Singular Behaviour of Electrons and of Composite Fermions in a Finite Effective Field

We consider the self-energy and quasiparticle spectrum, for both electrons interacting with phonons, and composite fermions interacting with gauge fluctuations. In both cases we incorporate the singular structure arising from Landau level quantization in a finite field. This is then used to determine the renormalised gap between the Fermi energy and the first excited states. The electron-phonon problem is treated for both Debye and Einstein phonons. In the case of composite f...

We calculate the effect of infrared fluctuations of the Chern-Simons gauge field on the single-particle Green's function of composite fermions in the half-filled Landau level via higher-dimensional bosonization on a curved Fermi surface. We find that composite fermions remain well-defined quasi-particles, with an effective mass given by the mean-field value, but with anomalously large damping and a spectral function that contains considerable weight away from the quasi-partic...

We analyze the linear response of a half filled Landau level to long wavelength and low frequency driving forces, using Fermi liquid theory for composite fermions. This response is determined by the composite fermions quasi--particle effective mass, $m^*$, and quasi--particle Landau interaction function $f(\theta-\theta')$. Analyzing infra--red divergences of perturbation theory, we get an exact expression for $m^*$, and conjecture the form of the $f(\theta-\theta')$. We then...

This is an introduction to the method of effective field theory. As an application, I derive the effective field theory of low energy excitations in a conductor, the Landau theory of Fermi liquids, and explain why the high-$T_c$ superconductors must be described by a different effective field theory.

An effective Hamiltonian for spinless electrons in the lowest Landau level (LLL) close to half filling is derived. As opposed to the treatment in standard Chern-Simons theories (CS) we first project to the LLL and only then apply a CS-transformation on the Hamiltonian. The transformed field operators act in the lowest Landau level only {\it and} have fermionic commutation relations for small wavenumbers ignoring gauge field fluctuations. When acting on the Hamiltonian at half...

We derive the quantum Boltzmann equation (QBE) of composite fermions at/near the $\nu = 1/2$ state using the non-equilibrium Green's function technique. The lowest order perturbative correction to the self-energy due to the strong gauge field fluctuations suggests that there is no well defined Landau-quasi-particle. Therefore, we cannot assume the existence of the Landau-quasi-particles {\it a priori} in the derivation of the QBE. Using an alternative formulation, we derive t...

We study the finite temperature properties of the gauge theory of nonrelativistic fermions by using RPA and ladder approximation. This gauge theory is relevant to two interesting systems: high-Tc superconductivity and electrons in the half-filled Landau level.

We propose a measure of the stability of composite fermions (CF's) at even-denominator Landau-level filling fractions. Assuming Landau-level mixing effects are not strong, we show that the CF liquid at $\nu=2+1/2$ in the $n=1$ Landau level cannot exist and relate this to the absence of a hierarchy of incompressible states for filling fractions $2+1/3 < \nu < 2+2/3$. We find that a polarized CF liquid should exist at $\nu=2+1/4$. We also show that, for CF states, the variation...

We calculate the fermion Green function and particle-hole susceptibilities for a degenerate two-dimensional fermion system with a singular gauge interaction. We show that this is a strong coupling problem, with no small parameter other than the fermion spin degeneracy, N. We consider two interactions, one arising in the context of the $t-J$ model and the other in the theory of half-filled Landau level. For the fermion self energy we show in contrast to previous claims that th...

We consider a two dimensional electron system in an external magnetic field at and near an even denominator Landau level filling fraction. Using a fermionic Chern--Simons approach we study the description of the system's low energy excitations within an extension of Landau's Fermi liquid theory. We calculate perturbatively the effective mass and the quasi--particle interaction function characterizing this description. We find that at an even denominator filling fraction the f...