Abstract: The thermal signatures of superconductivity in mesoscopic disks, rings and cylinders are calculated within the Ginzburg-Landau theory. In an applied perpendicular magnetic field H the heat capacity of mesoscopic samples shows a strong dependence on the realized vortex state; discontinuities are found at the critical field for different vorticities, as well as at the superconducting-to-normal state transition. The same applies to the intermediate state of type-I superconductors. Even the subtle changes in the fluxoid distribution inside the sample leave clear signatures on heat capacity, which is particularly useful for fully three-dimensional samples whose interior is often inaccessible by magnetometry. The heat-capacity jump ΔC(H) at the critical temperature exhibits quasiperiodic modulations as a function of magnetic field. In mesoscopic superconducting rings, these oscillations provide calorimetric verification of the Little-Parks effect.

Abstract: Because of strong flux confinement in mesoscopic superconductors, a giant vortex may appear in the ground state of the system in an applied magnetic field. This multiquanta vortex can then split into individual vortices (and vice versa) as a function of, e.g., applied current, magnetic field, or temperature. Here we show that such transitions can be identified by calorimetry, as the formation or splitting of a giant vortex results in a clear jump in measured heat capacity versus external drive. We attribute this phenomenon to an abrupt change in the density of states of the quasiparticle excitations in the vortex core(s), and further link it to a sharp change of the magnetic susceptibility at the transitionproving that the formation of a giant vortex can also be detected by magnetometry.

Abstract: Active crystal facets can generate special properties for various applications. Herein, we report a (001) faceted nanosheet-constructed hierarchically porous TiO2/rGO hybrid architecture with unprecedented and highly stable lithium storage performance. Density functional theory calculations show that the (001) faceted TiO2 nanosheets enable enhanced reaction kinetics by reinforcing their contact with the electrolyte and shortening the path length of Li+ diffusion and insertion-extraction. The reduced graphene oxide (rGO) nanosheets in this TiO2/rGO hybrid largely improve charge transport, while the porous hierarchy at different length scales favors continuous electrolyte permeation and accommodates volume change. This hierarchically porous TiO2/rGO hybrid anode material demonstrates an excellent reversible capacity of 250 mAh g(-1) at 1 C (1 C = 335 mA g(-1)) at a voltage window of 1.0-3.0 V. Even after 1000 cycles at 5 C and 500 cycles at 10 C, the anode retains exceptional and stable capacities of 176 and 160 mAh g(-1), respectively. Moreover, the formed Li2Ti2O4 nanodots facilitate reversed Li+ insertion-extraction during the cycling process. The above results indicate the best performance of TiO2-based materials as anodes for lithium-ion batteries reported in the literature.