  Hyperbolic materials are receiving significant attention due to their ability
to support electromagnetic fields with arbitrarily high momenta and, hence, to
achieve very strong light confinement. Here, based on first-principles
calculations and many-body perturbation theory, we explore the characteristic
of two-dimensional plasmon modes and its hyperbolic properties for two phases
of single layer boron hosting tilted Dirac cone, namely, the $hr$-$sB$ and
$8Pmmn$ borophene. In-plane anisotropy in borophene is manifested in the
structural, electronic, vibrational and optical properties. We find two
hyperbolic regimes for both phases of borophene, where the high-energy one is
located in the visible range. The $hr$-$sB$ borophene is characterised with an
intrinsic high carrier density and it supports strong hyperbolic plasmon modes
in the visible part of the spectrum. The $8Pmmn$ borophene, on the other hand,
resembles the prototypical Dirac material graphene, and upon carrier doping
acquires anisotropic Dirac plasmons in the mid-infrared. We have also
investigated the impact of the electron-phonon coupling and Landau damping on
these hyperbolic plasmon modes. Our results show that borophene, having high
anisotropy, intrinsic high carrier concentration, low-loss hyperbolic Dirac
plasmon modes, and high confinement can represent a promising candidate for
low-loss broad band surface plasmon polariton devices.
