Exotic emergent phenomena in the fractional quantum Hall effect
Open Access
- Author:
- Coimbatore Balram, Ajit
- Graduate Program:
- Physics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- April 28, 2016
- Committee Members:
- Jainendra Jain, Dissertation Advisor/Co-Advisor
Jainendra Jain, Committee Chair/Co-Chair
Nitin Samarth, Committee Member
Jorge Osvaldo Sofo, Committee Member
Thomas E Mallouk, Committee Member - Keywords:
- FQHE
topological phases
composite fermions - Abstract:
- When two-dimensional electron systems are subjected to a perpendicular magnetic field, they exhibit the marvelous phenomenon known as the fractional quantum Hall effect (FQHE). This arises as a result of the formation of composite fermions (CFs), which are bound states of electrons and an even number of vortices. The FQHE of electrons is understood as arising from the integer QHE (IQHE) of CFs. Alongside superconductivity, Bose-Einstein condensation and spin-liquids, the CF quantum fluid provides a model system for understanding strongly correlated systems and their collective behavior. Although it has been more than three decades since the experimental discovery of FQHE, the field continues to produce profound insights and pose interesting problems some of which have been addressed in this thesis.\\ A major unanswered question in the field of FQHE is the mechanism of FQHE for the 1/3 state in the second Landau leve (7/3 state). Numerical studies of this state have brought out the following puzzle: exact diagonalization studies suggest that the ground state and excitations of 1/3 state in the second Landau level are different from its counterpart in the lowest Landau level (LLL), while entanglement spectra of the two states point to the fact that they fall in the same universality class. Using methods from CF theory we show that the excitations of the 7/3 FQHE lie in the same universality class as those of the 1/3 state but are strongly modified due to screening by CF excitons, thereby settling the above discrepancy. \\ Armed with the exciton calculation, we illustrate that by imposing certain exclusion rules for CF excitons one can build the full spectrum of FQHE in the lowest Landau level. Equipped with the techniques to calculate the spectra of FQHE systems, we carry out an extensive study of FQHE of multi-component CFs (systems possessing degrees of freedom for eg: valley and spin degeneracy), which is applicable to FQHE in systems such as graphene, AlAs and GaAs quantum wells. We provide a comprehensive list of the possible fractions, their ground state energies and the critical ``Zeeman'' energies for the ``spin'' transitions between the states and compare them with the experimental observations. In the lowest Landau level of graphene, we find an excellent agreement between theory and experiments. However, in the second Landau level of graphene we find an unexpected spontaneous spin polarization of CFs. We predict that there are no spin transitions to be expected in the second Landau level of graphene, a result that could be tested out in experiments. We reanalyzed some old experimental data showing excitation modes below the Zeeman energy in the vicinity of 1/3 filling of the lowest Landau level whose theoretical origin was unexplained. Using methods of exact diagonalization and CF theory we demonstrate that these modes arise as a result of formation of trions of CFs which have sub-Zeeman energy due to skyrmion-like physics.\\ In the past couple of years, the Fermi wave vector of CFs has been measured very accurately in pioneering experiments at Princeton University. Motivated by these experiments we address the issue of the validity of Luttinger's theorem (which is a fundamental tenet of Landau Fermi liquid theory) for the Fermi sea of CFs. Our calculations suggest that the CF Fermi sea may violate Luttinger's theorem slightly. This not only provides a nontrivial example of a non-Fermi liquid, but gives new insight into the nature of the CF Fermi sea state and opens a new line of inquiry in the field of FQHE.