Related papers: Is the Composite Fermion a Dirac Particle?
We establish the quantum mechanics of composite fermions based on the dipole picture initially proposed by Read. It comprises three complimentary components: a wave equation for determining the wave functions of a composite fermion in ideal…
It is well known that there is a particle-hole symmetry for spin-polarized electrons with two-body interactions in a partially filled Landau level, which becomes exact in the limit where the cyclotron energy is large compared to the…
The half-filled Landau level is widely believed to be described by the Halperin-Lee-Read theory of the composite Fermi liquid (CFL). In this paper, we develop a theory for the particle-hole conjugate of the CFL, the Anti-CFL, which we argue…
When a fermionic quantum Hall system is projected into the lowest Landau level, there is an exact particle-hole symmetry between filling fractions $\nu$ and $1-\nu$. We investigate whether a similar symmetry can emerge in bosonic quantum…
The analogues of elementary particles have been extensively searched for in condensed matter systems because of both scientific interests and technological applications. Recently massless Dirac fermions were found to emerge as low energy…
Composite fermions (CFs) of the fractional quantum Hall effect are described as spherical products of electron and vortex spinors, built from underlying L=1/2 ladder operators aligned so that the spinor angular momenta Le and Lv are…
For interacting 2D electrons in the presence of magnetic field at half filling, the system forms a `composite Fermi liquid(CFL)' with emergent Fermi surface and exhibits metallic behavior, based on the standard Halperin, Lee, and Read(HLR)…
We construct explicit lowest-Landau-level wave functions for the composite-fermion Fermi sea and its low energy excitations following a recently developed approach [Pu, Wu and Jain, Phys. Rev. B 96, 195302 (2018)] and demonstrate them to be…
By developing an algorithm for evaluating the basis states for the composite fermions with negative effective magnetic field, we perform the composite-fermion-diagonalization study for the fully spin-polarized fractional quantum Hall states…
Much of the present day qualitative phenomenology of the fractional quantum Hall effect can be understood by neglecting the interactions between composite fermions altogether. For example the fractional quantum Hall effect at $\nu=n/(2pn\pm…
We reconsider the composite fermion theory of general Jain's sequences with filling factor $\nu=N/(4N\pm1)$. We show that Goldman and Fradkin's proposal of a Dirac composite fermion leads to a violation of the Haldane bound on the…
We consider the Hall conductivity of composite fermions in the theory of Halperin, Lee, and Read (HLR). We present a fully quantum mechanical numerical calculation that shows, under suitable conditions, the HLR theory exhibits a…
We construct an action for the composite Dirac fermion consistent with symmetries of electrons projected to the lowest Landau level. First we construct a generalization of the $g=2$ electron that gives a smooth massless limit on any curved…
Motivated by the observation of even denominator fractional quantum Hall effect in the $n=3$ Landau level of monolayer graphene [Y. Kim $\textit{et al.}$, Nature Physics $\textbf{15}$, 154 (2019)], we consider a Bardeen-Cooper-Schrieffer…
We discuss the possibility of the quantum Hall effect at half-filled Landau level in terms of the pairing of the composite fermions. In the absence of Coulomb energy, we show that the ground state of the system is described by the {\it…
We report on fixed phase diffusion Monte Carlo calculations that show that, even for a large amount of Landau level mixing, the energies of the Pfaffian and anti-Pfaffian phases remain very nearly the same, as also do the excitation gaps at…
We review the recently proposed Dirac composite fermion theory of the half-filled Landau level. This paper is based on a talk given at the Nambu Symposium at University of Chicago, March 11-13, 2016.
We present a particle-hole symmetric theory for a two-dimensional electron gas at filling factor one half. In this theory, elementary excitations are dipole-like fermions floating on top of the $\nu=1/2$ boson quantum Hall liquid. In the…
We study the integer quantum Hall plateau transition using composite fermion mean-field theory. We show that the topological $\theta = \pi$ term in the associated nonlinear sigma model [P. Kumar et al., Phys. Rev. B 100, 235124 (2019)] is…
Nonsymmorphic symmetries can give rise to Dirac semimetal (DSM) states. However, few studies have been conducted on DSMs in interacting systems. Here, we induce interacting DSM states in nonsymmorphic iridium oxides SrIrO$_3$, BaIrO$_3$ and…