Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session Y25: Fractional Quantum Hall Effect 2: theory and experiment |
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Sponsoring Units: DCMP Chair: Leonardo Ranzani, BBN Technology - Massachusetts Room: Room 217/218 |
Friday, March 10, 2023 8:00AM - 8:12AM |
Y25.00001: Fractional charge from auto-correlations and cross-correlations in shot noise experiments Navketan Batra, D. E Feldman Fractional charge is one of the key features of the fractional quantum Hall effect. Much of the fractional charge information comes from shot noise experiments. It has long been observed that the agreement between theoretical and experimental values of the quasiparticle charge often breaks down at low temperatures in shot-noise experiments with a constriction in a quantum Hall liquid. Recently, surprising evidence has emerged that the agreement only breaks down in experiments that measure current auto-correlations on one side of the constriction. Cross-correlations between the currents on the two sides of the constriction still show the theoretically predicted fractional charge. Yet, theory predicts that excess auto- and cross-correlations are simply opposite to each other in low-frequency experiments in the absence of long-range forces and upstream modes. In this talk, we address possible mechanisms for the observed discrepancy in non-ideal experimental systems. We find that cross-correlations provide a more reliable tool to measure fractional charge. |
Friday, March 10, 2023 8:12AM - 8:24AM |
Y25.00002: Anomalous magneto-oscillations at very low magnetic fields in ultra-high-mobility GaAs two-dimensional hole systems Casey S Calhoun, Chengyu Wang, Edwin Y Chung, Kirk W Baldwin, Loren N Pfeiffer, Mansour Shayegan GaAs two-dimensional (2D) holes are a promising platform for the study of many-body phenomena thanks to their large effective mass which implies a smaller Fermi energy and thus strong interaction between carriers. In addition, due to the strong spin-orbit interaction, 2D holes in GaAs demonstrate a tunable spin-orbit-induced subband splitting, anisotropic Fermi contours as well as nonlinear Landau levels, adding further complexity to their band structure. Here we present low-temperature magneto-transport measurements of an ultra-high-mobility 2D hole system confined to a symmetric (001) GaAs quantum well. The measurements reveal anomalous oscillations in magneto-resistance, periodic in 1/B, persisting beyond the damping of the Shubnikov-de Haas (SdH) oscillations at low fields. The frequency of these oscillations appears to be related to the difference between the SdH frequency for the two spin-orbit-split, heavy-hole subbands. However, the amplitude of the low-field oscillations does not match what is observed in the SdH oscillations. We discuss possible origins of these features. |
Friday, March 10, 2023 8:24AM - 8:36AM |
Y25.00003: Limits to mobility in ultrahigh-mobility GaAs two-dimensional electron systems Adbhut Gupta, Edwin Y Chung, Kirk W Baldwin, Kenneth W West, Mansour Shayegan, Loren N Pfeiffer Two dimensional electron systems (2DESs) in GaAs quantum wells are some of the cleanest materials that can be grown in a lab. Continuous improvement in their quality (mobility) through advances in molecular beam epitaxy has enabled emergence of several unexpected exotic many-body phases over the past few decades. With recent interest in GaAs 2DESs due to potential applications in topological quantum computing and continued search for new interaction-driven, many-body phases, it becomes imperative to understand what limits the mobility in modern ultrahigh-mobility 2DESs. We try to answer this question by presenting experimental mobility data for a wide variety of state-of-the-art GaAs 2DESs, and analyzing various scattering mechanisms that set the limits to mobility [1]. Ultraclean GaAs 2DESs with densities ranging from ~ 0.2 to 3 x 1011/cm2 exhibit an interesting trend in mobility, rising with density up to a new world record of ~57 x 106 cm2/Vs at a density of 1.55 x 1011/cm2, and then dropping. A careful comparison of experimental data and models explains the trends while providing guidelines to achieving 100 x 106 cm2/Vs mobility and beyond. |
Friday, March 10, 2023 8:36AM - 8:48AM |
Y25.00004: A numerical study of bounds in the correlations of fractional quantum Hall states Prashant Kumar, Frederick D M Haldane We numerically compute the guiding center static structure factor s(q) of various fractional quantum Hall (FQH) states to O((ql)6). Employing density matrix renormalization group on an infinite cylinder of circumference Ly, we study the two-dimensional problem using Ly/l » 1. The main findings of our work are: 1) the ground states that deviate away from the ideal conformal block wavefunctions, do not saturate the Haldane bound, and 2) the coefficient of O((ql)6) term appears to be bounded above by a value predicted by field theories proposed in the literature. |
