  In this note we prove that any minimal $2$-torus in $S^4$ has Morse index at
least $6$, with equality if and only if it is congruent to the Clifford torus
in some great $S^3\subset S^4$.For a minimal $2$-torus in $S^n$ with vanishing
Hopf differential, we show that its index is at least $n+3$, and that this
estimate is sharp: the equilateral $2$-torus fully embedded in $S^5\subset S^n$
as a homogeneous minimal surface in $S^n$ has index exactly $n+3$.
