Session A3: Invited Session: Second Landau Level: Quantum Phases

Evidence of low-lying gapped excitations in the $\nu =$5/2 quantum fluid

The competition between quantum phases that dictate the physics in the second Landau level (SLL) results in striking phenomena. A highly fascinating state is the even denominator fractional quantum Hall (FQHE) state at filling $\nu =$5/2 that is widely believed to support non-Abelian quasi-particle excitations. Our work explores the low-lying neutral excitation modes in the SLL by resonant inelastic light scattering measurements. At 5/2 the spectra revealed a band of gapped modes with peak intensity at energy of 0.07meV. These modes are interpreted as a roton minimum in the wave vector dispersion of spin-conserving excitations. The intensity of the roton band significantly diminishes by increasing the temperature to 250mK and it fully collapses for T\textgreater\ 250mK. This temperature dependence is consistent with activated magneto-transport of the incompressible quantum fluid at 5/2. A long wavelength spin wave mode (SW) is seen at the bare Zeeman energy, indicating that there is non-zero spin-polarization. Both, roton and SW modes appear only in a very narrow filling factor range of less than $\nu $\textless\ 5/2 $\pm$ 0.01. A gapless continuum of low-lying excitations emerges at filling factors slightly away from 5/2. This demonstrates a transition from an incompressible quantum Hall fluid at exactly $\nu =$5/2 to compressible states at very close filling factors. This work is in collaboration with A. Pinczuk, A. Levy, K. West, L. Pfeiffer, S. Mondal, J. Watson and M. Manfra.   

Spin transition in the second Landau level

The fractional quantum Hall effect (FQHE) states in the second Landau level have attracted growing interest and intensive theoretical and experimental investigations due to their being non-Abelian states. Recently, we systematically examined the spin polarization of the 8/3 and 12/5 states in a series of high quality two dimensional electron systems. Evidence of spin transition was observed for both states, suggesting a more complicated nature of the FQHE ground states in the second Landau level.   

Quantum Hall Interferometry and Detection of Anyonic Braiding Statistics

In two spatial dimensions quantum mechanical particles are not limited to being bosons or fermions as they are in three dimensions, but can be particles known as anyons. Such anyons come in two major varieties --- Abelian and non-Abelian --- both of which were long ago predicted to be realized in certain Fractional Quantum Hall (FQH) systems. However, experimental demonstration of anyonic braiding properties has remained elusive and very controversial. New results by Willett et. al. and Kang et. al. have been interpreted as evidence of anyonic braiding in Fabry Perot interferometers in the second Landau level. In this talk, I will discuss my current understanding of these works based on a number of recent publications.\\[4pt] References:\\[0pt] [1] arXiv:1112.3400, Braiding of Abelian and Non-Abelian Anyons in the Fractional Quantum Hall Effect, Sanghun An, P. Jiang, H. Choi, W. Kang, S. H. Simon, L. N. Pfeiffer, K. W. West, K. W. Baldwin\\[0pt] [2] Physical Review B 85, 201302, 2012, Telegraph noise and the Fabry-Perot quantum Hall interferometer, Bernd Rosenow, Steven H. Simon   

Quantifying disorder and its impact in the 2$^{\mathrm{nd}}$ Landau level

Strong electronic correlations are evident in the 2$^{\mathrm{nd}}$ Landau level (LL) of an ultra-high quality GaAs/AlGaAs two-dimensional electron gas (2DEG). The exotic fractional quantum Hall states at filling factors $\nu =$5/2 and 12/5, as well as the reentrant integer quantum Hall states flanking half-filling, are a few examples presently under intense investigation. While it is generally accepted that samples must be of extremely low disorder to exhibit correlations in the 2$^{\mathrm{nd}}$ LL, our understanding of how to quantify residual disorder and its impact on the states of interest remains primitive. In this talk we will critically examine how disorder is quantified for the 2DEG both at zero magnetic field and in the quantum Hall regime, and then compare the results of this analysis with measurements of the excitation gap at $\nu =$5/2 in samples in which disorder is varied in a well-defined manner. Our results highlight the very different impact on the excitation gap generated by different types of disorder and the limitations of presently employed characterization methods.   

Role of inter-composite fermion interactions in fractional quantum Hall effect

One of the important challenges in the field of the fractional quantum Hall effect (FQHE) is to understand the nature of states that cannot be explained as integer quantum Hall effect of weakly interacting composite fermions; such states include FQHE at 5/2, 7/3, 8/3, 12/5, 13/5, 19/8 in the second Landau level (of GaAs) and 4/11, 5/13, 3/8(?) in the lowest Landau level. I will report on results [1,2] that demonstrate that multipartite wave functions of composite fermions provide an excellent account of the low energy physics of the model 3-body and 4-body interaction Hamiltonians that have the Pfaffian and the Read-Rezayi wave functions as their exact ground states. The relevance of these wave functions to the Coulomb solutions at 5/2 and 13/5 is investigated through an adiabatic scheme connecting the two models. In particular, the multipartite wave functions are shown to shed light on the structure of the neutral and charged excitations and of unpaired composite fermions [1]. We find that the residual interaction between composite fermions also has substantial effect at certain other fractions; it is predicted to produce a paired FQHE of the anti-Pfaffian kind at 3/8 [3], and unconventional trion excitations at 7/3 [4].\\[4pt] [1] G. J. Sreejith, C. Toke, A. Wojs and J.K. Jain, PRL 107, 136802 (2011).\\[0pt] [2] G. J. Sreejith, Y.-H. Wu, A. Wojs and J.K. Jain, unpublished.\\[0pt] [3] S. Mukherjee, S. S. Mandal, A. Wojs, J.K. Jain, unpublished.\\[0pt] [4] A. C. Balram, Y.-H. Wu, G. J. Sreejith, A. Wojs, J. K. Jain, unpublished.