Fractional Quantum Hall States of Paired Composite Fermions

Piotr Sitko, Lucjan Jacak

Piotr Sitko, Lucjan Jacak

Masaru Onoda, T. Mizusaki, Takaharu Otsuka +1 more

Tongzhou Zhao, Ajit Coimbatore Balram, Jainendra K. Jain

Pairing of composite fermions provides a possible mechanism for fractional quantum Hall effect at even denominator fractions and is believed to serve as a platform for realizing quasiparticles with non-Abelian braiding statistics. We present results from fixed-phase diffusion Monte Carlo calculations which predict that substantial Landau level mixing can induce a pairing of composite fermions at filling factors ν=1/2 and ν=1/4 in the l=-3 relative angular momentum channel, thereby destabilizing the composite-fermion Fermi seas to produce non-Abelian fractional quantum Hall states.

S. B. Mulay, John J. Quinn, Mark Shattuck

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…