  The fine structure of attractive Fermi polarons in van der Waals
heterostructures based on monolayer transition metal dichalcogenides in the
presence of elastic strain is studied theoretically. The charged excitons
(trions), three particle bound states of two electrons and hole or two holes
and electron, do not show any strain-induced fine structure splitting compared
to neutral excitons whose radiative doublet is split by the strain into
linearly polarized components. The correlation of the trions with Fermi sea
holes gives rise to the attractive Fermi polarons. We show that it results in
the fine structure splitting of the polaron into states polarized along the
main axes of the strain tensor. The effect is related to the bosonic statistics
of Fermi polarons. We develop microscopic theory of the effect and calculate
the strain-induced splitting of Fermi polarons both for tungsten- and
molybdenum-based monolayers identifying the role of inter- and intravalley
exciton-electron interactions. The fine structure splitting of attractive Fermi
polaron is proportional both to excitonic splitting and the Fermi energy. The
Fermi polaron fine structure in bilayers is briefly analyzed and the role of
electron and trion localization in moire potentials is discussed.
