Finite-size calculations of FQHE states at filling ν=1/2

J. Dietel

David A. W. Hutchinson, John C. Inkson, J.M. Rowe

Orion Ciftja, Carlos Wexler

We investigate broken rotational symmetry (BRS) states for the fractional quantum Hall effect (FQHE) at $\frac{1}{3}$ filling of the valence Landau level (LL). Recent Monte Carlo calculations by Musaelian and Joynt [J. Phys.: Condens. Matter 8, L105 (1996)] suggest that Laughlin's state becomes unstable to a BRS state for some critical finite thickness value. We study in detail the properties of such state by performing a hypernetted-chain calculation that gives results in the thermodynamic limit, complementing other methods which are limited to a finite number of particles. Our results indicate that while Laughlin's state is stable in the lowest LL, in higher LL's a BRS instability occurs, perhaps indicating the absence of FQHE at partial fillings of higher LL's. Possible connections to the newly discovered liquid crystalline phases in higher LL's are also discussed.

Chi‐Fai Lo

Lotfi Belkhir, Jainendra K. Jain

Motivated by the observation of fractional quantum Hall effect (FQHE) at filling factor \ensuremath{\nu}=2+1/2 by Willett et al., we investigate the nature of the spin-singlet FQHE at \ensuremath{\nu}=1/2. We show that a simple trial wave function for the \ensuremath{\nu}=1/2 state, proposed earlier by one of us, is the exact nondegenerate ground state of a hard-core interaction model, and provide numerical evidence that it is adiabatically connected to the true Coulomb ground state.

Sreejith Ganesh Jaya

Materials exhibiting exotic quantum phenomena at a macroscopic level are of great interest because of its intrinsic value to Physics, and also because of its potential applications in technology. Strongly correlated electronic systems form interesting examples of these. Exploring them calls for a good understanding of its physics, and development of new tools that are applicable to their analysis. Robustness of the fractional quantum Hall effect (FQHE) makes it an ideal stage to study strongly correlated electron systems. The complexity of the FQHE problem stems directly from the strong interactions between the constituent particles and not from the specific nature of the material it is implemented in. This work attempts to gain a theoretical description of some of the less understood aspects of FQHE. FQHE in the lowest Landau level is well understood using the theory of weakly interacting emergent particles called composite fermions. Composite fermions formed in the second Landau level however appear to be strongly interacting. Of particular interest is the FQHE at 2 + 1/2 filling fraction, where the many body ground state is believed to be described by a paired state of composite fermions, represented by the Pfaffian wavefunction. Based on predicted properties of its excitations, there has been proposals for implementing topological quantum com- putations in this system. However a good understanding of the nature of these excitations is still lacking. This thesis introduces a class of many body wavefunctions called “bipartite composite fermion states” that provide a unified description of all excitations of the paired state at 5/2. In the bipartite composite fermion (BCF) picture, constituent composite fermions split into two partitions which are correlated to each other. Within each partition, they fill the lowest composite fermion Landau level of its partition. Properties of the BCF state can now be related to the properties of the individual partitions, which are well understood in terms of the composite fermion theory. In particular, we show that the excitations of BCF states are obtained by creating excitations in the individual partitions. The paired state with odd number of composite fermions should have an unpaired composite fermion. The BCF model predicts that this unpaired composite fermion behaves as an exciton in the quasiparticle and quasihole are in separate partitions. We confirm this prediction numerically in finite size systems. Generalizations of bipartite composite fermion functions to other filling fractions especially 2 + 4/7 and 2 + 3/5 are also studied. Idea of bipartite composite fermions can be generalized to the case of more partitions. Specifically, we look at tripartite composite fermion states which are similar to the bipartite states, except that these have three correlated partitions instead of two. Tripartite states have a filling fraction of ν = 3/5, and its particle hole conjugate is a candidate wavefunction for describing the ν = 2 + 2/5…