Fig. 3: Electronic and structural phases of T-Nb₂O₅ via Li intercalation.

a, Electronic and structural phase diagram of T-Nb₂O₅ film versus Li intercalation. The phase transitions and their reversibility are presented schematically. b, Structural model of the orthorhombic model system (Li₄Nb₁₆O₄₂), which was employed to simulate the conventional (pristine) unit cell of T-Nb₂O₅ (Nb_16.8O₄₂, shown in Supplementary Fig. 16), in which 4 Li are added per unit cell to replace the charge of the fractionally distributed 0.8 Nb atom/cell within the 4g layer. This model for T-Nb₂O₅ characterized by a Li₄Nb₁₆O₄₂ stoichiometry is considered as unlithiated and referred to as [T-Nb₂O₅] throughout. c, Total density of states (DOS) of the [T-Nb₂O₅] model unit cell. d,e, Total DOS with one and two extra Li intercalated into the (a × b × 3c) supercell of our simulation model (that is, Li_0.04-[T-Nb₂O₅] (d) and Li_0.08-[T-Nb₂O₅]) (e). f, Total DOS of the monoclinic Li_1.08-[T-Nb₂O₅] structure. g, Diffusion performance of the one extra Li in the primitive Li_0.12-[T-Nb₂O₅] unit cell, including free-energy profile and diffusion barrier (E_a). h, Evolution of the differential binding energy (ΔE_b) for low Li concentration within the supercell (2a × b × 2c) and at high concentration of Li within the primitive [T-Nb₂O₅] unit cell. i, The relative energy evolution of two lithiation states ([T-Nb₂O₅] and Li_1.08-[T-Nb₂O₅]) as a function of the monoclinic angle in the range between 90° and 92.5°.