In this study, a comprehensive experimental in situ analysis of the evolution of the occupied and unoccupied density of states as a function of the charging state of the Li x≤1CoO2 films has been done by using synchrotron X-ray photoelectron spectroscopy (SXPS), X-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS), and O K- and Co L 3,2-edges XANES. Our experimental data demonstrate the change of the Fermi level position and the Co3d–O2p hybridization under the Li+ removal and provide the evidence for the involvement of the oxygen states in the charge compensation. Thus, the rigid band model fails to describe the observed changes of the electronic structure. The Co site is involved in a Co3+ → Co4+ oxidation at the period of the Li deintercalation (x ∼ 0.5), while the electronic configuration at the oxygen site is stable up to 4.2 V. Further lowering of the Fermi level promoted by Li+ extraction leads to a deviation of the electronic density of states due to structural distortions, and the top of the O2p bands overlaps the Co3d state which is accompanied by a hole transfer to the O2p states. The intrinsic voltage limit of LiCoO2 has been determined, and the energy band diagram of Li x≤1CoO2 vs the evolution of the Fermi level has been built. It was concluded that Li x CoO2 cannot be stabilized at the deep Li deintercalation even with chemically compatible solid electrolytes.

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We investigate the dynamics of a spin-orbit (SO) coupled BECs in a time dependent harmonic trap and show the dynamical system to be completely integrable by constructing the Lax pair. We then employ gauge transformation approach to witness the rapid oscillations of the condensates for a relatively smaller value of SO coupling in a time independent harmonic trap compared to their counterparts in a transient trap. Keeping track of the evolution of the condensates in a transient trap during its transition from confining to expulsive trap, we notice that they collapse in the expulsive trap. We further show that one can manipulate the scattering length through Feshbach resonance to stretch the lifetime of the confining trap and revive the condensate. Considering a SO coupled state as the initial state, the numerical simulation indicates that the reinforcement of Rabi coupling on SO coupled BECs generates the striped phase of the bright solitons and does not impact the stability of the condensates despite destroying the integrability of the dynamical system.

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