  We introduce and analyze a novel metallic phase of two-dimensional (2d)
electrons, the Roton Fermi Liquid (RFL), which, in contrast to the Landau Fermi
liquid, supports both gapless fermionic and bosonic quasiparticle excitations.
The RFL is accessed using a re-formulation of 2d electrons consisting of
fermionic quasiparticles and $hc/2e$ vortices interacting with a mutual
long-ranged statistical interaction. In the presence of a strong
vortex-antivortex (i.e. roton) hopping term, the RFL phase emerges as an exotic
yet eminently tractable new quantum ground state. The RFL phase exhibits a
``Bose surface'' of gapless roton excitations describing transverse current
fluctuations, has off-diagonal quasi-long-ranged order (ODQLRO) at zero
temperature (T=0), but is not superconducting, having zero superfluid density
and no Meissner effect. The electrical resistance {\it vanishes} as $T \to 0$
with a power of temperature (and frequency), $R(T) \sim T^\gamma$ (with $\gamma
>1$), independent of the impurity concentration. The RFL phase also has a full
Fermi surface of quasiparticle excitations just as in a Landau Fermi liquid.
Electrons can, however, scatter anomalously from rotonic "current
fluctuations'' and "superconducting fluctuations'', leading to "hot" and "cold"
spots. Fermionic quasiparticles dominate the Hall electrical transport. We also
discuss instabilities of the RFL to a conventional Fermi liquid and a
superconductor. Precisely {\it at} the instability into the Fermi liquid state,
the exponent $\gamma =1$, so that $R(T) \sim T$. Upon entering the
superconducting state the anomalous quasiparticle scattering is strongly
suppressed. We discuss how the RFL phenomenology might apply to the cuprates.
