T2K is a long baseline accelerator neutrino experiment in Japan which studies
neutrino oscillations with a narrow-band muon neutrino beam peaked at 0.6 GeV.
In the present study the T2K setup is used
to search for light sterile neutrinos and constrain
$\theta_{24}$ and $\theta_{34}$ mixing elements in the 3+1 sterile neutrino
model. This is the first long baseline study of sterile neutrinos at T2K which is based on
SK data. To enhance the sensitivity to the effects related to the presence of
sterile neutrinos, a joint analysis is done using both charged-current and the
newly implemented neutral-current (NC) oscillation samples (NC$\pi^0$ with 2
rings observed and NC gamma de-excitation) at the far detector.
The analysis strategy and the results obtained for the current T2K
data (2010-2017 data taking) are presented. We set the most stringent limit on $\sin^2\theta_{24}$ for the sterile neutrino mass splitting $\Delta m^2_{41}<3\times 10^{-3}$eV$^2$, and exclude $\sin^2\theta_{24}>0.1$ and $|U_{\tau 4}|^2=\cos^2\theta_{24}\sin^2\theta_{34}>0.5$ at 90\% C.L. for $\Delta m^2_{41}=0.1$eV$^2$.