  By minimizing a thermodynamic-like potential, we unbiasedly sample the
potential energy landscape of soft and frictionless spheres under constant
shear stress. We obtain zero-temperature jammed states under desired shear
stresses and investigate their mechanical properties as a function of the shear
stress. As a comparison, we also obtain jammed states from the
quasistatic-shear sampling in which the shear stress is not well-controlled.
Although the yield stresses determined by both samplings show the same
power-law scaling with the compression from point $J$, i.e.~the jamming
transition point at zero temperature and shear stress, for finite size systems,
the quasistatic-shear sampling leads to a lower yield stress and a higher
critical volume fraction of point $J$. The shear modulus of jammed solids
decreases when increasing the shear stress. However, the shear modulus does not
decay to zero at yielding. This discontinuous change of the shear modulus
implies the discontinuous nature of the unjamming transition under nonzero
shear stress, which is further verified by the observation of a discontinuous
jump of the pressure from jammed solids to shear flows. The pressure jump
decreases upon decompression and approaches zero at the critical-like point
$J$, in analogy with well-known phase transitions under external field. The
analysis of force networks in jammed solids reveals that the force distribution
is more sensitive to the increase of the shear stress near point $J$. The force
network anisotropy increases with the shear stress. Weak particle contacts near
the average force and under large shear stresses exhibit asymmetric angle
distribution.
