Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session E27: Fractional Quantum Hall Effect II. |
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Sponsoring Units: FIAP Chair: Loren Pfeiffer, Princeton University Room: 290 |
Tuesday, March 14, 2017 8:00AM - 8:12AM |
E27.00001: Interplay between Quantum Well Width and Interface Roughness for Electron Transport Mobility in GaAs Quantum Wells Dobromir Kamburov, Kirk Baldwin, Kenneth West, Mansour Shayegan, Loren Pfeiffer We report transport mobility measurements for clean, two-dimensional (2D) electron systems confined to GaAs quantum wells (QWs), grown via molecular beam epitaxy, in two families of structures, a standard, symmetrically-doped GaAs set of QWs with Al$_{\mathrm{0.32}}$Ga$_{\mathrm{0.68}}$As barriers, and one with additional AlAs cladding surrounding the QWs. Our results indicate that the mobility in narrow QWs with no cladding is consistent with existing theoretical calculations where interface roughness effects are softened by the penetration of the electron wave function into the adjacent low barriers. In contrast, data from AlAs-clad wells show a number of samples where the 2D electron mobility is severely limited by interface roughness, exhibiting a 6$^{\mathrm{th}}$ power dependence on the quantum well width. These measurements across three orders of magnitude in mobility provide a road map of reachable mobilities in the growth of GaAs structures of different electron densities, well widths, and barrier heights. [Preview Abstract] |
Tuesday, March 14, 2017 8:12AM - 8:24AM |
E27.00002: Comparison the Photoluminescence and Magneto-transport Techniques for Measuring 2D Electron Density in GaAs Quantum Wells Loren Pfeiffer, Dobromir Kamburov, Kirk Baldwin, Kenneth West We compare photoluminescence (PL) and transport measurements as a measure of the electron density in clean, two-dimensional (2D) systems confined to GaAs quantum wells (QWs), grown via molecular beam epitaxy. We explore the PL shape evolution across a number of samples with different QWs and as-grown electron densities and study its correspondence with the density obtained in transport measurements. We also measure the 2D density in a top-gated quantum well sample in both PL and transport and find that they are in agreement to within a few percent. The PL measurements are sensitive to gate-induced 2D density changes as small as 10$^{\mathrm{9}}$ electrons/cm$^{\mathrm{2}}$. The spatial resolution of the PL 2D density measurement is 40$\mu $m, which is already substantially better than is possible in spatial maps with magneto-transport. Our results establish that PL could be used as a reliable technique for non-invasive measurements of small density variations with high spatial resolution. [Preview Abstract] |
Tuesday, March 14, 2017 8:24AM - 8:36AM |
E27.00003: Resistance Spike Enhancement at a Landau Level Crossing in a Two- subband 2D Electron System with a 1D Density Modulation Meng K. Ma, Md. Shafayat Hossain, M. A. Mueed, L. N. Pfeiffer, K. W. West, K. W. Baldwin, M. Shayegan When two Landau levels with different indices, subband, orbital, or spin, cross at the Fermi level, a resistance spike is often seen at low temperatures, signaling a ferromagnetic quantum Hall effect transition. The spike is believed to be a manifestation of extra dissipation at the boundary between the domains of quantum Hall states with different pseudo-spin. Here we report magneto-transport measurements in a two-subband 2D electron system (40 nm-wide GaAs quantum well with n $=$ 2.7 x 10$^{\mathrm{11}}$ cm$^{\mathrm{-2}})$ where a resistance spike is seen near $\nu =$ 6 at a crossing of Landau levels with different subband indices at temperatures ranging from 600 mK to 1 K. In our experiments, we impose a strain-induced, 1D periodic density modulation through the piezoelectric effect of stripes of negative e-beam resist placed on the sample surface. The data reveal a significant amplification of the resistance spike at $\nu =$ 6. We also observe that the level of enhancement depends the period of the stripes; the stripes with a 225 nm period give the strongest enhancement and lower the temperature onset to below-300 mK. We discuss possible implications of the observations. [Preview Abstract] |
Tuesday, March 14, 2017 8:36AM - 8:48AM |
