Vito Scarola

Cooper instability of composite fermions

When confined to two dimensions and exposed to a strong magnetic field, electrons screen the Coulomb interaction in a topological fashion; they capture an even number of quantum vortices and transform into particles called ‘composite fermions’ (refs 1,2,3). The fractional quantum Hall effect occurs in such a system when the ratio (or ‘filling factor’, ν) of the number of electrons and the degeneracy of their spin-split energy states (the Landau levels) takes on particular values. The Landau level filling ν = 1/2 corresponds to a metallic state in which the composite fermions form a gapless Fermi sea. But for ν = 5/2, a fractional quantum Hall effect is observed instead; this unexpected result is the subject of considerable debate and controversy. Here we investigate the difference between these states by considering the theoretical problem of two composite fermions on top of a fully polarized Fermi sea of composite fermions. We find that they undergo Cooper pairing to form a p-wave bound state at ν = 5/2, but not at ν = 1/2. In effect, the repulsive Coulomb interaction between electrons is overscreened in the ν = 5/2 state by the formation of composite fermions, resulting in a weak, attractive interaction.

Rotons of composite fermions: Comparison between theory and experiment

A major obstacle toward a quantitative verification, by comparison to experiment, of the theory of the excitations of the fractional quantum Hall effect has been the lack of a proper understanding of disorder. We circumvent this problem by studying the neutral magneto-roton excitations, whose energy is expected to be largely insensitive to disorder. The calculated energies of the roton at 1/3, 2/5 and 3/7 fillings of the lowest Landau level are in good agreement with those measured experimentally. Quantitative tests of the theory of the fractional quantum Hall effect (FQHE) have focused in the past primarily on the gap to charged excitation, determined experimentally from the temperature dependence of the longitudinal resistance. A factor of two discrepancy between theory and experiment has persisted over the years, believed to be caused by disorder for which a quantitatively reliable theoretical treatment is not available at the moment. In recent years there has been tremendous experimental progress in the measurement of the energy of the neutral magneto-roton excitation [1], both by inelastic Raman scattering [2–4] and by ballistic phonon absorption [5–7], and its energy has been determined at Lan-dau level fillings of 1/3, 2/5, and 3/7. While the neutral magneto-roton is of great interest in its own right, being the lowest energy excitation of the FQHE state, the chief motivation of this work is the observation that the disorder is not likely to affect its energy significantly, in contrast to the energy of the charged excitation, because the roton has a much weaker dipolar coupling to disorder due to its overall charge neutrality, and the coupling is further diminished because the disorder in modulation doped samples is typically smooth on the scale of the size (on the order a magnetic length) of the spatially localized roton. There is also compelling experimental evidence for the insensitivity of the roton energy to disorder: the same roton energy was found for samples for which the gaps in transport experiments differed by as much as a factor of two [5]. The roton therefore provides a wonderful opportunity for testing the quantitative validity of our understanding of the excitations of the fractional quantum Hall state. With this goal in mind, we have undertaken a comprehensive and realistic calculation of the roton energy at several filling factors in the lowest Landau level (LL). The neutral excitation of the FQHE will be treated in the framework of the composite fermion …

Phonon drag effect in single-walled carbon nanotubes

A variational solution of the coupled electron-phonon Boltzmann equations is used to calculate the phonon drag contribution to the thermopower in a one-dimensional system. A simple formula is derived for the temperature dependence of the phonon drag in metallic single-walled carbon nanotubes. Scattering between different electronic bands yields nonzero values for the phonon drag as the Fermi level varies.

Structures for interacting composite fermions: Stripes, bubbles, and fractional quantum Hall effect

Much of the present day qualitative phenomenology of the fractional quantum Hall effect can be understood by neglecting the interactions between composite fermions altogether. For example, the fractional quantum Hall effect at v=n/(2pn ′ 1) corresponds to filled composite-fermion Landau levels, and the compressible state at v = ½p to the Fermi sea of composite fermions. Away from these filling factors, the residual interactions between composite fermions will determine the nature of the ground state. In this paper, a model is constructed for the residual interaction between composite fermions, and various possible states are considered in a variational approach. Our study suggests the formation of composite-fermion stripes, bubble crystals, as well as fractional quantum Hall states for appropriate situations.

Possible pairing-induced even-denominator fractional quantum Hall effect in the lowest Landau level.

We report on our theoretical investigations that point to the possibility of a fractional quantum Hall effect with partial spin polarization at nu = 3/8. The physics of the incompressible state proposed here involves p-wave pairing of composite fermions in the spin reversed sector. The temperature and magnetic field regimes for the realization of this state are estimated.

The Phase Diagram of the

Interesting non-Abelian states, e.g., the Moore-Read Pfaffian and the anti-Pfaffian, offer candidate descriptions of the

\nu=5/2

\nu = 5/2

Fractional Quantum Hall Effect: Effects of Landau Level Mixing and Non-Zero Width

fractional quantum Hall state. But the significant controversy surrounding the nature of the

Excitonic collapse of higher Landau level fractional quantum Hall effect

\nu = 5/2

Phase Diagram of Bilayer Composite Fermion States

state has been hampered by the fact that the competition between these and other states is affected by small parameter changes. To study the phase diagram of the