2013

Geometric Aspects and Neutral Excitations in the Fractional Quantum Hall Effect

Yang, Bo

Understand

In this thesis, I will present studies on the collective modes of the fractional quantum Hall states, which are bulk neutral excitations reflecting the incompressibility that defines the topological nature of these states.

It was first pointed out by Haldane that the non-commutative geometry of the fractional quantum Hall effects (FQHE) plays an important role in the intra-Landau-level dynamics.
The geometrical aspects of the FQHE will be illustrated by calculating the linear response to a spatially varying electromagnetic field, and by a numerical scheme for constructing model wavefunctions for the neutral bulk excitations.
Compared to early studies of the magneto-roton modes with single mode approximation (SMA), the scheme presented in this thesis is good not only in the long wavelength limit, but also for large momenta where the neutral excitations evolve into quasihole-quasiparticle pair.

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One should note that even in the IQHE, the interaction plays an important role for the dynamics of the quasiparticle and quasiholes. In realistic electron systems with spin degrees of freedom, the interplay of the Coulomb interaction and the Zeeman splitting also leads to interesting physics in quantum Hall ferromagnet. For example, see S.L. Sondhi, A. Karlhede, S.A. Kivelson and E.H. Rezayi, Phys. Rev. B. 47, 16419 (1993). In this thesis, we are only referring to the fundamental aspects of the incompressibility of the IQHE when the Landau levels are fully filled
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