E27.00004: Observation of Anisotropic Stripe Phases at Even Denominator Fillings $\nu $ $=$ 3/2, 5/2 and 7/2 in a Narrow AlAs Quantum Well Md. Shafayat Hossain, M. A. Mueed, Meng K. Ma, Yoon Jang Chung, L. N. Pfeiffer, K. W. West, K. W. Baldwin, M. Shayegan Anisotropic stripe phases are observed at high-index, half-filled Landau levels in high quality 2D carrier systems with high mobility. Here, we report the observation of such phases at filling factors $\nu =$ 3/2, 5/2 and 7/2 under tilted magnetic field in a narrow (56.6 {\AA}-wide) AlAs quantum well where electrons occupy an out of plane (Z) valley with a density of 3x10$^{\mathrm{11}}$ cm$^{\mathrm{-2}}$ and a modest mobility of about 7 m$^{\mathrm{2}}$/Vs. At a critical tilting angle, when $\nu =$ 3/2 undergoes a transition from the N$=$ 0 (Z0$\uparrow )$ to the N$=$ 1 (Z1$\downarrow )$ Landau level, a resistance spike emerges, indicating a ferromagnetic transition. For higher tilting angles, the ground state at $\nu =$ 3/2 develops into a stripe phase with the resistance along B$_{\mathrm{\vert \vert }}$ exhibiting a minimum whose value is about 6 times smaller (in a Hall-bar geometry) than the resistance perpendicular to B$_{\mathrm{\vert \vert }}$ which shows a maximum. Similar phenomenon happens for $\nu =$ 5/2 and 7/2, when they undergo transitions from Z0$\uparrow $ to Z2$\downarrow $ and Z0$\uparrow $ to Z3$\downarrow $, respectively, at yet higher tilt angles. Furthermore, the anisotropic phases appear to be quite robust as they persist even at 1.8 K. [Preview Abstract] |
Tuesday, March 14, 2017 8:48AM - 9:00AM |
E27.00005: Fractional Quantum Hall Bilayers at Half-Filling: Tunneling-driven Non-Abelian Phase Donna Sheng, Wei Zhu, Zhao Liu, Duncan Haldane Multicomponent quantum Hall systems with internal degrees of freedom provide a fertile ground for the emergence of exotic quantum liquids. Here we investigate th e possibility of non-Abelian topological order in the half-filled fractional quantum Hall (FQH) bilayer sys tem driven by the tunneling effect between two layers. By means of the state-of-the-art density-matrix re normalization group, we unveil “finger print” evidence of the non-Abelian Moore-Read Pfaffian state emerging in the intermediate-tunneling regime, including the ground-state degeneracy on the torus geometry and the topol ogical entanglement spectroscopy (entanglement spectrum and topological entanglement entropy) on the sphe rical geometry, respectively. Remarkably, the phase transition from the previously identified Abelian (331) Halperin state to the non-Abelian Moore-Read Pfaffian state is determined to be continuous, which is signaled by the continuous evolution of the universal part of the entanglement spectrum, and discontinuities in the excitat ion gap and the derivative of the ground-state energy. Our results provide a “proof-of-principle” demonstration of realizing a non-Abelian state through coupling different degrees of freedom. [Preview Abstract] |
Tuesday, March 14, 2017 9:00AM - 9:12AM |
E27.00006: Chern-Simons Composite Fermion Theory of Fractional Chern Insulators Ramanjit Sohal, Luiz Santos, Eduardo Fradkin Fractional Chern Insulators (FCIs) are a class of two dimensional interacting lattice systems that realize the Fractional Quantum Hall effect in the absence of Landau levels produced by a uniform magnetic field. Time-reversal symmetry breaking effects that are responsible for non-trivial Berry curvatures in FCIs occur on length scales comparable to the lattice constants, rendering the analytical approaches much more challenging than for Landau levels. It is expected that strong lattice effects should modify the structure of hierarchical states. We formulate a Chern-Simons composite fermion theory for FCIs, whereby bare fermions are mapped into composite fermions (bound states of particles and flux) coupled to a discretized dynamical Chern-Simons gauge field defined on the same lattice as the fermions. We apply this construction to kagome and other lattices, and determine a rich structure of gapped topological phases characterized by fractionalized elementary excitations. [Preview Abstract] |
Tuesday, March 14, 2017 9:12AM - 9:24AM |
E27.00007: Interlayer pairing symmetry of composite fermions in quantum Hall bilayers Hiroki Isobe, Liang Fu We study the pairing symmetry of the interlayer paired state of composite fermions in quantum Hall bilayers. In such systems, quantized Hall conductances are observed when each layer is at even-denominator filling fractions. For short layer distances, the incompressible phase is dictated by the formation of an excitonic superfluid phase. In contrast, at larger distance, the bilayer system is described by two composite Fermi liquids with interlayer interactions. Based on the Halperin-Lee-Read (HLR) theory, we analyze the effect of the long-range Coulomb interaction and the internal Chern-Simons gauge fluctuation with the random-phase approximation beyond the leading order contribution in small momentum expansion, and observe that the interlayer paired states with a relative angular momentum $l=+1$ is energetically favored for filling $\nu=\frac{1}{2}+\frac{1}{2}$ and $\frac{1}{4}+\frac{1}{4}$. The degeneracy between states with $\pm l$ is lifted by the interlayer density-current interaction arising from the interplay of the long-range Coulomb interaction and the Chern-Simons term in the HLR theory. Reference: H. Isobe and L. Fu, arXiv:1609.09063. [Preview Abstract] |
