Roton Fermi liquid: A metallic phase of two-dimensional electrons

We introduce and analyze a 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 reformulation 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 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 at zero temperature (T=0), but is not superconducting, having zero superfluid density and no Meissner effect. The electrical resistance vanishes as T --> 0 with a power of temperature (and frequency), R(T) similar to 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." Current fluctuations induced by the gapless rotons scatter anomalously only at "hot spots" on the Fermi surface (with tangents parallel to the crystalline axes), while superconducting fluctuations give rise to an anomalous lifetime over the entire Fermi surface except near the (incipient) nodal points ("cold spots"). Fermionic quasiparticles dominate the Hall electrical transport. We also find three dominant instabilities of the RFL phase: an instability to a conventional Fermi-liquid phase driven by vortex condensation, a BCS-type instability toward fermion pairing, and a (nonpairing) superconducting instability. Precisely at the instability into the Fermi-liquid state, the exponent gamma saturates the bound, gamma=1, so that R(T) - T. Upon entering the superconducting state the rotons are gapped out, and the anomalous quasiparticle scattering is strongly suppressed. We discuss how the RFL phase might underlie the strange metallic state of the cuprates near optimal doping, and outline a phenomenological picture to accommodate the underdoped pseudogap regime and the overdoped Landau-Fermi-liquid phase.