Related papers: The Fractional Hall hierarchy from duality
We study strongly correlated ground states of dipolar fermions in a honeycomb optical lattice with spatial variations in hopping amplitudes. Similar to a strained graphene, such nonuniform hopping amplitudes produce valley-dependent…
We derive the effective Hamiltonian for the composite fermion in double-layer quantum Hall systems with inter-layer tunneling at total Landau-level filling factor $\nu=1/m$, where $m$ is an integer. We find that the ground state is the…
We quantum mechanically analyze the fractional quantum Hall effect in graphene. This will be done by building the corresponding states in terms of a potential governing the interactions and discussing other issues. More precisely, we…
The Fermionic Chern-Simons approach has had remarkable success in the description of quantum Hall states at even denominator filling fractions $\nu=\frac{1}{2m}$. In this paper we review a number of recent works concerned with modeling this…
We solve models of $N$ species of fermions in the lowest Landau level with $U(N)$-invariant interactions in the $N\gg 1$ limit. We find saddles of the second quantized path integral at fixed chemical potential corresponding to fractional…
When confined to two dimensions and exposed to a strong magnetic field, electrons screen the Coulomb interaction in a topological fashion; they capture and even number of quantum vortices and transform into particl es called `composite…
We introduce a variant of dipole representation for composite fermions in a half-filled Landau level, taking into account the symmetry under exchange of particles and holes. This is implemented by a special constraint on composite fermion…
We derive a microscopic theory of the composite fermions describing the low-lying edge excitations in the fractional quantum Hall liquid. Using the composite fermion transformation, one finds that the edge states of the $\nu=1/m$ system in…
We consider the ``fractional quantum Hall atom" in the vanishing Zeeman energy limit, and investigate the validity of Hund's maximum-spin rule for interacting electrons in various Landau levels. While it is not valid for {\em electrons} in…
The fractional quantum Hall (FQH) effect arises from strong electron correlations in a quantising magnetic field, and features exotic emergent phenomena such as electron fractionalisation. Using the diagrammatic Monte Carlo approach with…
Recently, a Dirac (particle-hole symmetric) description of composite fermions in the half-filled quantum Hall system was proposed [D. T. Son, Phys. Rev. X 5, 031027 (2015)], and we study its possible consequences on BCS (Cooper) pairing of…
The occurrence of incompressible quantum fluid states of a two dimensional system is a result of electron--electron interactions in a highly degenerate fractionally filled Landau level. Novel quasiparticles (QP's) called composite Fermions…
The mean field composite Fermion (MFCF) picture has been qualitatively successful when applied to electrons (or holes) in the lowest Landau level. Because the energy scales associated with Coulomb interactions and with Chern-Simons gauge…
The idea of statistical transmutation plays a crucial role in descriptions of the fractional quantum Hall effect. However, a recently conjectured duality between a critical boson and a massless 2-component Dirac fermion extends this notion…
The structure of fractional fillings of higher Landau levels including spin subbands is systematically derived for the first time. Using topology-type commensurability arguments for 2D charged system in the presence of strong quantizing…
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…
Bosonization dualities relate two different Chern-Simons-matter theories, with bosonic matter on one side replaced by fermionic matter on the other. We first describe a more general class of non-Abelian bosonization dualities. We then…
The mean field (MF) composite Fermion (CF) picture successfully predicts the band of low lying angular momentum multiplets of fractional quantum Hall systems for any value of the magnetic field. This success cannot be attributed to a…
In a recent proposal of the half-filled Landau level, the composite fermions are taken to be Dirac particles and particle-hole symmetric. Cooper pairing of these composite fermions in different angular momentum channels, $\ell$, can give…
We report the observation of the fractional quantum Hall effect in the lowest Landau level of a two-dimensional electron system (2DES), residing in the diluted magnetic semiconductor Cd(1-x)Mn(x)Te. The presence of magnetic impurities…