Friday, March 10, 2023 8:48AM - 9:00AM |
Y25.00005: Galilei invariance and geometric oscillations about the half-filled Landau level. Yen-Wen Lu, Prashant Kumar, Michael Mulligan Geometric oscillation measurements by Kamburov et al. [Phys. Rev. Lett. 113, 196801 (2014)] called into question the long held belief that the half-filled lowest Landau level of electrons is a Fermi liquid-metallic state of nonrelativistic composite fermions, finding the oscillation minima to be determined by the electron density for ν 1/2. These (and subsequent) measurements highlight the incompleteness of our understanding of the half-filled Landau level: mean-field treatments of the Dirac (Son) and nonrelativistic (Halperin-Lee-Read) composite fermion theories give identical predictions for the locations of oscillation minima; if the effects of Chern-Simons gauge field fluctuations (ignored in any mean-field treatment) are included, the comparison between theory and experiment improves dramatically. Here we study the extent to which the disagreement between composite fermion mean-field theory and experiment might instead be attributed to an approximate Galilei symmetry using the Dirac composite fermion mean-field theory. We further comment on the relevance of an approximate Galilei symmetry to metallic states found at other even-denominator filling fractions. |
Friday, March 10, 2023 9:00AM - 9:12AM |
Y25.00006: Full Classification of Transport on an Equilibrated ν=5/2 Edge Sourav Manna, Ankur Das, Moshe Goldstein, Yuval Gefen The nature of the bulk topological order of the ν=5/2 non-Abelian fractional quantum Hall state is a long-standing open question. There is more than one candidate, compatible with the experimental findings, namely anti-Pfaffian (APf) and particle-hole-Pfaffian (PHPf) states in full or partial thermal equilibration regimes [Banerjee et al. Nature 559, 205–210 (2018)]. Previous proposals can only characterize the APf state and its different edge equilibration regimes [Park et al. PRL 125, 157702 (2020)], or, alternatively identify the underlying non-Abelian models relying on the conditions of no edge equilibration which is hard to achieve in experiments [Yutushui et al. PRL 128, 016401 (2022)]. Here we propose a set of electrical shot noise measurements which can distinguish both between APf and PHPf bulk phases as well as between full or partial edge thermal equilibration regimes. Our scheme is implementable in the existing experimental platform. |
Friday, March 10, 2023 9:12AM - 9:24AM |
Y25.00007: Odd viscosity in rotating Bose Einstein condensates Seth W Musser, Hart Goldman, Senthil Todadri We discuss the phenomenology of odd viscosity in rotating Bose Einstein condensates and propose a diagnostic of its presence. We provide a microscopic prediction for it in several rotating geometries, and provide suggestions for manipulating its value. Finally, we discuss the experimental outlook for its detection. |
Friday, March 10, 2023 9:24AM - 9:36AM |
Y25.00008: Signatures of emergent supersymmetry in the ν=5/2 fractional quantum Hall effect Songyang Pu, Ajit C Balram, Zlatko Papic The Moore-Read Pfaffian state has two low-lying neutral excitations, a magnetoroton mode and a neutral fermion mode. Recently, Gromov, Martinec, and Ryu proposed a theory which formulated the two modes as supersymmetric partners of each other [1]. Inspired by their work, we construct wave functions for the two modes in different closed geometries. We evaluate the variational energies of the two wave functions in large system sizes and find signatures of supersymmetry for an interaction in the vicinity of the second Landau level Coulomb point. We also compare the constructions of the neutral excitation modes from previous approaches and find they give identical description in the long-wavelength limit. |
Friday, March 10, 2023 9:36AM - 9:48AM |
Y25.00009: Measuring topological entanglement entropy using Maxwell relation Sarath Sankar, Cheolhee Han, Eran Sela Topological entanglement entropy (TEE) is an important characteristic of topological order, but there is currently no protocol to measure it experimentally. There exists a nontrivial connection between TEE and thermodynamic entropy: in a point contact formed between the edge states of a topological phase, the thermodynamic entropy change between the ultraviolet (weak backscattering) and infrared (strong backscattering) fixed points equals the TEE. We propose a protocol to experimentally measure this change in the thermodynamic entropy, and thereby measure TEE, by making use of a Maxwell relation. We illustrate how the proposed TEE measurement would work for the experimentally relevant fractional quantum Hall case with filling factor 1/3.