Tuesday, March 14, 2017 9:24AM - 9:36AM |
E27.00008: Microwave spectroscopy as a probe of the interaction between a Wigner solid and composite fermion liquid Anthony Hatke, Lloyd Engel, Yang Liu, Hao Deng, Mansour Shayegan, Loren Pfeiffer, Ken West, Kirk Baldwin For a two dimensional electron system containing a single occupied subband the fractional quantum Hall effect (FHQE) series terminates at filling factor $\nu=1/5$. For $\nu<1/5$ the system forms a Wigner solid, pinned by residual disorder, which exhibits a resonance in its microwave spectrum due to pieces of the solid oscillating within the disorder potential. Here we perform microwave spectroscopy measurements of a unique double quantum well (DQW). This DQW was grown to have a high mobility, relatively high density in the majority layer that exhibits a number of well-known FQHE states for $\nu<1$ and a minority layer with a relatively low density such that at over the range of observable FQHE states in the majority layer the minority layer will form a Wigner solid. Our microwave spectroscopy measurements are sensitive to the solid formed in the minority layer and probe the interaction between the Wigner solid and the composite fermion liquid. We find that the peak frequency of the pinning mode resonance oscillates with the majority-layer filling due to FQHE states and discuss our observations in terms of the formation of a Wigner solid comprised of image charges in the majority layer. [Preview Abstract] |
Tuesday, March 14, 2017 9:36AM - 9:48AM |
E27.00009: Density Functional Theory of the Fractional Quantum Hall Effect Jianyun Zhao, Manisha Thakurathi, Manish Jain, Diptiman Sen, Jainendra Jain We formulate density functional theory for the FQHE in the LLL, properly incorporating the non-perturbative physics of the repulsive interaction and the finite temperature entropy of the FQHE state. Two key ingredients of our theory are a) a microscopically derived exchange correlation interaction, and b) minimization of the free energy with respect to the composite-fermion density in various Λ levels, as opposed to the total electron density. An application of this approach to the FQHE edge brings out its rather complex structure, showing that, in general, edge reconstruction extends much more deeply into the interior than previously suspected, and is washed out by very small temperatures. As another application, we obtain analytically the change in the density profile of composite-fermion Fermi sea exposed to the potential due to a Wigner crystal in a nearby layer, and find unexpectedly rich patterns. [Preview Abstract] |
Tuesday, March 14, 2017 9:48AM - 10:00AM |
E27.00010: Quantum Anomalous Hall Insulator of Composite Fermions Yinhan Zhang, Junren Shi We show that a weak hexagonal periodic potential can transform a two-dimensional electron gas with an even-denominator magnetic filling factor into an quantum anomalous hall insulator of composite fermions, giving rise to the fractionally quantized Hall effect. The system provides a realization of the Haldane honeycomb-net model, albeit in a composite fermion system. We further propose a trial wave function for the state, and numerically evaluate its relative stability against the competing Hofstadter state. Possible sets of experimental parameters are proposed. [Preview Abstract] |
Tuesday, March 14, 2017 10:00AM - 10:12AM |
E27.00011: Microscopic analysis of protected edges without symmetry Sriram Ganeshan, Michael Levin The $\nu = 2/3$ fractional quantum Hall state has been shown to have protected gapless edge modes even if all symmetries are broken, including charge conservation. In this talk, we investigate the robustness of these edge modes in a concrete model. The model we consider describes a 2/3 edge that is strongly proximity-coupled to an adjacent superconductor. Our model clarifies the obstruction to gapping the edge and provides insights into the corresponding anomaly --- which is beyond the U(1) chiral anomaly associated with charge conservation symmetry. As a by-product of this analysis, we derive edge theories for Abelian quantum Hall states without any U(1) symmetries. [Preview Abstract] |
Tuesday, March 14, 2017 10:12AM - 10:24AM |
