Theory and Applications of Composite Fermion Edge States

We derive a microscopic theory of the composite fermion-type quasiparticles describing the low-lying edge excitations in the fractional quantum Hall liquid with ν = 1/ m . Using the composite fermion transformation, one finds that the edge states of the system in a disc sample are described by the Calogero–Sutherland-like model (CSLM) in the one-dimensional limit. This result presents the consistency between one-dimensional and two-dimensional statistics. It is shown that the low-lying excitations, indeed, have the chiral Luttinger liquid behaviors because there is a gap between the right-and left-moving excitations of the CSLM.We derive a microscopic theory of the composite fermion-type quasiparticles describing the low-lying edge excitations in the fractional quantum Hall liquid with ν = 1/ m . Using the composite fermion transformation, one finds that the edge states of the system in a disc sample are described by the Calogero–Sutherland-like model (CSLM) in the one-dimensional limit. This result presents the consistency between one-dimensional and two-dimensional statistics. It is shown that the low-lying excitations, indeed, have the chiral Luttinger liquid behaviors because there is a gap between the right-and left-moving excitations of the CSLM.

arXiv:cond-mat/9704124Communications in Theoretical PhysicsApr 30, 19982 citations

A Microscopic Model of Edge States of Fractional Quantum Hall Liquid: From Composite Fermions to Calogero-Sutherland Model

Yue Yu

Based on the composite fermion approach, we derive a microscopic theory describing the low-lying edge excitations in the fractional quantum Hall liquid with $ν=\frac{ν^*}{\tildeϕν^*+1}$ . For $ν^*>0$ , it is found that the composite fermion model reduces to an SU $(ν^*)$ Calogero-Sutherland model in the one-dimensional limit, whereas it is not exact soluble for $ν^*<0$ . However, the ground states in both cases can be found and the low-lying excitations can be shown the chiral Luttinger liquid behaviors since a gap exists between the right- and left-moving sectors in each branch of the azimuthal excitations.Based on the composite fermion approach, we derive a microscopic theory describing the low-lying edge excitations in the fractional quantum Hall liquid with $ν=\frac{ν^*}{\tildeϕν^*+1}$. For $ν^*>0$, it is found that the composite fermion model reduces to an SU$(ν^*)$ Calogero-Sutherland model in the one-dimensional limit, whereas it is not exact soluble for $ν^*<0$. However, the ground states in both cases can be found and the low-lying excitations can be shown the chiral Luttinger liquid behaviors since a gap exists between the right- and left-moving sectors in each branch of the azimuthal excitations.

arXiv:cond-mat/9906123Jun 9, 19990 citations

Study of inter-composite fermion interaction

Seung-Yeop Lee, Jainendra K. Jain, V. W. Scarola

APSMar 1, 20010 citations

Relevance of Inter-Composite-Fermion Interaction to the Edge Tomonaga-Luttinger Liquid

Sudhansu S. Mandal, Jainendra K. Jain

It is shown that Wen's effective theory correctly describes the Tomonaga-Luttinger liquid at the edge of a system of noninteracting composite fermions. However, the weak residual interaction between composite fermions is found to be a relevant perturbation. The filling factor dependence of the Tomonaga-Luttinger parameter is estimated for interacting composite fermions in a microscopic approach and satisfactory agreement with experiment is achieved. It is suggested that the electron field operator may not have a simple representation in the effective one-dimensional theory.It is shown that Wen's effective theory correctly describes the Tomonaga-Luttinger liquid at the edge of a system of noninteracting composite fermions. However, the weak residual interaction between composite fermions is found to be a relevant perturbation. The filling factor dependence of the Tomonaga-Luttinger parameter is estimated for interacting composite fermions in a microscopic approach and satisfactory agreement with experiment is achieved. It is suggested that the electron field operator may not have a simple representation in the effective one-dimensional theory.

arXiv:cond-mat/0207615Physical Review LettersAug 8, 200248 citations

Second Generation of Composite Fermions

M. O. Goerbig, Pascal Lederer, C. Morais Smith

arXiv:cond-mat/0308021Aug 1, 20030 citations

Based on the composite fermion approach, we derive a microscopic theory describing the low-lying edge excitations in the fractional quantum Hall liquid with

ν=\frac{ν^*}{\tildeϕν^*+1}

. For

ν^*>0

, it is found that the composite fermion model reduces to an SU

(ν^*)

Calogero-Sutherland model in the one-dimensional limit, whereas it is not exact soluble for

ν^*<0

. However, the ground states in both cases can be found and the low-lying excitations can be shown the chiral Luttinger liquid behaviors since a gap exists between the right- and left-moving sectors in each branch of the azimuthal excitations.