By means of the Fermi-liquid approach, the effects of exchange and correlations are considered in a layered two-dimensional electron gas. A graphical derivative technique is introduced to obtain the contributions to the interparticle interactions from different channels. It is shown that the interaction in the particle - hole channel can induce the metal - insulator phase transition when the Fermi momentum is comparable with the inverse interlayer spacing, . It is also shown that the Cooper-like scattering processes give rise to the scaling of the Fermi liquid response as Im , which leads to the linear temperature dependence of the quasiparticle damping. The possibility of superconductivity in the region between the insulator and normal metal phases, accounting for the particle - hole excitations, is discussed. The effect of the spin fluctuations on the superconductivity due to the particle - hole excitations is also considered.
Using the Fermi-liquid approach with vertex corrections, the effects of exchange and correlation are considered in a layered two-dimensional electron gas. It is shown that the interaction in the particle–hole channel can induce the metal–insulator phase transition when the Fermi momentum is comparable with the inverse interlayer spacing, pF ≈︂ /1c. The possibility of superconductivity in the region between the insulator and normal metal phases, taking into account the particle–hole excitations, is discussed. A smooth crossover from weak to strong coupling superconductivity with the decrease of the 2D carrier density is obtained. The results suggest a new way in the explanation of the phase diagram of layered high-Tc superconductors.
The Cooper instability in an interacting Fermi gas is examined by using the perturbational diagram approach. A graphical derivative method based on Ward's identity is introduced to represent the contributions to the interparticle interactions from different channels. It is shown that pairing instability for the electrons excited from the Fermi sea may happen as a result of the presence of holes even when the original interaction is repulsive. Thus, in contrast to the Cooper instability caused by a given attractive interaction, the pairing instability can be induced by the particle - hole excitations. The application of the results to a layered two-dimensional Fermi gas is considered.
Proceeding from the simplest field theoretical model of 2D metal, the normal phase Green functions of the weakly interacting fermions and the order parameter fluctuations (responsible for the attraction between fermions) are obtained. It is shown that taking into consideration the fluctuations mentioned leads to a considerable reduction of the fermion wave function renormalization constant (quasiparticle weight) as well as to a linear dependence of the quasiparticle damping on the temperature. A general dependence of 2D Fermi liquid properties on the fermion density is discussed. The relevance of the proposed model to the marginal behavior of the Fermi liquid of high--
Tc superconductors, in particular, to their linear temperature dependence of the resistivity is indicated.
The pairing instability induced by either a given attractive interaction or particle-hole excitations is examined by using the perturbational diagram approach. A graphical functional derivative method based on Ward's identity is developed to represent the contributions to the interparticle interactions from different channels. It is shown that pairing instability for the electrons excited from the Fermi sea may happen due to the presence of holes even when the original interaction is repulsive. Thus, in contrast to the Cooper instability caused by a given attractive interaction, the pairing instability can be induced by the particle-hole excitations. The scattering diagrams from this model allows one to evaluate the two particle vertex function and Tc by using the pole condition of the vertex function. It has been found that Tc can reach quite high values and gives rise to the bell shape. The application of the results to a layered 2D Fermi gas is considered.
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 $T\ensuremath{\rightarrow}0$ with a power of temperature (and frequency), $R(T)\ensuremath{\sim}{T}^{\ensuremath{\gamma}}$ (with $\ensuremath{\gamma}>1$), 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 $\ensuremath{\gamma}$ saturates the bound, $\ensuremath{\gamma}=1$, so that $R(T)\ensuremath{\sim}T$. 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.
We consider possible superconducting instabilities in a two-dimensional Fermi system with short-ranged repulsive interactions between electrons. The possibility of an unusual superconducting paring due to the Kohn-Luttinger mechanism is examined. The quasiparticle scattering amplitude is shown to possess an attractive harmonic in second-order perturbation theory for finite values of the energy transfer. The corresponding singularity in the pairing vertex leads to a superconducting pairing of the electron excitations with finite energies. We identify the energy transfer in the Cooper channel as the binding energy of the excited pair. At low enough temperatures, the Fermi system is a mixture of normal electron excitations and fluctuating d-wave Cooper pairs possessing a finite gap.