  It was recently discovered that in spite of the scalar nature of its order
parameter, the charge order in 1T-TiSe2 can be chiral. This is made possible by
the emergence of orbital order in conjunction with the charge density
modulations. Here we show that a closely related charge and orbital ordered
state arises in 2H-TaS2. In both materials, the microscopic mechanism driving
the transition is based on the interaction between three differently polarized
displacement waves. The relative phase shifts between these waves lead both to
the formation of orbital order and to the breakdown of inversion symmetry. In
contrast to 1T-TiSe2 however, the presence of a mirror plane in the lattice of
2H-TaS2 prevents the distorted structure in this material from being chiral,
and a polar charge and orbital ordered state arises instead. It is stressed
that bulk experiments are indispensable in differentiating between the chiral
and polar phases.
