Hamiltonian Theory of Fractionally Filled Chern Bands, and Disorder in Quantum Hall Antiferromagnets

Grants and Contracts Details


It has recently been realized that the fractional quantum Hall effect seen in low- density two-dimensional electron gases in semiconductors is a special case of a more general phenomenon: Strongly correlated states in a fractionally filled Chern band, that is, a band with a nontrivial band topology. At the same time, quantum Hall systems with internal symmetries such as spin, layer, or valley symmetries, exhibit a profound sensitivity to disorder, which can have nonper- turbative effects on their physical properties. Intellectual Merit: The research proposed here will investigate fractionally filled Chern bands by an exact mapping to composite fermion variables recently found by the PI and R. Shankar. This is an analytical, though approximate method. As such it of- fers some advantages over the numerical methods which have hitherto been used to find fractional-quantum Hall like states in Chern bands. Our approach is operator-based (un- like wavefunction approaches), is applicable in the thermodynamic limit (unlike numerics), and can be used to compute response functions and the response to disorder (prohibitive in numerics). Furthermore, it can be used to explore compressible states (analogues of the half-filled Landau level), and incompressible states without analogue in the semiconductor systems. The research proposed here will also extend the work of the PI and H. A. Fertig in the bilayer = 1 quantum Hall state to other such states with internal symmetries, which all have low-energy charged excitations which are topological. This leads to a nonperturbative reorganization of the ground state under the influence of disorder, leading to a series of ground state phase transitions as the strength of the disorder increases, the emergence of new collective modes (observable by inelastic light scattering and nuclear magnetic resonance) and new mechanisms of transport. Broader Impacts: The PI is a co-organizer of what is envisaged to be a series of Winter Schools in India. One of them has already taken place and the next is planned to occur in 2014. In a separate initiative, the PI has been engaged for some time in the reorganization of the University Honors Program. In the current system, faculty members from many disciplines are encouraged to come together to create “constellations” of courses which explore a single theme from many different perspectives. The PI is part of such a group which is engaged in creating a constellation based on the theme of Time. The physics angle will emphasize the age of the universe, the arrow of time, the complementarity between energy and time, and relativity. The mathematics angle would focus on predictability in classical mechanics/chaos. The chemistry/biology angle will focus on the time-scales of evolution on the large scale, circadian rhythms on the medium scale, and the rate of molecular reactions that make up the life of a cell on the small scale. The psychology angle would examine our perception of time. The third long-term committment the PI has is to man a booth at the Aspen Center for Physics during the kids barbecue, held every week during the summers. Last but not least, the education of a graduate student and the mentoring of a postdoc will form an integral part of the proposed project.
Effective start/end date8/1/141/31/19


  • National Science Foundation: $270,000.00


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