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 _ { sym } ( n ) can not 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 can not rule out the supersoft high-density E _ { sym } ( n ) .
Furthermore , we find the stiffer high-density E _ { sym } ( n ) based on the existence of 2.14 M _ { \odot } NSs leads to a strong constraint of \Lambda _ { 1.4 } \geq 348 ^ { +88 } _ { -51 } for the dimensionless tidal deformability of the canonical 1.4 M _ { \odot } NS .