Theory of Novel Excitations in the Fractional Quantum Hall Effect

TECHNICAL SUMMARY

This award supports theoretical research on the excitations of the fractional quantum Hall effect state. While definite progress has been made toward clarifying the physics of some of the excitations of the fractional quantum Hall effect state, many important issues remain unexplored. Employing a combination of numerical tools, such as exact diagonalization and quantum Monte Carlo techniques, and analytical approaches, including effective Chern Simons field theory, bosonization, and conformal field theory, the PI aims to address the following questions:

(1) Does the fractional quantum Hall effect spectrum contain new magneto-roton collective modes at higher energies? If so, how will they manifest in inelastic light scattering or optical absorption experiments?

(2) Do composite fermions generically form pairs in the lowest Landau level, and if so, how can they be observed?

(3) How does an externally injected electron couple into high energy excitations of the fractional quantum Hall state? How many higher Landau-like levels of composite fermions are real? What is the nature of the neutral and charged excitations in higher electronic Landau levels? How does the spin degree of freedom alter the nature of excitations?

(4) How are the fractional quantum Hall effect excitations affected by an anisotropy in the interaction?

(5) What is the microscopic description of the edge excitations of more complex states, such as 2/5, and how does it compare to the predictions of the effective theory?

The PI will work closely with experimental groups. The graduate students supported by this grant will receive a broad training ranging from massively parallel numerical computations to semiconductor physics to quantum field theory. The PI and his student will also devote a portion of their time in conveying the excitement of various physical phenomena and concepts in two dimensions to school students at all levels, with hands-on activities including various possible crystal structures in two dimensions, two dimensional models of gravity, and interference of waves in two dimensions. These will be combined to form an educational module entitled 'Fun with Physics in Flatland', to be incorporated into existing educational and outreach programs at Penn State.

NON-TECHNICAL SUMMARY

This award supports theoretical study of collective quantum states of matter known as the fractional quantum Hall effect. These emerge when electrons confined to two dimensions are exposed to a strong magnetic field. This study will focus on excited states and their energies which are largely unexplored. Experimental efforts are beginning to investigate these excited states in hitherto inaccessible regimes. In this context, the PI's research is poised to make timely contributions to the interpretation of experiments. Employing a combination of numerical and analytical tools, the PI aims to investigate specific theoretical questions; some are related to predictions of new electronic states of matter in quantum Hall systems that might form the basis for a new high performance computer that exploits the manipulation of quantum mechanical states for its operation.

During the course of this research, the PI will work closely with experimental groups. Graduate students supported by this award will receive a broad training ranging from computation to advanced analytical theoretical methods. The PI and his student will also devote a portion of their time in conveying the excitement of various physical phenomena and concepts in two dimensions to school students at all levels, with hands-on activities including various possible crystal structures in two dimensions, two dimensional models of gravity, and interference of waves in two dimensions. These will be combined to form an educational module entitled 'Fun with Physics in Flatland', to be incorporated into existing educational and outreach programs at Penn State.