First-Matsubara-frequency rule in a Fermi liquid. Part II: Optical conductivity and comparison to experiment

Motivated by recent optical measurements on a number of strongly correlated electron systems, we revisit the dependence of the conductivity of a Fermi liquid, \sigma(\Omega,T), on the frequency \Omega and temperature T. Using the Kubo formalism and taking full account of vertex corrections, we show that the Fermi liquid form Re\sigma^{-1}(\Omega,T)\propto \Omega^2+4\pi^2T^2 holds under very general conditions, namely in any dimensionality above one, for a Fermi surface of an arbitrary shape (but away from nesting and van Hove singularities), and to any order in the electron-electron interaction. We also show that the scaling form of Re\sigma^{-1}(\Omega,T) is determined by the analytic properties of the conductivity along the Matsubara axis. If a system contains not only itinerant electrons but also localized degrees of freedom which scatter electrons elastically, e.g., magnetic moments or resonant levels, the scaling form changes to Re\sigma^{-1}(\Omega,T)\propto \Omega^2+b\pi^2T^2, with 1\leq b<\infty. For purely elastic scattering, b =1. Our analysis implies that the value of b\approx 1, reported for URu_2Si_2 and some rare-earth based doped Mott insulators, indicates that the optical conductivity in these materials is controlled by an elastic scattering mechanism, whereas the values of b\approx 2.3 and b\approx 5.6, reported for underdoped cuprates and organics, correspondingly, imply that both elastic and inelastic mechanisms contribute to the optical conductivity.Comment: 18 pages, 10 figure

Relaxation of high-energy quasiparticle distributions: electron-electron scattering in a two-dimensional electron gas

A theory is developed for the evolution of the non-equilibrium distribution of quasiparticles when the scattering rate decreases due to particle collisions. We propose a "modified one-collision approximation" which is most effective for high-energy quasiparticle distributions. This method is used to explain novel measurements of the non-monotonic energy dependence of the signal of scattered electrons in a 2D system. The observed effect is related to a crossover from the ballistic to the hydrodynamic regime of electron flow.Comment: 6 pages, 3 figure

Effects of Electron-Electron Scattering on Electron-Beam Propagation in a Two-Dimensional Electron-Gas

We have studied experimentally and theoretically the influence of electron-electron collisions on the propagation of electron beams in a two-dimensional electron gas for excess injection energies ranging from zero up to the Fermi energy. We find that the detector signal consists of quasiballistic electrons, which either have not undergone any electron-electron collisions or have only been scattered at small angles. Theoretically, the small-angle scattering exhibits distinct features that can be traced back to the reduced dimensionality of the electron system. A number of nonlinear effects, also related to the two-dimensional character of the system, are discussed. In the simplest situation, the heating of the electron gas by the high-energy part of the beam leads to a weakening of the signal of quasiballistic electrons and to the appearance of thermovoltage. This results in a nonmonotonic dependence of the detector signal on the intensity of the injected beam, as observed experimentally.Comment: 9 pages, 7 figure

A Magnetic-Field-Effect Transistor and Spin Transport

A magnetic-field-effect transistor is proposed that generates a spin-polarized current and exhibits a giant negative magnetoresitance. The device consists of a nonmagnetic conducting channel (wire or strip) wrapped, or sandwiched, by a grounded magnetic shell. The process underlying the operation of the device is the withdrawal of one of the spin components from the channel, and its dissipation through the grounded boundaries of the magnetic shell, resulting in a spin-polarized current in the nonmagnetic channel. The device may generate an almost fully spin-polarized current, and a giant negative magnetoresistance effect is predicted.Comment: 4 pages, 3 figure

Angle-Resolved Spectroscopy of Electron-Electron Scattering in a 2D System

Electron-beam propagation experiments have been used to determine the energy and angle dependence of electron-electron (ee) scattering a two-dimensional electron gas (2DEG) in a very direct manner by a new spectroscopy method. The experimental results are in good agreement with recent theories and provide direct evidence for the differences between ee-scattering in a 2DEG as compared with 3D systems. Most conspicuous is the increased importance of small-angle scattering in a 2D system, resulting in a reduced (but energy-dependent) broadening of the electron beam.Comment: 4 pages, 4 figure

Non-Magnetic Spinguides and Spin Transport in Semiconductors

We propose the idea of a "spinguide", i.e. the semiconductor channel which is surrounded with walls from the diluted magnetic semiconductor (DMS) with the giant Zeeman splitting which are transparent for electrons with the one spin polarization only. These spinguides may serve as sources of a spin-polarized current in non-magnetic conductors, ultrafast switches of a spin polarization of an electric current and, long distances transmission facilities of a spin polarization (transmission distances can exceed a spin-flip length). The selective transparence of walls leads to new size effects in transport.Comment: 4 pages, 2 figure

The electrical resistance of spatially varied magnetic interface. The role of normal scattering

We investigate the diffusive electron transport in conductors with spatially inhomogeneous magnetic properties taking into account both impurity and normal scattering. It is found that the additional interface resistance that arises due to the magnetic inhomogeneity depends essentially on their spatial characteristics. The resistance is proportional to the spin flip time in the case when the magnetic properties of the conducting system vary smoothly enough along the sample. It can be used to direct experimental investigation of spin flip processes. In the opposite case, when magnetic characteristics are varied sharply, the additional resistance depends essentially on the difference of magnetic properties of the sides far from the interface region. The resistance increases as the frequency of the electron-electron scattering increases. We consider also two types of smooth interfaces: (i) between fully spin-polarized magnetics and usual magnetic (or non-magnetic) conductors, and (ii) between two fully oppositely polarized magnetic conductors. It is shown that the interface resistance is very sensitive to appearing of the fully spin-polarized state under the applied external field

Loop cosmology: regularization vs. quantization

It is argued that it is the regularization of the classical Hamiltonian —the first step in loop cosmology in order to build a well-defined quantum theory— that is already able to avoid the Big Bang and Big Rip singularities, rather than the usually invoked quantum corrections coming from the quantization of the Hamiltonian. To prove such statement, the classical regularized Hamiltonian corresponding to loop gravity is obtained, and it is shown that it coincides, up to terms of order planck, with the so-called effective Hamiltonian which is calculated from the quantum regularized Hamiltonian using semi-classical techniques. From that comparison it is concluded that both types of singularities are avoided at the "classical level" already, i.e., using loop cosmology, in the sense that only the quantum nature of the geometry is invoked (the loop cut-off) in order to construct the regularized Hamiltonian and to fix the parameter on which it depends. Such finding constitutes a key manifestation of the intrinsic power of loop gravity, as compared with other alternatives