Electric field modulation of superconductivity and kondo effect in LaAl$_{1-x}$Cr$_{x}$O$_{3}$/SrTiO$_{3}$ interfaces

Two dimensional electron gas exhibit superconductivity and spin orbit coupling (SOC) at the interfaces of two insulators LaXO$_{\mathrm{3}}$/SrTiO$_{\mathrm{3}}$ (where X $=$ Al, Ti and Ga) [1-3], whereas no conductivity is seen when X site is replaced by Cr and Mn [4]. We present low temperature measurements of LaAl$_{\mathrm{1-x}}$Cr$_{\mathrm{x}}$O$_{\mathrm{3}}$/SrTiO$_{\mathrm{3}}$ interfaces for Cr doping of x $=$0, 0.1, 0.2. We show a sharp superconducting transition (T$_{\mathrm{c}})$ at 175 mK for undoped sample (x $=$ 0) which becomes broader for the Cr doping of x $=$ 0.1 with Tc of 100 mK. Further Cr doping to x $=$ 0.2 indicate no sign of superconductivity. We have analyzed the results with hall carrier density and SOC as a function of Cr doping. The temperature dependent sheet resistance below 50 K display an upturn for x $=$ 0 which becomes more pronounced with Cr doping. We discuss the result on the basis of kondo scattering which can be modulated by varying the carrier density. \\[4pt] [1] N. Reyren et al., Science 317, 1196 (2007).\\[0pt] [2] J. Biscaras et al., Nature Communications 1,89 (2010).\\[0pt] [3] J. Biscaras et al., Phys. Rev. Lett. 108, 247004 (2012).\\[0pt] [4] R. Colby et al.,~Phys. Rev. B\textbf{88}, 155325 (2013).\\[0pt]