Bulletin of the American Physical Society
APS March Meeting 2010
Volume 55, Number 2
Monday–Friday, March 15–19, 2010; Portland, Oregon
Session Y2: Composite Fermions: Recent Advances in States and Excitations |
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Sponsoring Units: DCMP APS Chair: Vito Scarola, Virginia Polytechnic Institute and State University Room: Oregon Ballroom 202 |
Friday, March 19, 2010 8:00AM - 8:36AM |
Y2.00001: Collective mode dispersions of fractional quantum Hall states Invited Speaker: The rich correlation physics in two-dimensional electron systems is governed by the dispersion of its excitations. In the fractional quantum Hall regime, excitations involve fractionally charged quasi particles and the collective modes exhibit dispersion minima at large momenta referred to as rotons. These rotons are difficult to access with conventional techniques because of the lack of penetration depth or sample volume. Our method overcomes the limitations of conventional methods and traces the dispersion of excitations across momentum space for buried systems involving small material volume. We used surface acoustic waves, launched across the 2D system, to allow incident radiation to trigger these excitations at large momenta. Optics probed their resonant absorption. Our technique unveils the full dispersion of such excitations of several prominent fractional quantum Hall ground states of the 2D electron system, which has so far been inaccessible for experimentation [1]. This work has been carried out in collaboration with I. V. Kukushkin, V. W. Scarola, V. Umansky, K. von Klitzing.\\[4pt] [1] I. V. Kukushkin, J. H. Smet, V. W. Scarola, V. Umansky, K. von Klitzing, Science 324, 1044 (2009). [Preview Abstract] |
Friday, March 19, 2010 8:36AM - 9:12AM |
Y2.00002: Collective Excitations of Composite Fermions Across Multiple $\Lambda$ Levels Invited Speaker: The collective behavior of electrons in the fractional quantum Hall states results in the creation of so-called composite fermions, quasi-particles formed by electrons attached to an even number of quantized vortices, each having one unit of flux quantum $hc/e$. This leads to formation of $\Lambda$ levels--effective kinetic energy levels resembling Landau levels for such quasi-particles. The composite fermion (CF) theory predicts collective excitations corresponding to an excitation of CF from $\Lambda =0$ level to $\Lambda =1$ level at filling factor $\nu =1/3$, with a roton minimum. A similar mode of collective excitations is also predicted in a theory based on single mode approximation (SMA) in which the excited state is the density wave modulation over the ground state. This collective mode is detected by Raman scattering and other experiments. More recently, however, Hirjibehedin {\em et. al.}\footnote{C.F.Hirjibehedin {\em et. al.}, Phys. Rev. Lett. {\bf 95}, 066803 (2005).} have discovered that this mode is not a single mode, as believed earlier, but splits into two as the wavevector is increased. By definition, the SMA cannot accommodate a doublet. We show that the observed new mode finds a natural explanation within the CF theory. We consider\footnote{D.Majumder, S.S.Mandal, and J.K.Jain, Nature Physics {\bf 5}, 403 (2009).} excitations of CF from $\Lambda =0$ level to $\Lambda =2$ and 3 levels, apart from $\Lambda =1$ level that had only been considered before for the lowest mode. By extensive numerical calculation for 200 particles, we find that these three modes of excitations tend to come closer at small wavevectors, the highest mode merges first with the middle mode as we decrease wavevector and finally the middle mode merges with the lowest mode at a very small wavevector in the thermodynamic limit. We attribute this merging at longwavelength to $100\%$ overlap between these three excited states. The observed gap between the two modes is comparable with the theoretical estimation. Further, the prediction of new roton minima in higher modes of excitations are also confirmed in a recent experiment.\footnote{T.David {\em et al.}, (in preparation).} Similar study for $\nu=2/5$ state will also be discussed and will be compared with the recent experiment.\footnote{Ibid.} [Preview Abstract] |
Friday, March 19, 2010 9:12AM - 9:48AM |
Y2.00003: Traversing the States of the Second Landau Level - loss of spin polarization away from $\nu$=3 Invited Speaker: The presence of competing liquid and solid ground states as well as intriguing quantum Hall fluids such as that at filling $\nu$=5/2 create great current interest in the partially filled N=1 Landau level. We probe the low-lying collective excitations in quantum phases of the second Landau level by resonant inelastic light scattering. Our work demonstrates that measurements of spin excitations reveal key insights on states of spin, indicating that full spin polarization is lost in the partially populated N=1 Landau level. The long wavelength spin wave mode is seen at the bare Zeeman energy in the fully spin polarized quantum Hall state at $\nu$=3. At filling factors slightly lower ($\nu$=2.97), the intensity of the spin wave mode attenuates and a broad continuum of low-lying excitations emerges. Under these conditions, sharp and broad modes coexist. While the coexistence of spectral features has not been explained, the observation could manifest the presence of mixed quantum phases and some loss of spin polarization. Further below $\nu$=3, near the odd-denominator quantum Hall state at $\nu$=8/3, the continuum dominates at low temperature. A spin wave at the Zeeman energy is not recovered, suggesting loss of spin polarization. In contrast, a well defined spin wave at the Zeeman energy occurs in the analog quantum Hall state at $\nu$=2/3 of the N=0 Landau level [1]. Near the even-denominator state at $\nu$=5/2 light scattering spectra display similar continua of low-lying excitations. At high temperatures (T$\geq$2K) a sharp spin wave is recovered while the broad continuum persists. The absence of a well defined spin wave band at the bare Zeeman energy seems to manifest tendencies towards loss of full spin polarization in the partially populated N=1 Landau level. These findings indicate that spin degrees of freedom have significant impact on the physics of competing phases with filling factors that are in the range 3$\geq\nu\geq$2. This work is in collaboration with A. Pinczuk, J. Yan, Y. Gallais, L.N. Pfeifer and K.W. West. \\[4pt] [1] Y. Gallais et al., Physical Review Letters \textbf(100) 046804 (2008) [Preview Abstract] |
Friday, March 19, 2010 9:48AM - 10:24AM |
Y2.00004: Paired Composite Fermions Invited Speaker: The physics of electrons in half-filled Landau-levels is intimately related to that of free electrons via the composite fermion transformation. Analyzing different experimental systems where half filled Landau-levels occur, we find that a pairing instability is ubiquitous. For our analysis, we construct a general family of BCS paired composite fermion wavefunctions, which can be expressed for various pairing channels, and show that these are applicable in the context of both single-layer and bilayer quantum Hall systems. In the single layer, these states generalize, but remain in the same topological phase as, the Moore-Read Pfaffian state for the half-filled Landau level. It is shown that for a wide range of experimentally relevant inter-electron interactions in the second Landau-level, the groundstate can be very accurately represented in this form [1]. Going towards the lowest-Landau-level, the composite fermion Fermi-liquid is naturally obtained as a limiting case of the same wavefunctions. In the double layer, we show that the ground-state at $\nu=1/2+1/2$ is a paired composite Fermion state at intermediate to large layer separation [2], and review how this paired phase connects to the exciton condensate at small layer separation [3].\\[0pt] [1] G. M\"oller, S. H. Simon, Phys. Rev. B {\bf 77}, 075319 (2008).\\[0pt] [2] G. M\"oller, S. H. Simon, E. H. Rezayi, Phys. Rev. Lett. {\bf 101}, 176803 (2008).\\[0pt] [3] G. M\"oller, S. H. Simon, E. H. Rezayi, Phys. Rev. B {\bf 79}, 125106 (2009). [Preview Abstract] |
Friday, March 19, 2010 10:24AM - 11:00AM |
Y2.00005: Anomalous structure in the single particle spectrum of the fractional quantum Hall effect Invited Speaker: Using a pulsed tunneling technique known as ``Time Domain Capacitance Spectroscopy,'' we obtain high fidelity and high resolution measurements of the single particle spectrum of the two-dimensional electronic system (2DES) in the fractional quantum Hall regime. The method produces spectra with precisely calibrated energy and density axes and with no observable heating of the 2DES for tunneling energies as high as 30 meV. In spectra taken as a function of both energy and density, we observe prominent, fan-like, structure emanating from filling factors $\nu=1$ and $\nu=1/2$ which appears only when the 2DES is cooled to very low temperatures. The same structure appears in spectra from different samples, but it is most pronounced in the samples with the lowest disorder and appears only in high magnetic fields. Some of the feature's energies agree qualitatively and quantitatively with what might be expected for composite fermions, which have proven effective for interpreting other experiments in this regime. At the same time, a simple model with electrons localized on ordered lattice sites (a Coulomb glass) and including exchange also generates structures that are, in some ways, similar to those observed in the experiment. However, both models predict additional structure that is not observed in the experiment, and neither is expected to be applicable across the entire range of filling fractions where we observe structure. Further work is needed to clarify which, if either, of these two models is correct at any given density, as well as to understand any possible equivalence of the two models. The dramatic and unexpected structures revealed by this measurement suggest more surprises are to come with higher resolutions and lower temperatures. [Preview Abstract] |
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