  The transition metal dichalcogenide 1T-TaS2 attract growing attention because
of the formation of rich density-wave (DW) and superconducting transitions.
However, the origin of the incommensurate DW state at the highest temperature
(~ 550 K), which is "the parent state" of the rich physical phenomena, is still
uncovered. Here, we present a natural explanation for the triple-q
incommensurate DW in 1T-TaS2 based on the first-principles Hubbard model with
on-site U. We apply the paramagnon interference mechanism that gives the
nematic order in Fe-based superconductors. The derived order parameter has very
unique characters: (i) the orbital-selective nature, and (ii) the
unconventional sign-reversal in both momentum and energy spaces. The present
study will be useful for understanding rich physics in 1T-TaS2, 1T-VSe2, and
other transition metal dichalcogenides.
