Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session S40: Fractional Quantum Hall Effect |
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Sponsoring Units: FIAP Chair: Wei Pan, Sandia National Laboratories Room: Colorado Convention Center 503 |
Wednesday, March 7, 2007 2:30PM - 2:42PM |
S40.00001: Probing phase separation in the fractional quantum Hall fluid at $\nu = 1/3$ Javier Groshaus, Irene Dujovne, Yann Gallais, Cyrus Hirjibehedin, Aron Pinczuk, Brian Dennis, Loren Pfeiffer, Ken West We report on measurements of low lying collective excitation modes in the fractional quantum Hall (FQH) fluid at $\nu = 1/3$ by resonant inelastic light scattering. While observations of long wavelength modes provide the signature of the presence of the incompressible quantum fluid, evidence of non-uniform fluids in light scattering spectra is found in the observation of magneto-roton modes that require breakdown of wave vector conservation due to loss of translation symmetry. In the energy range of magneto-rotons there are two excitation modes at slightly different energy. One of the modes is clearly identified with the incompressible phase. To interpret the other one we conjecture that due to weak residual-disorder compressible phases coexist with the incompressible phase at $\nu = 1/3$. Within this picture the second magneto-roton is associated with the compressible phases that coexist with the Laughlin fluid. The experimental studies reported here probe non- uniformity in the fluids and offer insights into excitations and mechanisms that are linked to activated transport in the FQH regime. [Preview Abstract] |
Wednesday, March 7, 2007 2:42PM - 2:54PM |
S40.00002: Valley Susceptibility Measurements of Composite Fermions around Filling Factor $\nu$ = 3/2 Nathaniel Bishop, Medini Padmanabhan, Kamran Vakili, Yakov Shkolnikov, Etienne De Poortere, Mansour Shayegan In the composite fermion (CF) picture, the fractional quantum Hall (FQH) states are simply the integer quantum Hall states of the particle-flux CF quasiparticles. We report magnetotransport measurements of FQH states in an AlAs quantum well around Landau level filling factor $\nu$ = 3/2, demonstrating that the carriers are CFs with a valley degree of freedom. By observing valley level crossings for these FQH states as a function of applied symmetry breaking strain, we determine the CF valley susceptibility, defined as the change of CF valley polarization with strain. The results can be explained well by a simple Landau level fan diagram for CFs. The measured valley susceptibility for CFs is found to be significantly enhanced over that measured for electrons in this system,\footnote{O. Gunawan et al, Phys. Rev. Lett. 97, 186404 (2006)} and comparable to earlier measurements of the spin susceptibility in GaAs heterostructures.\footnote{R. R. Du et al, Phys. Rev. Lett. 75, 3926 (1995)} [Preview Abstract] |
Wednesday, March 7, 2007 2:54PM - 3:06PM |
S40.00003: Gap and mass measurements of composite fermions at $\nu$=5/3 in a 2D electron system with tunable valley occupation Medini Padmanabhan, Nathaniel Bishop, Yakov Shkolnikov, Etienne De Poortere, Mansour Shayegan In the composite fermion (CF) picture, the fractional quantum Hall state appearing at the filling factor of 5/3 is analogous to the integer quantum Hall state at $\nu$=1. We report energy gap measurements at $\nu$=5/3 in AlAs quantum wells which reveal a persistent gap even when the two anisotropic in-plane valleys are degenerate. This is reminiscent of the finite gap for the integer quantum effect for electron systems at $\nu$=1 in the g*=0 limit. As a symmetry breaking strain is controllably applied to the system, we observe a linear increase of gap followed by saturation, both of which are qualitatively consistent with a simple CF fan diagram. We also report mass measurements for the same state which suggest a mass enhancement for CFs by a factor of three over the electron band mass at a magnetic field of about 15T. [Preview Abstract] |
