Ruling out the supersoft high-density symmetry energy from the discovery of PSR J0740+6620 with mass $2.14^{+0.10}_{-0.09}M_\odot$

Using the very recently reported mass $2.14^{+0.10}_{-0.09}M_\odot$ of PSR J0740+6620 together with the data of finite nuclei and the constraints on the equation of state of symmetric nuclear matter at suprasaturation densities from flow data in heavy-ion collisions, we show that the symmetry energy $E_{\rm sym}(n)$ cannot be supersoft so that it becomes negative at suprasaturation densities in neutron stars (NSs) and thus may make the NS have a pure neutron matter core. This is in contrast to the fact that using the mass $2.01 \pm 0.04 M_\odot$ of PSR J0348+0432 as the NS maximum mass cannot rule out the supersoft high-density $E_{\rm sym}(n)$. Furthermore, we find the stiffer high-density $E_{\rm sym}(n)$ based on the existence of $2.14M_\odot$ NSs leads to a strong constraint of $\Lambda_{1.4} \ge 348^{+88}_{-51}$ for the dimensionless tidal deformability of the canonical $1.4M_\odot$ NS.