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Register a new userNature of quasiparticle excitations in the fractional quantum Hall effect
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We investigate the 1/3 fractional quantum Hall state with one and two quasiparticle excitations. It is shown that the quasiparticle excitations are best described as excited composite fermions occupying higher composite-fermion quasi-Landau levels. In particular, the composite-fermion wave function for a single quasiparticle has 15% lower energy than the trial wave function suggested by Laughlin, and for two quasiparticles, the composite fermion theory also gives new qualitative structures.
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Low lying excitations of electron liquids in the fractional quantum Hall (FQH) regime are studied by resonant inelastic light scattering methods. We present here results from charge and spin excitations of FQH states in the lowest spin-split Landau levels that are of current interest. In the range of filling factors $2/5 geq u geq 1/3$, we find evidence that low energy quasiparticle excitations can be interpreted with spin-split composite fermion quasi-Landau levels. At FQH states around $ u=3/2$, we find well-defined excitations at 4/3 and 8/5 that are consistent with a spin-unpolarized population of quasi-Landau levels.
We study the minimal excitations of fractional quantum Hall edges, extending the notion of levitons to interacting systems. Using both perturbative and exact calculations, we show that they arise in response to a Lorentzian potential with quantized flux. They carry an integer charge, thus involving several Laughlin quasiparticles, and leave a Poissonian signature in a Hanbury-Brown and Twiss partition noise measurement at low transparency. This makes them readily accessible experimentally, ultimately offering the opportunity to study real-time transport of Abelian and non-Abelian excitations.
New low-lying excitations are observed by inelastic light scattering at filling factors $ u=p/(phi p pm 1)$ of the fractional quantum Hall regime with $phi=4$. Coexisting with these modes throughout the range $ u leq 1/3$ are $phi=2$ excitations seen at 1/3. Both $phi=2$ and $phi=4$ excitations have distinct behaviors with temperature and filling factor. The abrupt first appearance of the new modes in the low energy excitation spectrum at $ u lesssim 1/3$ suggests a marked change in the quantum ground state on crossing the $phi=2 to phi=4$ boundary at $ u = 1/3$.
Suppose a classical electron is confined to move in the $xy$ plane under the influence of a constant magnetic field in the positive $z$ direction. It then traverses a circular orbit with a fixed positive angular momentum $L_z$ with respect to the center of its orbit. It is an underappreciated fact that the quantum wave functions of electrons in the ground state (the so-called lowest Landau level) have an azimuthal dependence $propto exp(-imphi) $ with $mgeq 0$, seemingly in contradiction with the classical electron having positive angular momentum. We show here that the gauge-independent meaning of that quantum number $m$ is not angular momentum, but that it quantizes the distance of the center of the electrons orbit from the origin, and that the physical angular momentum of the electron is positive and independent of $m$ in the lowest Landau levels. We note that some textbooks and some of the original literature on the fractional quantum Hall effect do find wave functions that have the seemingly correct azimuthal form $proptoexp(+imphi)$ but only on account of changing a sign (e.g., by confusing different conventions) somewhere on the way to that result.
We have experimentally identified fractional quasiparticle creation in a tunneling process through a local fractional quantum Hall (FQH) state. The local FQH state is prepared in a low-density region near a quantum point contact (QPC) in an integer quantum Hall (IQH) system. Shot-noise measurements reveal a clear transition from elementary-charge tunneling at low bias to fractional-charge tunneling at high bias. The fractional shot noise is proportional to T1(1 ? T1) over a wide range of T1, where T1 is the transmission probability of the IQH edge channel. This binomial distribution indicates that fractional quasiparticles emerge from the IQH state to be transmitted through the local FQH state. The study of this tunneling process will enable us to elucidate the dynamics of Laughlin quasiparticles in FQH systems.
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