Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session W2: Progress in Understanding the Nature of the 5/2 Fractional Quantum Hall State |
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Sponsoring Units: DCMP GQI Chair: Steven Simon, Alcatel-Lucent Room: Spirit of Pittsburgh Ballroom BC |
Thursday, March 19, 2009 11:15AM - 11:51AM |
W2.00001: Finite-Layer Thickness Stabilizes the Pfaffian State for the 5/2 Fractional Quantum Hall Effect: Wave Function Overlap and Topological Degeneracy Invited Speaker: The fractional quantum Hall effect (FQHE) in the second orbital Landau level at even-denominator filling factor 5/2 remains mysterious and is currently motivating many scientists not only because of its connection to a possible implementation of a fault tolerant topological quantum computer (Das Sarma et al., PRL 94, 166802(2005)). In this work, we theoretically consider the effect of the quasi-two-dimensional nature of the experimental fractional quantum Hall systems on a number of FQHE states in the lowest three orbital Landau levels. Our primary result is that the finite width of the quasi-two-dimensional systems produce a physical environment sufficient to stabilize the Moore-Read Pfaffian state thought to describe the FQHE at filling factor 5/2. This conclusion is based on exact calculations performed in the spherical and torus geometries, studying wave function overlap and ground state degeneracy. Furthermore, our results open the possibility of creating optimal experimental systems where the 5/2 FQHE state would more likely be described by the Moore-Read Pfaffian. We also discuss the role of the three-body interaction Hamiltonian that produces the Moore-Read Pfaffian as an exact ground state and particle-hole symmetry in the FQHE at 5/2. We acknowledge support from Microsoft Project Q. Work done in collaboration with Sankar Das Sarma, Thierry Jolicoeur, and Kwon Park. [Preview Abstract] |
Thursday, March 19, 2009 11:51AM - 12:27PM |
W2.00002: Understanding the 5/2 fractional quantum Hall effect without the Pfaffian wave function Invited Speaker: The fractional quantum Hall effect (FQHE) in the second Landau level has attracted attention, because the lowest Landau level theories do not straightforwardly generalize to these states, and several of the porposed models feature excitations with non-Abelian braiding statistics, with possible applications in topological quantum computing. In particular, the FQHE states at $\nu=5/2$ and 7/2, which have no lowest Landau level analogons, are usually understood in terms of the paired composite fermion model proposed by Moore and Read. I present an alternative understanding of the 5/2 FQHE within the composite fermion theory. I argue that the residual interaction between composite fermions plays a crucial role in establishing incompressibility at 5/2. The low-energy spectrum and the activation gap are estimated with the help of a perturbative procedure that incorporates inter-composite- fermion interactions. This approach is amenable to systematic improvement, and produces ground as well as excited states. It, however, does not relate to non-Abelian statistics in any obvious manner. The emergence of incoompressiblity due to inter-composite-fermion interactions is also observed other fractions in the second Landau level, notably at $\nu=2+2/5$ and 2+3/8. [Preview Abstract] |
Thursday, March 19, 2009 12:27PM - 1:03PM |
W2.00003: Density Matrix Renormalization Group Studies of Incompressible Fractional Quantum Hall States Invited Speaker: In this talk I introduce a powerful technique, the density-matrix renormalization group (DMRG), for studying ground and excited state properties of incompressible FQH states on the sphere. This method not only reproduces the numerical results obtained earlier in the exact diagonalization studies, but we are able to extend our understanding of the ground-state and low-lying excited state properties of these FQH states to substantially larger system sizes. We address a very important open problem in fractional quantum Hall physics, namely, if the half-filled second Landau level state can exhibit non-Abelian statistics. By studying large systems on the sphere, and extrapolating to the thermodynamic limit, we determine that the ground state for this filling fraction is fully polarized for shifts corresponding to both the Moore-Read Pfaffian state and its particle-hole conjugate (anti-Pfaffian). This result is found to be robust against small variations of the interaction, strongly supporting the argument favoring a non-Abelian state. We further extend the application of this technique to identify other incompressible Hall states in the second Landau level. [Preview Abstract] |
