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We study the role of anisotropy on the transport properties of composite fermions near Landau level filling factor $ u=1/2$ in two-dimensional holes confined to a GaAs quantum well. By applying a parallel magnetic field, we tune the composite fermion Fermi sea anisotropy and monitor the relative change of the transport scattering time at $ u=1/2$ along the principal directions. Interpreted in a simple Drude model, our results suggest that the scattering time is longer along the longitudinal direction of the composite fermion Fermi sea. Furthermore, the measured energy gap for the fractional quantum Hall state at $ u=2/3$ decreases when anisotropy becomes significant. The decrease, however, might partly stem from the charge distribution becoming bilayer-like at very large parallel magnetic fields.
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Composite fermions in fractional quantum Hall (FQH) systems are believed to form a Fermi sea of weakly interacting particles at half filling $ u=1/2$. Recently, it was proposed (D. T. Son, Phys. Rev. X 5, 031027 (2015)) that these composite fermions are Dirac particles. In our work, we demonstrate experimentally that composite fermions found in monolayer graphene are Dirac particles at half filling. Our experiments have addressed FQH states in high-mobility, suspended graphene Corbino disks in the vicinity of $ u=1/2$. We find strong temperature dependence of conductivity $sigma$ away from half filling, which is consistent with the expected electron-electron interaction induced gaps in the FQH state. At half filling, however, the temperature dependence of conductivity $sigma(T)$ becomes quite weak as expected for a Fermi sea of composite fermions and we find only logarithmic dependence of $sigma$ on $T$. The sign of this quantum correction coincides with weak antilocalization of composite fermions, which reveals the relativistic Dirac nature of composite fermions in graphene.
A quantum statistical theory is developed for a fractional quantum Hall effects in terms of composite bosons (fermions) each of which contains a conduction electron and an odd (even) number of fluxons. The cause of the QHE is by assumption the phonon exchange attraction between the conduction electron (electron, hole) and fluxons (quanta of magnetic fluxes). We postulate that c-fermions with emph{any} even number of fluxons have an effective charge (magnitude) equal to the electron charge $e$. The density of c-fermions with $m$ fluxons, $n_phi^{(m)}$, is connected with the electron density $n_{mathrm e}$ by $n_phi^{(m)}=n_{mathrm e}/m$, which implies a more difficult formation for higher $m$, generating correct values $me^2/h$ for the Hall conductivity $sigma_{mathrm H}equiv j/E_{mathrm H}$. For condensed c-bosons the density of c-bosons-with-$m$ fluxons, $n_phi^{(m)}$, is connected with the boson density $n_0$ by $n_phi^{(m)}=n_0/m$. This yields $sigma_{mathrm H}=m,e^2/h$ for the magnetoconductivity, the value observed of the QHE at filling factor $ u=1/m$ ($m=$odd numbers). Laughlins theory and results about the fractional charge are not borrowed in the present work.
Via the application of parallel magnetic field, we induce a single-layer to bilayer transition in two-dimensional electron systems confined to wide GaAs quantum wells, and study the geometric resonance of composite fermions (CFs) with a periodic density modulation in our samples. The measurements reveal that CFs exist close to bilayer quantum Hall states, formed at Landau level filling factors $ u=1$ and 1/2. Near $ u=1$, the geometric resonance features are consistent with half the total electron density in the bilayer system, implying that CFs prefer to stay in separate layers and exhibit a two-component behavior. In contrast, close to $ u=1/2$, CFs appear single-layer-like (single-component) as their resonance features correspond to the total density.
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 may be explained by strongly interacting composite Fermions with full SU(4) symmetric underlying degrees of freedom. The FQHE gaps are measured from temperature dependent transport to be up 10 times larger than in any other semiconductor system. The remarkable strength and unusual hierarcy of the FQHE described here provides a unique opportunity to probe correlated behavior in the presence of expanded quantum degrees of freedom.
The interplay between interaction and disorder-induced localization is of fundamental interest. This article addresses localization physics in the fractional quantum Hall state, where both interaction and disorder have nonperturbative consequences. We provide compelling theoretical evidence that the localization of a single quasiparticle of the fractional quantum Hall state at filling factor $ u=n/(2n+1)$ has a striking {it quantitative} correspondence to the localization of a single electron in the $(n+1)$th Landau level. By analogy to the dramatic experimental manifestations of Anderson localization in integer quantum Hall effect, this leads to predictions in the fractional quantum Hall regime regarding the existence of extended states at a critical energy, and the nature of the divergence of the localization length as this energy is approached. Within a mean field approximation these results can be extended to situations where a finite density of quasiparticles is present.
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