  We address the existence and stability of one-dimensional (1D) holes and
kinks and two-dimensional (2D) vortex-holes nested in extended binary Bose
mixtures, which emerge in the presence of Lee-Huang-Yang (LHY) quantum
corrections to the mean-field energy, along with self-bound quantum droplets.
We consider both the symmetric system with equal intra-species scattering
lengths and atomic masses, modeled by a single (scalar) LHY-corrected
Gross-Pitaevskii equation (GPE), and the general asymmetric case with different
intra-species scattering lengths, described by two coupled (spinor) GPEs. We
found that in the symmetric setting, 1D and 2D holes can exist in a stable form
within a range of chemical potentials that overlaps with that of self-bound
quantum droplets, but that extends far beyond it. In this case, holes are found
to be stable in 1D and they transform into pairs of stable out-of-phase kinks
at the critical chemical potential at which localized droplets turn into
flat-top states, thereby revealing the connection between localized and
extended nonlinear states. In contrast, spinor nature of the asymmetric systems
may lead to instability of 1D holes, which tend to break into two gray states
moving in the opposite directions. Such instability arises due to spinor nature
of the system and it affects only holes nested in extended
modulationally-stable backgrounds, while localized quantum droplet families
remain completely stable, even in the asymmetric case, while 1D holes remain
stable only close to the point where they transform into pairs of kinks. We
also found that symmetric systems allow fully stable 2D vortex-carrying
single-charge states at moderate amplitudes, while unconventional instabilities
appear also at high amplitudes. Symmetry also strongly inhibits instabilities
for double-charge vortex-holes, which thus exhibit unexpectedly robust
evolutions at low amplitudes.
