrying angular momentum, in the BCS regime but not the BEC regime because of the subtle relations between the order parameter and density. The energy spectrum shows the number of the in-gap state branches corresponds to the vorticity of a vortex, and an explanation based on a topological correspondence is provided.