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

A theory for a Fermi-liquid-like state in a system of charged bosons at filling factor one is developed, working in the lowest Landau level. The approach is based on a representation of the problem as fermions with a system of constraints, introduced by Pasquier and Haldane (unpublished). This makes the system a gauge theory with gauge algebra W_infty. The low-energy theory is analyzed based on Hartree-Fock and a corresponding conserving approximation. This is shown to be equ...

The fully spin polarized composite fermion (CF) Fermi sea at half filled lowest Landau level has a Fermi wave vector $k^*_{\rm F}=\sqrt{4\pi\rho_e}$, where $\rho_e$ is the density of electrons or composite fermions, supporting the notion that the interaction between composite fermions can be treated perturbatively. Away from $\nu=1/2$, the area is seen to be consistent with $k^*_{\rm F}=\sqrt{4\pi\rho_e}$ for $\nu<1/2$ but $k^*_{\rm F}=\sqrt{4\pi\rho_h}$ for $\nu>1/2$, where ...

Mechanism of the particle-flux separation in the Chern-Simons gauge theory coupled with nonrelativistic fermions is studied in a nonperturbative method. This problem is very important for the composite fermion approach to the fractional quantum Hall effect. We show that due to repulsive interactions between electrons the composite fermions are stable quasiexcitations in the half-filled Landau level at low temperature.

We calculate the specific heat of composite fermion system in the half-filled Landau level. Two different methods are used to examine validity of the quasiparticle approximation when the two-body interaction is given by $V(q) = V_0 / q^{2-\eta}$ ($1 \le \eta \le 2$). The singular part of the specific heat is calculated from the free energy of the gauge field, which is compared with the specific heat calculated from the quasiparticle approximation via the singular self-energy ...

We theoretically predict the radiation-induced ``zero-resistance state'' near half filling of the lowest Landau level, which is caused by the photon-assisted transport in the presence of oscillating density of states due to composite fermion Landau levels, and is analogous to the radiation-induced ``zero-resistance state'' of electrons at low magnetic fields. Based on a non-perturbative theory, we show that the radiation field does not break the bound state of electrons and f...

We develop a unified approach to both infrared and ultraviolet asymptotics of the fermion Green functions in the condensed matter systems that allow for an effective description in the framework of the Quantum Electrodynamics. By applying a path integral representation to the previously suggested form of the physical electron propagator we demonstrate that in the massless case this gauge invariant function features a "stronger-than-a-pole" branch-cut singularity instead of th...

We study the low energy effective theory for a non-Fermi liquid state in 2+1 dimensions, where a transverse U(1) gauge field is coupled with a patch of Fermi surface with N flavors of fermion in the large N limit. In the low energy limit, quantum corrections are classified according to the genus of the 2d surface on which Feynman diagrams can be drawn without a crossing in a double line representation, and all planar diagrams are important in the leading order. The emerging t...

While an ordinary Fermi sea is perturbatively robust to interactions, the paradigmatic composite-fermion (CF) Fermi sea arises as a non-perturbative consequence of emergent gauge fields in a system where there was no Fermi sea to begin with. A mean-field picture suggests two Fermi seas, of composite fermions made from electrons or holes in the lowest Landau level, which occupy different areas away from half filling and thus appear to represent distinct states. We show that in...

In this paper we propose a new way of organizing many-body perturbation theory in the Path-integral formulation where a set of quasi-particle wave-functionals $\psi$'s are introduced and are identified with quasi-particles in Landau Fermi liquid theory. We show how Fermi liquid theory can be obtained through $\psi$'s in this new framework of perturbation theory, where the only assumption is adiabaticity between non-interacting and interacting states and the quasi-particle ren...

We study in this paper the properties of a gas of fermions coupling to a U(1) gauge field at wavevectors $q<\Lambda<<k_F$ at dimensions larger than one, where $\Lambda<<k_F$ is a high momentum cutoff and $k_F$ is the fermi wave vector. In particular, we shall consider the $e^2\to\infty$ limit where charge and current fluctuations at wave vectors $q<\Lambda$ are forbidden. Within a bosonization approximation, effective actions describing the low energy physics of the system ar...