E27.00012: Dephasing in a 5/2 quantum Hall Mach-Zehnder interferometer due to the presence of neutral edge modes Yehuda Dinaii, Moshe Goldstein, Yuval Gefen Non-Abelian statistics is an intriguing feature predicted to characterize quasiparticles in certain topological phases of matter. This property is both fascinating on the theoretical side and the key ingredient for the implementation of future topological quantum computers. A smoking gun manifestation of non-Abelian statistics consists of demonstrating that braiding of quasiparticles leads to transitions among different states in the relevant degenerate Hilbert manifold. This can be achieved utilizing a Mach-Zehnder interferometer, where Coulomb effects can be neglected, and the electric current is expected to carry clear signatures of non-Abelianity. Here we argue that attempts to measure non-Abelian statistics in the prominent quantum Hall fraction of 5/2 may fail; this can be understood by studying the corresponding edge theory at finite temperatures and bias. We find that the presence of neutral modes imposes stronger limitations on the experimental conditions as compared to quantum Hall states that do not support neutral edge modes. We discuss how to overcome this hindrance. Interestingly, neutral-mode-induced dephasing can be quite different in the Pfaffian state as compared to the anti-Pfaffian state, if the neutral and charge velocities are comparable. [Preview Abstract] |
Tuesday, March 14, 2017 10:24AM - 10:36AM |
E27.00013: Anomalous behavior of the $N =$ 2 bubble states in a tilted field Pengjie Wang, Ruoxi Zhang, Hailong Fu, Pujia Shan, Lingjie Du, Xiaoxue Liu, Loren Pfeiffer, Ken West, Rui-Rui Du, Xi Lin We have carried out the activation energy gap measurements of the $N =$ 2 bubble states using tilted-field technique in two GaAs/AlGaAs samples with Corbino geometry. The bubble states are expected to have decreasing gaps with the increasing tilted angle. In the conventional bubble states, surprisingly, we found that the energy gaps were nonlinear with the total magnetic field, which suggests that Zeeman effect isn't the only cause of the gap weakening. We also found a bubble state's energy gap with opposite in-plane field dependence, which occurred at an unusual filling factor for the bubble states. [Preview Abstract] |
Tuesday, March 14, 2017 10:36AM - 10:48AM |
E27.00014: Quasiparticle tunneling at an odd-denominator fractional quantum Hall state Hailong Fu, Pujia Shan, Pengjie Wang, Loren Pfeiffer, Ken West, Xi Lin In the fractional quantum Hall (FQH) state, the effective charge and interaction parameter of quasiparticles can be extracted through weak tunneling theory [1]. Weak tunneling theory has been applied in the even-denominator 5/2 FQH state's edge-current-tunneling to search for the non-Abelian statistics [2,3,4,5], but weak tunneling theory has not been quantitatively verified in the simpler odd-denominator Laughlin FQH state with similar configurations. We measured edge-current-tunneling within a quantum point contact at the 5/3 FQH state, and the interaction parameter is close to the theoretical prediction 1/3. [1] Phys. Rev. B \textbf{44}, 5708 (1991). [2] Science \textbf{320}, 899 (2008). [3] Phys. Rev. B \textbf{85}, 165321 (2012). [4] Phys. Rev. B \textbf{90}, 075403 (2014). [5] PNAS \textbf{113}, 12386 (2016). [Preview Abstract] |
Tuesday, March 14, 2017 10:48AM - 11:00AM |
E27.00015: Generalized Pseudopotentials for the Anisotropic Fractional Quantum Hall Effect Bo Yang, Zi-Xiang Hu, Ching Hua Lee, Zlatko Papic Haldane pseudopotentials have played a key role in the study of the fractional quantum Hall (FQH) effect as they allow an arbitrary rotationally-invariant interaction to be expanded over projectors onto the two-particle eigenstates of relative angular momentum. Here we introduce a more general class of pseudopotentials that form a complete basis in the cases where rotational symmetry is explicitly broken, e.g., due to tilted magnetic field or anisotropic band structure. Similar to the standard isotropic pseudopotentials, the generalized pseudopotentials are also parametrized by a unimodular metric, which groups the effective interactions into equivalence classes, and is particularly useful in determining optimal model Hamiltonians of the anisotropic FQH fluids. We show that purely anisotropic pseudopotentials lead to new types of bound ``molecular" states for a few particles in an infinite plane. We discuss realizations of the generalized pseudopotentials in systems with tilted magnetic field, as well as fractional Chern insulators harboring intrinsic anisotropy due to the underlying lattice structure. [Preview Abstract] |
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