  Hexagonal warping (HW) in three-dimensional topological insulators is, by
now, well-known. We show that non-Hermitian (NH) loss/gain can generate an
exceptional HW effect in double Weyl-semimetals (DWSM). This unique feature of
DWSMs has distinctive effects on Fermi surface topology. Importantly, in the
presence of such a $k^3$ spin orbit coupling mimicking term, the symmetry
associated with the DWSMs is changed, leading to four exceptional points, among
which two are degenerate. Introducing a driving field removes this degeneracy.
The combined action of the NH warping and driving parameters leads to notable
effects, including merging and tuning of exceptional points. We analyze the
topological nature of the generated exceptional contours by evaluating several
topological invariants, such as winding number, vorticity, and NH Berry
curvature. We hope that our theoretical results would initiate possible
experiments exploring NH HW effects.
