Recent Progress on Three Longstanding Puzzles in Fractional Quantum Hall Effect

by Jainendra K. Jain (Penn State University)

Tuesday 12 Nov 2013, 11:00 → 12:00 Europe/Stockholm

Nordita West (122:026)

I will begin with an introduction, meant for non-experts, to the composite fermion theory of the fractional quantum Hall effect. In the remainder of the talk, I will report on our recent progress on three outstanding puzzles: (i) An insulating state had been observed in between 1/5 and 2/9 liquids two decades ago. I will describe our recent work [1] that gives convincing arguments that this re-entrant insulator is a crystal of composite fermions, and also predicts a rich phase diagram of crystal phases at low fillings. (ii) We have made a convincing case [2] that an observation of fully spin polarized fractional quantum Hall effect at 4/11 will represent a new kind of fractional quantum Hall effect of composite fermions. We predict that the 4/11 state observed a decade ago is partially spin polarized, and predict the critical Zeeman energy where a transition into a fully spin polarized state will occur. (iii) It has been known for almost two decades that the model of weakly interacting composite fermions predicts too many states in the excited bands. We have shown [3] that a model of interacting composite fermions can be constructed that produces an excellent description of the excited states as well, thus extending the range of validity of the composite fermion theory. [1] "Competing Crystal Phases in the Lowest Landau Level," A. C. Archer, K. Park, J. K. Jain, PRL 111, 146804 (2013). [2] "The Enigmatic 4/11 State: A Prototype for Unconventional Fractional Quantum Hall Effect," S. Mukherjee, S. S. Mandal, Y.H. Wu, A. Wojs, and J. K. Jain, preprint. [3] "Theory of Excitations of the Fractional Quantum Hall Effect: Exclusion Rules for Bound Excitons," A. C. Balram, A. Wojs, and J. K. Jain, preprint.