Thursday, March 19, 2009 1:03PM - 1:39PM |
W2.00004: Intrinsic Gap of the 5/2 Fractional Quantum Hall State and Tilted Field Experiments Invited Speaker: Nearly twenty years since the first discovery of a an even denominator fractional quantum Hall state (FQHE), a complete understanding of the the 5/2-state continues to be among the most important questions in semiconductor physics. It is widely believed that this unique state of matter is theoretically best described by the Moore-Read Pfaffian wavefunction,resulting from a BCS-like pairing of composite fermions [1]. In recent years this wavefunction has received special interest owing to its non-abelian quantum statistics which underlies a new paradigm for topological (fault tolerant) quantum computation. However, in spite of several important theoretical advancements, an unequivocal experimental verification of the Moore-Read description is still missing. We present results from a study of the 5/2 state in a sample with the lowest electron density reported to date (by nearly a factor of two) [2]. This allows for the observation of the 5/2 in a regime where the cyclotron energy is smaller than the Coulomb interaction energy. We discuss our results in the context of previous work, and we examine the role of disorder on the activation energy gap. Measurements of the energy gap for the 5/2 and the 7/3 FQH states in a tilted field geometry also reveals an unexpected and contrasting dichotomy between the two. Whereas the 7/3 FQH gap is observed to be enhanced by an applied parallel magnetic field, the 5/2 gap is strongly suppressed, in spite of the two gaps being energetically comparable at zero parallel fields in our sample. This calls into question the prevailing theoretical belief that they should behave similarly if both are spin-polarized, and raises doubt as to whether or not the 5/2 state is indeed described by a spin-polarized Pfaffian Moore-Read wavefunction. \\[4pt] [1] G. Moore and N. Read, Nucl. Phys. B 360, 362 (1991).\\[0pt] [2] C.R. Dean, B.A. Piot, P. Hayden, S. Das Sarma, G. Gervais, L.N. Pfeiffer, K.W. West, Phys. Rev. Lett. 100, 146803 (2008).\\[0pt] [3] C.R. Dean, B.A. Piot, P. Hayden, S. Das Sarma, G. Gervais, L.N. Pfeiffer, K.W. West, Phys. Rev. Lett. 101, 186806 (2008). [Preview Abstract] |
Thursday, March 19, 2009 1:39PM - 2:15PM |
W2.00005: Observations of Low-lying Collective Excitations in Quantum Phases of the Second Landau Level Invited Speaker: Astonishing quantum phases emerge in partially populated higher Landau levels of 2D electron systems. There are even-denominator fractional quantum Hall fluids in the second (N=1) Landau level, and quantum Hall phases that mingle and compete with alternate ground states. Such findings are striking manifestations of novel collective states that emerge from fundamental interactions in 2D. This talk considers results of inelastic light scattering studies of low-lying excitation modes of quasiparticles in these quantum Hall regimes. Experiments in the states of the lowest (N=0) Landau level uncover interplay from interactions in the spin and charge degrees of freedom and the impact of spin textures is clearly seen in spectra of low-lying spin excitations [1,2]. More recent work, explores excitations of the quantum Hall fluids that reside in the N=1 Landau level [3]. These experiments discovered the intriguing collapse of the long wavelength ferromagnetic spin wave for filling factors that are slightly below filling factor nu=3. While the collapse of the spin wave at fillings near nu=1had been linked to loss of spin polarization due to formation of spin textures, the low-lying excitation modes seen in the N=1 level below nu=3 seem much more complex because a sharp spin wave does not recover for fractional quantum Hall states such as nu=8/3 and 5/2. These measurements suggest significant roles for quasiparticle spin in the competing quantum phases that emerge in the second Landau level. This work is a collaboration with T. D. Rhone, J. Yan, Y. Gallais, I. Dujovne, C. Hirjibehedin, J. Groshaus, B.S. Dennis, L.N. Pfeiffer and K.W. West. \\[4pt] [1] J. Groshaus et al., Physical Review Letters 100, 086806 (2008). \\[0pt] [2] Y. Gallais et al., Physical Review Letters 100, 046804 (2008). \\[0pt] [3] T.D. Rhone et al., contributed talk at this meeting. [Preview Abstract] |
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