اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدComposite-particles (Boson, Fermion) Theory of Fractional Quantum Hall Effect
110
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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.
قيم البحث
اقرأ أيضاً
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.
We observe geometric resonance features of composite fermions on the flanks of the even denominator { u} = 1/2 fractional quantum Hall state in high-mobility two-dimensional electron and hole systems confined to wide GaAs quantum wells and subjected
to a weak, strain-induced, unidirectional periodic potential modulation. The features provide a measure of how close to { u} = 1/2 the system stays single-component and supports a composite fermion Fermi sea before transitioning into a { u} = 1/2 fractional quantum Hall state, presumably the two-component {Psi}331 state.
We review the construction of a low-energy effective field theory and its state space for abelian quantum Hall fluids. The scaling limit of the incompressible fluid is described by a Chern-Simons theory in 2+1 dimensions on a manifold with boundary.
In such a field theory, gauge invariance implies the presence of anomalous chiral modes localized on the edge of the sample. We assume a simple boundary structure, i.e., the absence of a reconstructed edge. For the bulk, we consider a multiply connected planar geometry. We study tunneling processes between two boundary components of the fluid and calculate the tunneling current to lowest order in perturbation theory as a function of dc bias voltage. Particular attention is paid to the special cases when the edge modes propagate at the same speed, and when they exhibit two significantly distinct propagation speeds. We distinguish between two geometries of interference contours corresponding to the (electronic) Fabry-Perot and Mach-Zehnder interferometers, respectively. We find that the interference term in the current is absent when exactly one hole in the fluid corresponding to one of the two edge components involved in the tunneling processes lies inside the interference contour (i.e., in the case of a Mach-Zehnder interferometer). We analyze the dependence of the tunneling current on the state of the quantum Hall fluid and on the external magnetic flux through the sample.
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 ex
plained 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. W
e 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.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
