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We report observation of the fractional quantum Hall effect (FQHE) in high mobility multi-terminal graphene devices, fabricated on a single crystal boron nitride substrate. We observe an unexpected hierarchy in the emergent FQHE states that…
The fractional quantum hall effect (FQHE) is a milestone of modern day physics, its disovery paved the way for the study of fractional charges which do not obey abelian physics. However, all FQHE require an external magnetic field in order…
Evidence for developing fractional quantum Hall effect (FQHE) at filling fraction $\nu{=}1/6$ and $1/8$ has recently been reported in wide GaAs quantum wells [Wang \emph{et al.}, PRL {\bf 134}, 046502 (2025)]. In this article, we…
A topological interpretation of the electron--electron interaction under FQHE conditions gives rise to the existence of some kind of composite fermions. The interaction term is similar to the Coulomb interaction and produces punctures in…
We demonstrate that formulating the composite-fermion theory of the fractional quantum Hall (FQH) effect in terms of quaternions greatly expands its reach and opens the door into many interesting issues that were previously beyond the reach…
We study the \nu=5/2 even-denominator fractional quantum Hall effect (FQHE) over a wide range of magnetic (B) field in a heterojunction insulated gate field-effect transistor (HIGFET). The electron density can be tuned from n=0 to 7.6…
We review the fermionic Chern-Simons field theory for the Fractional Quantum Hall Effect (FQHE). We show that in this field theoretic approach to the problem of interacting electrons moving in a plane in the presence of an external magnetic…
The fractional quantum Hall effect (FQHE) at the filling factor with an even denominator, 5/2, occurs despite the expectation, due to the electron statistics, that the denominator must be an odd number. It is believed that the Cooper…
We investigate, using finite size numerical calculations, the spin-polarized fractional quantum Hall effect (FQHE) in the first excited Landau level (LL). We find evidence for the existence of an incompressible state at $\nu = \frac{7}{3} =…
The unexpected appearance of a fractional quantum Hall effect (FQHE) plateau at $\nu=2+6/13$~ [Kumar \emph{et al.}, Phys. Rev. Lett. {\bf 105}, 246808 (2010)] offers a clue into the physical mechanism of the FQHE in the second Landau level…
We have experimentally studied the fractional quantum Hall effect (FQHE) in SiGe/Si/SiGe quantum wells in relatively weak magnetic fields, where the Coulomb interaction between electrons exceeds the cyclotron splitting by a factor of a few…
We consider a collection of fermions in a strong magnetic field coupled by a purely three body repulsive interaction, and predict the formation of composite fermions, leading to a remarkably rich phase diagram containing a host of…
The fractional quantum Hall (FQH) effect is reported in a high mobility CdTe quantum well at mK temperatures. Fully-developed FQH states are observed at filling factor 4/3 and 5/3 and are found to be both spin-polarized ground state for…
One of the most intriguing phenomena in nature is the fractional quantum Hall effect (FQHE) observed in the half-filled second Landau level which, arising in even-denominator filling factors, $\nu=5/2$ and $7/2$, is completely different…
The residual interaction between composite fermions (CFs) can express itself through higher order fractional Hall effect. With the help of diagonalization in a truncated composite fermion basis of low-energy many-body states, we predict…
In this paper we study fractional quantum Hall composite fermion wavefunctions at filling fractions \nu = 2/3, 3/5, and 4/7. At each of these filling fractions, there are several possible wavefunctions with different spin polarizations,…
A microscopic Hamiltonian theory of the FQHE, developed by Shankar and myself based on the fermionic Chern-Simons approach, has recently been quite successful in calculating gaps in Fractional Quantum Hall states, and in predicting…
The fractional quantum Hall effect (FQHE), observed in two-dimensional (2D) charged particles at high magnetic fields, is one of the most fascinating, macroscopic manifestations of a many-body state stabilized by the strong Coulomb…
The fractional quantum Hall effect is a very particular manifestation of electronic correlations in two-dimensional systems in a strong perpendicular magnetic field. It arises as a consequence of a strong Coulomb repulsion between electrons…
The fractional quantum Hall effect (FQHE) is studied in the semiclassical limit in the framework of the Hofstadter model with a short-range interaction between fermions. In the mean-field approximation, the repulsion between fermions leads…