## Grants and Contracts Details

### Description

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.

Status | Finished |
---|---|

Effective start/end date | 8/1/14 → 1/31/19 |

### Funding

- National Science Foundation: $270,000.00

## Fingerprint

Explore the research topics touched on by this project. These labels are generated based on the underlying awards/grants. Together they form a unique fingerprint.