Anomalies of upper critical field in the spinel superconductor ${\mathrm{LiTi}}_2{\mathrm{O}}_{4-\delta }$

High-field electrical transport and point-contact tunneling spectroscopy are used to investigate superconducting properties of spinel oxide ${\mathrm{LiTi}}_2{\mathrm{O}}_{4-\delta }$ films with various oxygen contents. It is striking that although the superconducting transition temperature and energy gap are almost unchanged, an isotropic upper critical field $B_{\mathrm{c}2}$ up to 26.0 T is observed in the oxygen-rich sample, which is more than twice the $B_{\mathrm{c}2}$ of 11.3 T in the anoxic one. The change of the dominating pair-breaking mechanism from the orbital effect to the spin flip at $B_{\mathrm{c}2}$ is achieved by tuning oxygen contents, which can be explained by the appearance of small Fermi pockets due to extra oxygen. Our paper provides deep understanding of the intrinsic relation between $B_{\mathrm{c}2}$ and the complex Fermi surface, and contributes a promising way to enhance $B_{\mathrm{c}2}$ for practical superconductors.

Figure 1

(a) $\rho \left(T\right)$ curves of ${\mathrm{LiTi}}_2{\mathrm{O}}_{4-\delta }$ films S1–S3. (b)–(e) $\rho \left(B\right)$ curves of S1 (b), (c) and S3 (d), (e) from 2 to 10 K with $\mathrm{\Delta }T=2\mathrm{K}$. The magnetic field is perpendicular (b), (d) and parallel (c), (e) to $ab$ plane. The grey dotted lines in (b) and (c) are linearly extrapolated from experimental data.

Figure 2

(a) The normalized $dI/dV\left(V\right)$ measured at 6 K of S1 and S3 with magnetic field of 7 and 16 T, respectively. (b) Field-dependent normalized $\mathrm{\Delta }$ of S1 and S3 at 2.5 K. (c) The normalized $dI/dV\left(V\right)$ of S1 and S3 measured at 6 K and 0 T. (d) Temperature-dependent $\mathrm{\Delta }$ of S1 and S3 at 0 T.

Figure 3

(a) $\rho \left(T\right)$ curve of ${\mathrm{LiTi}}_2{\mathrm{O}}_{4-\delta }$ film S4. Inset: Zoom-in $\rho \left(T\right)$ curve. (b), (c) $\rho \left(B\right)$ curves of S4 where magnetic field is parallel (b) and perpendicular (c) to $ab$ plane, respectively. (d) $B_{\mathrm{c}2}-T$ phase diagram of ${\mathrm{LiTi}}_2{\mathrm{O}}_{4-\delta }$ films. The solid lines are deduced from the WHH theory.

Figure 4

The correlation between $B_{\mathrm{c}2}$ and RRR of ${\mathrm{LiTi}}_2{\mathrm{O}}_{4-\delta }$ films. $B_{\mathrm{c}2}^{\mathrm{orb}}$ are estimated by $-0.69T_{\mathrm{c}}(d{B}_{\mathrm{c}2}/dT){|}_{T_{\mathrm{c}}}$. $B_{\mathrm{P}}$ is determined by $\mathrm{\Delta }/\left(\sqrt{2}{\mu }_{\mathrm{B}}\right)$. $B_{\mathrm{P}}^{*}$ is derived from Ref. [21]. The red dots stand for $B_{\mathrm{c}2}$ at 2 K. The black dotted, blue dashed, and red solid lines are guides to the evolution of the corresponding critical field.