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Friday, March 10, 2023 9:48AM - 10:00AM |
Y25.00010: Evidence for fractional quantum Hall state of 6-flux composite fermions in a system with significant Landau level mixing Siddharth Kumar Singh, Adbhut Gupta, Pranav Thekke Madathil, Chengyu Wang, Loren N Pfeiffer, Kirk W Baldwin, Mansour Shayegan Termination of the fractional quantum Hall effect (FQHE) states and the emergence of Wigner crystal phases at very low Landau level filling factors (ν<<1) has been of continued interest for decades [1,2,3]. Recently, in ultra-high-quality, dilute GaAs 2D electron systems, Chung et al. [3] reported strong evidence for FQHE at ν=1/7, 2/13, 2/11 which fall in the ν=p/(6p±1) Jain series of FQHE states, interpreted as integer (p = 1, 2) quantum Hall effect of 6-flux composite fermions (6CFs). These states are surrounded by strongly-insulating phases which are generally believed to be Wigner crystals. Here, we study a record high quality 2D electron system confined to a 35-nm-wide AlAs quantum well with density 9.6×1010 cm-2 [4]. The AlAs 2D electrons have a much larger effective mass (≈0.45me) and a smaller dielectric constant (≈10) compared to GaAs 2D electrons. Qualitatively, similar to the GaAs 2D electrons, we observe a strong insulating behavior setting at ν<1/5 , as well as a clear minimum in magnetoresistance at ν=2/11 and an inflection at ν=1/7 which is very reminiscent of the first report of FQHE at ν=1/7 [1]. The data provide evidence for developing FQHE states of 6CFs at very small fillings. This is very surprising since in our sample the Landau level mixing parameter κ, defined as the ratio of the Coulomb and cyclotron energies, is ≈4 and larger Landau level mixing has the tendency to favour Wigner crystal over FQHE in the lowest Landau level [5,6]. Our data should inspire theory calculations that accurately incorporate the role of Landau level mixing in competing many-body phases of 6CFs at extremely low fillings around ν=1/6. |
Friday, March 10, 2023 10:00AM - 10:12AM |
Y25.00011: Critical exponents of the plateau-to-plateau transitions in the fractional quantum Hall regime Chia-Tse Tai, Pranav Thekke Madathil, Kevin A Villegas Rosales, Yoon Jang Chung, Loren N Pfeiffer, Kirk W Baldwin, Ken West, Mansour Shayegan Scaling in disordered, quantum Hall systems has been studied extensively with the emergence of a single extended state (Ec), characterized by a power-law divergence of the localization length [ξ∝(E-Ec)-ν] in the zero temperature limit [1]. Experimentally, scaling has been investigated mostly by measuring the plateau-to-plateau transitions between integer quantum Hall states [2,3]. Improvements in epitaxially-grown GaAs quantum wells have led to ultra-high-quality 2D electron systems [4] which show a plethora of fractional quantum Hall states enabling us to investigate the scaling behavior in the fractional filling regime. We obtain the critical exponents by studying the temperature dependence of the longitudinal resistivity in a series of GaAs quantum wells with varying well widths ranging from 20 to 70 nm. While recent calculations in the fractional quantum Hall regime suggest identical critical exponents in the integer and fractional states [5], we report differing exponents as we transition between the fractional states. |
Friday, March 10, 2023 10:12AM - 10:24AM |
Y25.00012: A minimal integer quantum Hall state with an emergent super-symmetric edge and its fractional descendants Jeffrey Teo, Yichen Hu, Ramanjit Sohal We present the theory of a short-range entangled quantum Hall state at filling number ν=4. The topological state is constructed by many-body interacting electrons in a coupled-wire model. There is no adiabatic path connecting it with conventional integer quantum Hall states because its thermal Hall conductance is characterized by the unconventional chiral central charge c=12. The conformal field theory SO(24)1 that describes the gapless boundary edge has an emergent super-symmetry. It is the super-symmetric extension of the bosonic E8 Wess-Zumino-Witten theory, and its integral vertex excitations on the edge occupy a unimodular lattice at dimension 12. In addition, we present the theories of a family of long-range entangled fractional quantum Hall states that partially fill the SO(24)1 state. All fractional descendants in the family carry emergent super-symmetric edge theories and are pairwise related by a generalized notion of particle-hole conjugation. |
Friday, March 10, 2023 10:24AM - 10:36AM |
Y25.00013: Composite fermion mass in ultra-high-quality, two-dimensional electrons Pranav Thekke Madathil, Kevin A Villegas Rosales, Edwin Y Chung, Loren N Pfeiffer, