Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session C42: Quantum Hall Effect: Materials, Geometries, & nu = 2 |
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Sponsoring Units: FIAP Chair: Michael Zudov, University of Minnesota Room: Hilton Baltimore Holiday Ballroom 3 |
Monday, March 18, 2013 2:30PM - 2:42PM |
C42.00001: Very Narrow Intersubband Excitations in High Mobility 2DESs Ursula Wurstbauer, Aron Pinczuk, John Watson, Sumit Mondal, Michael J. Manfra, Ken W. West, Loren N. Pfeiffer We report the observation of very narrow collective intersubband excitations (ISBE) of 2D electron systems (2DESs) with ultra-high mobility ($\mu \ge $15x10$^{\mathrm{6}}$ cm$^{\mathrm{2}}$/Vs) in high quality GaAs quantum structures. These findings from resonant inelastic light scattering (RILS) experiments are used as tools for exploration of links between transport mobility and collective electron behavior in 2DES of high perfection. We find that the line-widths of collective ISB modes can be as low as 80$\mu $eV. Comparison of ISBE measurements from several samples exhibits a variation in line-width of more than a factor of two. There is, however, a surprising lack of direct correlation between ISBE line-width with mobility in the range 15$\ge \mu \ge $24x10$^{\mathrm{6}}$ cm$^{\mathrm{2}}$/Vs. Measurements of ISBE by RILS will be evaluated as a method to explore the interplay of quality (as indicated by mobility) and fundamental interactions in the fractional quantum Hall effect. [Preview Abstract] |
Monday, March 18, 2013 2:42PM - 2:54PM |
C42.00002: Growth of high mobility, in-situ back-gated two-dimensional electron gases in GaAs/AlGaAs quantum wells John Watson, Sumit Mondal, Michael Manfra Investigations of the energy scales of many-body phenomena in high mobility two-dimensional electron gases (2DEGs) often require the ability to tune the electron density in a single device. Electrostatic gating is often the method of choice, but traditional device designs are less than ideal. The 2DEG density in top-gated devices is often hysteretic and/or unstable over time due to intervening doping layers, and traditional back-gates applied to mechanically thinned substrates typically require large gate voltages ($\sim$ 100 V) to achieve significant modulation of the electron density due to the large gate-channel separation ($\sim$ 150 $\mu $m). We report on the growth of a series of high mobility 2DEGs in 30 nm GaAs/AlGaAs quantum wells in which the density is modulated by an in-situ grown back-gate. Such in-situ gates can be grown close to the 2DEG ($\sim$ 1 $\mu $m) and without doping layers between the 2DEG and gate. We discuss heterostructure design parameters and device processing conditions leading to low gate leakage currents, low ohmic contact resistances, and high electron mobilities (10$^{7}$ cm$^{2}$/Vs) at low temperature (T $=$ 300 mK). [Preview Abstract] |
Monday, March 18, 2013 2:54PM - 3:06PM |
C42.00003: Anisotropic Fermi Contour of (001) GaAs Holes in Parallel Magnetic Fields Dobromir Kamburov, Mansour Shayegan, Loren Pfeiffer, Kenneth West, Kirk Baldwin, Roland Winkler We demonstrate tuning the dispersion anisotropy in a high-mobility (001) GaAs two-dimensional hole system through the application of an in-plane magnetic field. We employ surface-strain-induced commensurability oscillations to probe directly the anisotropy and the size of the Fermi contours. The experimental data are in semi-quantitative agreement with the results of a parameter-free energy band model. We find a severe spin-dependent anisotropy of the 2D hole Fermi contours stemming from the combined effect of the strong coupling of the parallel field to the orbital motion, the large spin-orbit interaction in the GaAs valence band, and heavy hole-light-hole coupling. [Preview Abstract] |
Monday, March 18, 2013 3:06PM - 3:18PM |
C42.00004: Anisotropic Fermi Contour of Composite Fermions in Tilted Magnetic Fields Mansour Shayegan, Dobromir Kamburov, Yang Liu, M.A. Mueed, Sukret Hasdemir, Loren Pfeiffer, Kenneth West, Kirk Baldwin We employ surface-strain-induced commensurability oscillations of hole-flux composite fermions to study the effect of parallel magnetic field on their Fermi contours in high-quality C-doped (001) GaAs hole quantum wells. Our measurements reveal that the composite fermion Fermi contours are significantly distorted in the presence of parallel field. Along the direction of the parallel field, the Fermi wave vectors shrink while in the perpendicular direction they grow, and at 25 T parallel field, the relative distortion reaches 50{\%}. [Preview Abstract] |
Monday, March 18, 2013 3:18PM - 3:30PM |
C42.00005: Unconventional Quantum Hall Effect and Tunable Spin Hall Effect in monolayer ${\rm MoS_2}$ Xiao Li, Fan Zhang, Qian Niu We analyze the Landau level (LL) structure in a monolayer ${\rm MoS_2}$ and find a field-dependent unconventional quantum Hall plateau sequence $\nu=\cdots$ $-2M-6$, $-2M-4$, $-2M-2$, $-2M-1$, $\cdots$, $-5$, $-3$, $-1$, $0$, $2$, $4$ $\cdots$. Due to orbital asymmetry, the low-energy Dirac fermions become heavily massive and the LL energies grow linearly with $B$, rather than with $\sqrt{B}$. Spin-orbital couplings break spin and valley degenerate LL's into two distinct groups, and LL crossing effects appear in the valence bands only. In a p-n junction, spin-resolved fractionally quantized conductance appears in two-terminal measurements with a controllable spin-polarized current that can be probed at the interface. We also show that the zero-field spin Hall conductivity has some interesting tunability. For more information, please refer to arXiv: 1207.1205. [Preview Abstract] |
Monday, March 18, 2013 3:30PM - 3:42PM |
C42.00006: Landau level crossing and enhanced g-factor of a 2-dimentional hole gas in Ge/SiGe quantum well Rai Moriya, Yusuke Hoshi, Yoshihisa Inoue, Satoru Masubuchi, Kentaro Sawano, Yasuhiro Shiraki, Noritaka Usami, Tomoki Machida Strained Ge has been received much attention due to its small effective mass and large hole mobility. Moreover, two-dimetional hole gas (2DHG) provide additional band-structure effects such as mixing and non-parabolicity, thus makes this system fascinating for studying quantum transport. On the other hand, the detail study on the quantum Hall effect (QHE) on this system is still missing. We measured angular dependence of QHE in the single layer (SL) and bi-layer (BL) 2DHG in the strained Ge/SiGe quantum well (QW). Clear Landau level (LL) crossing and anti-crossing have been observed in BL 2DHG system. We extracted hole g-factor g$\sim$38 almost independent of Landau filling factor. This g-factor is largest among all the reported value for Ge. Interestingly, observed behavior is distinct form SL 2DHG. LL crossing is not observed on SL QW in our measurement, and estimated g-factor for the single layer 2DHG is g$\sim$1, order of magnitude smaller than BL sample. We think this giant enhancement of effective g-factor in BL 2DHG attribute to the interlayer interaction between the two layers. Our finding reveals the possibility of large g-factor modulation by tuning interlayer coupling in bi-layer 2DHG system. [Preview Abstract] |
Monday, March 18, 2013 3:42PM - 3:54PM |
C42.00007: The Integer and Fractional Quantum Hall Effect in the Lowest Landau Level of Valley Degenerate 2D Electrons on Hydrogen Terminated Si(111) Tomasz M. Kott, Binhui Hu, S.H. Brown, B.E. Kane We report low temperature magnetotransport measurements on a high mobility ($\mu=325\,000\,$cm$^{2}$/V$\,$sec) 2D electron system on a H-terminated Si(111) surface. In Si(111), there are six degenerate, anisotropic valleys which can affect the magnetotransport in unexpected ways. While low magnetic field data indeed show a six-fold valley degenerate system, we observe the integral quantum Hall effect at all filling factors $\nu\leq 6$, indicating a magnetic-field-induced breaking of the valley degeneracy. Additionally, we find that $\nu=2$ develops in an unusually narrow temperature range, which might indicate the existence of a novel broken-symmetry valley phase. Finally, we observe an extended, exclusively even numerator, fractional quantum Hall hierarchy surrounding $\nu=3/2$ with denominators up to 15. This hierarchy is consistent with two-fold valley-degenerate composite fermions. We determine activation energies and provide the first estimate the composite fermion mass in a multi-valley system. [Preview Abstract] |
Monday, March 18, 2013 3:54PM - 4:06PM |
C42.00008: Heat equation approach to geometric changes of the torus Laughlin-state Zhenyu Zhou, Zohar Nussinov, Alexander Seidel We study the second quantized -or guiding center- description of the torus Laughlin state. Our main focus is the change of the guiding center degrees of freedom with the torus geometry, which we show to be generated by a two-body operator. We demonstrate that this operator can be used to evolve the full torus Laughlin state at given modular parameter $\tau$ from its simple (Slater-determinant) thin torus limit, thus giving rise to a new presentation of the torus Laughlin state in terms of its ``root partition'' and an exponential of a two-body operator. This operator therefore generates in particular the adiabatic evolution between Laughlin states on regular tori and the quasi-one-dimensional thin torus limit. We make contact with the recently introduced notion of a ``Hall viscosity'' for fractional quantum Hall states, to which our two-body operator is naturally related, and which serves as a demonstration of our method to generate the Laughlin state on the torus. [Preview Abstract] |
Monday, March 18, 2013 4:06PM - 4:18PM |
C42.00009: Fractional Quantum Hall states on an infinite cylinder: topological properties and edge exponents using the iDMRG Michael Zaletel, Roger Mong, Joel Moore, Frank Pollmann Exact diagonalization has been a tremendously successful approach to quantum Hall numerics, but is limited for certain applications due to finite size effects. We show how the infinite density matrix renormalization group (iDMRG) can be adapted to study microscopic quantum Hall Hamiltonians on a cylinder of infinite length. Using iDMRG to obtain the set of topologically degenerate ground states in their matrix product state form allows us to determine the energy, charge, quantum dimension and topological spin of the quasi-particles. When a trapping potential around the cylinder is introduced the fluid collapses into an infinitely long strip, an ideal geometry for extracting the central charge and edge exponents without the usual finite size effects. [Preview Abstract] |
Monday, March 18, 2013 4:18PM - 4:30PM |
C42.00010: Coherent State Wave-Functions on a Torus with a Constant Magnetic Field Mikael Fremling We study two alternative definitions of localized states in the lowest Landau level (LLL) on a torus. The first is to project a delta function onto the LLL, while the other is to put all the $N$ zeros of the wave function at the same point, thus localizing the function at the vicinity of the antipodal point. These two families of localized states both have many properties in common with the coherent states on the plane and on the sphere, viz. a simple resolution of unity and a self-reproducing kernel. However, only the projected delta function gives maximally localized states. We also show how to project expressions containing holomorphic derivatives and nonholomorphic coordinates onto the LLL, and briefly discuss the importance of this for constructing hierarchical QH wave functions. [Preview Abstract] |
Monday, March 18, 2013 4:30PM - 4:42PM |
C42.00011: Exactly solvable 1D lattice model for the Laughlin states on torus geometries Zheng-Yuan Wang, Masaaki Nakamura We study the fractional quantum Hall (FQH) states on a thin torus where the 2D continuum system in a magnetic field can be reduced into a 1D lattice model with short-range interaction. We introduce a minimal model with exact ground states in Laughlin series (flling factors of the lowest Landau level $\nu=1/q$).The model has the same degrees of freedom as that of the pseudo-potential for the Laughlin wave function, and it naturally derives general properties of the Laughlin wave function such as the $Z_2$ properties (the FQH effect is limited only odd q for fermions). The obtained exact ground states have high overlaps with the Laughlin states and well describe their properties, the incompressibility and the fractional charge excitations. The physical quantities such as the correlation functions are calculated analytically by using matrix product method. We also compute the entanglement spectrum and show the diamond structure of the FQH states on torus geometries. Thus, our model gives a simple reference model to describe the Laughlin states. (arXiv:1206.3071) [Preview Abstract] |
Monday, March 18, 2013 4:42PM - 4:54PM |
C42.00012: Advantages of studying the fractional quantum Hall effect in a cylindrical geometry Sonika Johri, Z. Papic, Zi-xiang Hu, R.N. Bhatt, Peter Schmitteckert We report results of numerical studies of the fractional quantum Hall effect in the cylindrical geometry using exact diagonalization as well as density-matrix renormalization group techniques. We provide convergence benchmarks that illustrate the advantage of the cylinder over the sphere, based on the number of sweeps and basis elements that need to be kept in order to achieve the desired accuracy for the ground state at $\nu=5/2$ filling [1]. Further, we address several issues of interest that can be studied more directly using the cylindrical geometry. These include (i) transitions between the hierarchy of fractional quantum Hall states as a function of the confining potential; (ii) quasiparticle tunneling between the two edges of the cylinder; and (iii) generalized off-diagonal long-range order as a probe of the local geometry fluctuations in fractional quantum Hall liquids due to confinement potential or mass anisotropy.\\[4pt] [1] Zi-Xiang Hu, Z. Papic, S. Johri, R. N. Bhatt, Peter Schmitteckert, Phys. Lett. A \textbf{376}, 2157 (2012) [Preview Abstract] |
Monday, March 18, 2013 4:54PM - 5:06PM |
C42.00013: Shot Noise Signatures of Charge Fractionalization in the $\nu=2$ Quantum Hall edge Mirco Milletari', Bernd Rosenow We investigate the effect of non-equilibrium and interactions on shot noise in $\nu=2$ quantum Hall edges, where interactions between the two co-propagating edge modes are expected to give rise to charge fractionalization. We consider a setup consisting of a Hall bar pinched by two Quantum point contacts (QPCs). The first QPC selectively drives out of equilibrium the outer edge mode only, which then interacts with the unbiased inner one over the distance between the two QPCs. We describe the edge modes by two coupled chiral Luttinger liquids, and employ the method of non-equilibrium bosonization to study the relaxation dynamics of the inner one. We find that even asymptotically the edge distribution function does not thermalize, but instead depends in a sensitive way on the interaction strength between the two edge modes. We compute shot noise and Fano factor from the asymptotic distribution function of the inner edge mode at the second QPC, and from comparison with a reference model of fractionalized excitations we find that the Fano factor can be close to the value of the fractionalized charge. [Preview Abstract] |
Monday, March 18, 2013 5:06PM - 5:18PM |
C42.00014: Anomalous Energy Gaps of the Odd Denominator Fractional Quantum Hall States in Different Spin Branches of the Second Landau Level Ethan Kleinbaum, Ashwani Kumar, Michael Manfra, Loren Pfeiffer, Ken West, Gabor Csathy The nature of the fractional quantum Hall states forming in the second Landau level, including those with odd denominator Landau level filling factors, remain unknown. Conjectures of nonconventional origins have lead to the investigation of several odd denominator states in the lower spin branch of the second Landau level, such as the ones at $\nu$=2+1/3 and 2+2/3. We report first measurements of the energy gaps in the upper spin branch of the second Landau level at $\nu$=3+1/3, 3+2/3, 3+1/5 and 3+4/5. A comparison of the energy gaps of these states to those of their counterparts in the lower spin branch reveals a surprising reversal in the relative magnitudes of the states at partial filling factors 1/3 and 1/5. We explore possible explanations of this unusual observation. The work at Purdue was supported by the DOE BES contract no. DE-SC0006671. K.K. West and L.N. Pfeiffer acknowledge the support of the Princeton NSF-MRSEC and the Moore Foundation. [Preview Abstract] |
Monday, March 18, 2013 5:18PM - 5:30PM |
C42.00015: Ground states at the filling factors $\nu=7/3$ and $8/3$ in the second Landau level Toru Ito, Naokazu Shibata, Kentaro Nomura The Laughlin state successfully describe the fractional quantum Hall state at $\nu=1/3$ in the lowest Landau level. However, it is known that the Laughlin wavefunction has little overlap with the ground state wavefunction at $\nu=7/3$ in the second Landau level. The ground states at $\nu=7/3$ and $8/3$ are still unknown.To determine the ground states at these fillings, we use the exact diagonalization method and density-matrix renormalization group (DMRG) method. We calculate overlaps between the ground state and the trial wavefunctions, the ground state energies, and the ground-state pair-correlation functions. We find that the ground state wavefunction at $\nu=8/3$ have very high overlap between the parafermion state, and the ground state energy of the parafermion state is lower than that of the Laughlin state. Further, the short-range structures of pair-correlation functions are significantly different from that of the Lauglin state.From these results, we consider that the parafermion state is a strong candidate of the ground state at $\nu=7/3$ and $\nu=8/3$. [Preview Abstract] |
Monday, March 18, 2013 5:30PM - 5:42PM |
C42.00016: 7/3 fractional quantum Hall effect: topology, trion excitations and edge states Ajit C. Balram, Ying-Hai Wu, G.J. Sreejith, Arkadiusz W\'{o}js, J.K. Jain Exact diagonalization studies on finite systems show that the quasihole and quasiparticle excitations in the 7/3 fractional quantum Hall (FQH) state are qualitatively distinct from those of the 1/3 state, suggesting the possibility of different topological origins for the two states. We perform composite-fermion diagonalization on larger systems and also evaluate the entanglement spectrum, which shows that in spite of these strong finite size deviations, the 7/3 and 1/3 FQH states have the same topological structure in the thermodynamic limit. Nonetheless, there are substantial non-topological differences between the two, arising from the stronger residual interaction between composite fermions at 7/3. In particular, we show that the lowest energy charged excitations of the 7/3 state are complex trions of composite fermions, which have a much larger size than the charged excitations at 1/3. We discuss many observable consequences of our results. [Preview Abstract] |
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