  It is well known that two-dimensional (2D) bosons in homogeneous space cannot
undergo real Bose-Einstein condensation, and the superfluid to normal phase
transition is Berezinskii-Kosterlitz-Thouless (BKT) type, associated with
vortex-antivortex pair unbinding. Here we point out a 2D bosonic system whose
low energy physics goes beyond conventional paradigm of 2D {\it homogeneous}
bosons, i.e., intralayer excitons in monolayer transition metal
dichalcogenides. With intrinsic valley-orbit coupling and valley Zeeman energy,
exciton dispersion becomes linear at small momentum, giving rise to a series of
novel features. The critical temperature of Bose-Einstein condensation of these
excitons is nonzero, suggesting true long-range order in 2D homogeneous system.
The dispersion of Goldstone mode at long wavelength has the form
$\varepsilon(\boldsymbol{q})\sim\sqrt{q}$, in contrast to conventional linear
phonon spectrum. The vortex energy deviates from the usual logarithmic form
with respect to system size, but instead has an additional linear term.
Superfluid to normal phase transition is no longer BKT type for system size
beyond a characteristic scale, without discontinuous jump in superfluid
density. With the recent experimental progress on exciton fluid at thermal
equilibrium in monolayer semiconductors, our work points out an experimentally
accessible system to search for unconventional 2D superfluids beyond BKT
paradigm.
