A note on 0-bipolar knots of concordance order two

Let $\mathcal{T}$ be the group of smooth concordance classes of topologically slice knots, and ${0}\subset\cdots\subset $\mathcal{T}${n+1}\subset$\mathcal{T}${n}\subset \cdots\subset $\mathcal{T}$_{0}\subset $\mathcal{T}$$ be the bipolar filtration. In this paper, we show that a proper collection of the knots employed by Hedden, Kim, and Livingston to prove ${\mathbb{Z}}_2^{\mathrm{\infty }}<\mathcal{T}$ can be used to see ${\mathbb{Z}}_2^{\mathrm{\infty }}<{\mathcal{T}}_0\mathrm{/}{\mathcal{T}}_1$.