Wednesday, March 7, 2007 3:06PM - 3:18PM |
S40.00004: Localized quasielectrons in fractional quantum Hall states Hans Hansson, Maria Hermanns, Susanne Viefers We show that fractional quantum Hall states with localized quasielectrons (as opposed to quasiholes) can be obtained, within the framework of conformal field theory, as a correlator of electron operators and a novel kind of nonlocal operators. Our construction facilitates the calculation of Berry phases, and can be generalized to non-Abelian QH states. [Preview Abstract] |
Wednesday, March 7, 2007 3:18PM - 3:30PM |
S40.00005: Numerical test of bosonization of the 1/3 FQHE edge Shivakumar Jolad, Chia-Chen Chang, Jainendra Jain We report on numerical tests of Wen's conjecture expressing the fermionic field operator in terms of the bosonic edge excitations for the edge of the 1/3 FQHE state. Our studies extend the previous work of Palacios and MacDonald [1], wherein they identify the boson excitations to Stone operators [2], to larger systems and obtain more accurate thermodynamic limits for various matrix elements for the hard-core interaction. We also study the excitations using the Coulomb ground state, available for up to 9 electrons. A combination of exact diagonalization and Monte Carlo method is used to study systems containing up to 40 particles. The results are in agreement with those in Ref. [1] for small systems, but offer insight into the detailed approach to the thermodynamic limit and the effect of interaction on the results. \newline \newline [1] J. J. Palacios and A.H. MacDonald, PRL 76, 119 (1996). \newline [2] M. Stone, PRB 42, 8399 (1990) [Preview Abstract] |
Wednesday, March 7, 2007 3:30PM - 3:42PM |
S40.00006: Pinning mode of 2D electron stripe phase around 9/2 Landau level filling G. Sambandamurthy, R.M. Lewis, H. Zhu, Y.P. Chen, L.W. Engel, D.C. Tsui, L.N. Pfeiffer, K.W. West We present finite frequency conductivity measurements on ultra high mobility two-dimensional electron systems in GaAs/AlGaAs. At low temperature $T\leq 150$ mK, strong anisotropy of the DC resistivities [1] for higher Landau levels (LL) near half filling is present, and is taken to be due to a striped phase, in which the charge density is anisotropically modulated. In our AC studies, we observe a sharp resonance at $f_{pk}\approx 100 $ MHz in the real part of the diagonal conductivity, in range of LL filling $\nu$ between 4.4 and 4.6, when the AC electric field is polarized along the ``hard" direction, nominally perpendicular to the stripes. The resonance vanishes for $T\geq$ 120 mK. No resonance is observed with the electric field along the easy direction, parallel to the stripes. Resonances are present [2] in both orientations, in the bubble phases found at higher and lower $\nu $ than the stripe phase.\\ 1. M. P. Lilly {\em et al.}, Phys. Rev. Lett. {\bf 82,} 394 (1999);\\ R. R. Du {\em et al.}, Solid State Comm. {\bf 109}, 389 (1999).\\ 2. R. M. Lewis {\em et al.}, Phys. Rev. Lett. {\bf 89}, 136804 (2002). [Preview Abstract] |
Wednesday, March 7, 2007 3:42PM - 3:54PM |
S40.00007: RF resonance of two dimensional electron systems in higher Landau levels: Effect of in-plane magnetic fields H. Zhu, G. Sambandamurthy, L. Engel, D. C. Tsui, L. Pfeiffer, K. West We report measurements of the RF diagonal conductivity, Re$[\sigma _{xx} (f)]$, of ultrahigh mobility 2D electron systems with Landau level (LL) filling factor $4<\nu <6$, in the presence of an in-plane magnetic field, $B_{//}$. For nearly half integer filled higher LL's, such samples are thought to show electron stripe phases, which can be reoriented by application of $B_{//}$ [1,2]. With $B_{//} =0$, and $\nu \approx$ 9/2 and 11/2, a resonance around 100 MHz is observed when the microwave electric field $E_{m}$ is along $<1\bar{1}0>$, nominally perpendicular to the stripes, but no resonance is seen when $E_{m}$ is along $<110>$ [3]. $B_{//}$ can switch the resonance on and off depending on the orientations of $B_{//}$ and $E_{m}$ relative to the crystal. However, in the presence of $B_{//}$, a simple comparison with the DC results [1,2] is not possible, since the resonance can be present even for $E_{m}$ along lower DC resistivity direction, which would be thought to be parallel to the stripes. For example, around $6^{o}$ tilting of the magnetic field along $<1\bar{1}0>$, $B_{//} \approx$ 0.28 T, resonances are observed with $E_{m}$ along both orientations. [1] W. Pan {\it et al}., PRL {\bf 83}, 820 (1999). [2] M. P. Lily {\it et al}., PRL {\bf 83}, 824 (1999). [3] G. Sambandamurthy {\it et al}., this conference. [Preview Abstract] |
Wednesday, March 7, 2007 3:54PM - 4:06PM |
S40.00008: Variational studies of nematic phase of half-filled Landau level 2 dimensional electron gas (2DEG) system Quoc Doan, Efstratios Manousakis We study the ground state of a nematic phase of the 2DEG at filling fraction $\nu = 1/2$. The pair distribution function and the interaction energy are calculated using a variational wavefunction having Jastrow pair-correlations of the form $\Pi_ {i < j}(z_i-z_j)^2$ and an elliptical Fermi surface. The ratio between the major and minor axes of the ellipse is used as the broken symmetry parameter. First we used the Fermi hypernetted chain (FHNC/0) approximation and we find that for strong enough magnetic field and below a critical value of the broken symmetry parameter the nematic phase is energetically favorable. We find that the nematic phase can be realized when the energy difference between the nematic and the symmetric phase are of the same order of magnitude to the characteristic temperature below which the anisotropic transport in 2DEG was observed. Furthermore, the Monte Carlo (MC) method was used to calculate the energy and the pair distribution function using the same wavefunction in order to verify the accuracy of these results. The comparison of the results obtained with FHNC/0 and MC will be presented at the meeting. [Preview Abstract] |
Wednesday, March 7, 2007 4:06PM - 4:18PM |
S40.00009: Short-range disorder induced RIQHE in the lowest Landau level Wanli Li, D. R. Luhman, D. C. Tsui, L. N. Pfeiffer, K. W. West We have studied the magneto-transport of two dimensional electron systems with various amount of short-range alloy disorder. Our samples are Al$_x$Ga$_{1-x}$As-Al$_{0.32}$Ga$_ {0.68}$As heterostructures with the Al concentration $x$ ranging from 0 to 0.85\%, and the electron mobility varies from 1.2$\times $10$^7$cm$^2$/V.s down to 8.9$\times $10$^5$cm$^2 $/V.s within this $x$ range. We have two major observations in the high magnetic field regime. First, we have found that the amplitude of the fractional quantum Hall gaps is independent on $x$. Second, and more surprisingly, we have observed a $\nu $=1 reentrant integer quantum Hall effect (RIQHE) between the Landau level filling factor $\nu $=2/3 and $\nu $=3/5 in the sample with $x$=0.85\%. Between the quantum Hall Plateaus of $\nu $=2/3 and $\nu $=3/5, the Hall resistance is observed to be quantized to $h/e^2$ while the longitudinal resistance reaches a deep minimum. [Preview Abstract] |
Wednesday, March 7, 2007 4:18PM - 4:30PM |
S40.00010: New structures in graphene FQHE Csaba Toke, Paul Lammert, Vincent Crespi, Jainendra Jain We explore how the specific properties of graphene - valley degeneracy and linear dispersion of low-energy carriers - affect the fractional quantum Hall effect. We consider the SU(2) and SU(4) limits, which are relevant depending on whether the Zeeman splitting is large or small. In the former limit interaction-induced integral plateaus, large pseudoskyrmions, fractional sequences, even/odd numerator effects, composite-fermion pseudoskyrmions, and a pseudospin-singlet composite-fermion Fermi sea are expected to occur. While the lowest graphene Landau level is formally equivalent to the lowest GaAs Landau level with zero Zeeman splitting, it is predicted that the second Landau level of graphene shows more robust fractional quantum Hall effect than the second Landau level of GaAs. In the SU(4) symmetric limit new composite fermions states become possible without analog in GaAs; these involve an essential interplay between the spin and valley degeneracies. The structure of these states, their excitations, and their experimental consequences will be described. A composite fermion Fermi sea with an SU(2)xSU(2) symmetry is predicted at certain even denominator filling factors. [Preview Abstract] |
Wednesday, March 7, 2007 4:30PM - 4:42PM |
S40.00011: A new collective mode in the fractional quantum Hall liquid Giovanni Vignale, Ilya Tokatly We apply the methods of continuum mechanics to the study of the collective modes of the fractional quantum Hall liquid. Our main result is that at long wavelength there are {\it two} distinct modes of oscillations, while previous theories predicted only {\it one}. The two modes are shown to arise from the internal dynamics of shear stresses created by the Coulomb interaction in the liquid. Our prediction is supported by recent light scattering experiments, which report the observation of two long-wavelength modes in a quantum Hall liquid. [Preview Abstract] |
Wednesday, March 7, 2007 4:42PM - 4:54PM |
S40.00012: Interpretation of quantum Hall effect from angular momentum theory and Dirac equation. Keshav Shrivastava It is found that when suitable modifications to the g values are made, the effective charge of a particle is determined by e$_{eff}$ =(1/2)ge, which enters in the Dirac equation to yield the fractional charges. The calculated values of the fractional charges agree with the data on fractional charge deduced from the quantum Hall effect. Therefore, the Dirac equation can accommodate not only particles of charges 0 and $\pm $ 1 but also fractional charges such as 1/3 and 2/3. This means that spin and charge get coupled. There are two g values for two signs of the spin. Hence 4 eigen values emerge, two for positive spin and two for negative spin. Therefore a 4x4 matrix has to be added to the eigen value E in the Dirac equation. This matrix has interesting anticommuting properties. K. N. Shrivastava, Phys. Lett. A 113,435-6(1986);115, 459(1986)(E). K. N. Shrivastava, Phys. Lett. A 326, 469-472(2004) K. N. Shrivastava, Mod. Phys. Lett. B 13, 1087-1090(1999); 14, 1009-1013(2000). [Preview Abstract] |
Wednesday, March 7, 2007 4:54PM - 5:06PM |
S40.00013: A simple view on the quantum Hall system Emil J. Bergholtz, Anders Karlhede The physics of the quantum Hall system becomes very simple on a thin torus. Remarkably, however, the rich structure of the system still exists in this limit. On the very thin torus the many body problem reduces to a one-dimensional classical electrostatic problem and both the abelian and the non-abelian quantum Hall states are manifested as gapped one-dimensional crystals, Tao-Thouless states, with fractionally charged excitations that appear as domain walls between degenerate ground states. These states represent, but are extreme forms of, the observed states in the bulk and their qualitative properties (such as quasiparticle degeneracies, quantum numbers, relative size of the gaps etc.) remain the same. For the gapless states, there is a phase transition at finite thickness to phases different from the gapped crystals. At half-filling in the lowest Landau level, this new phase is a Luttinger liquid of neutral dipoles which is adiabatically connected to the gapless state observed in the bulk. The existence of the gapless phase on the thin (but finite) torus provides an explicit microscopic example of how weakly interacting quasiparticles moving in a reduced (zero) magnetic field emerge as the low energy sector of strongly interacting electrons in a strong magnetic field. [Preview Abstract] |
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