  It is known that the expanders arising as increasing sequences of level sets
of warped cones, as introduced by the second-named author, do not coarsely
embed into a Banach space as soon as the corresponding warped cone does not
coarsely embed into this Banach space. Combining this with non-embeddability
results for warped cones by Nowak and Sawicki, which relate the
non-embeddability of a warped cone to a spectral gap property of the underlying
action, we provide new examples of expanders that do not coarsely embed into
any Banach space with nontrivial type. Moreover, we prove that these expanders
are not coarsely equivalent to a Lafforgue expander. In particular, we provide
infinitely many coarsely distinct superexpanders that are not Lafforgue
expanders. In addition, we prove a quasi-isometric rigidity result for warped
cones.
