Time domain THz studies of thin film spinel superconductor LiTi$_2$O$_4$*

Recent advances in growth of high-quality crystalline thin films of the only known spinel superconductor (SC) LiTi$_2$O$_4$ have allowed the discovery of an anomalous anisotropic magnetoresistance in its normal state [1]. We have used time domain terahertz spectroscopy, a contactless transport measurement, to determine the ac conductivity of LiTi$_2$O$_4$ and to examine the BCS nature of the superconducting state. We obtained the temperature dependence of the SC gap as well as the London penetration depth, and also found a hint of a second gap. We will discuss and compare these results in terms of the known dc transport properties [1].\newline [1] K. Jin, et al. Nature Communications, 6, 7183, 2015.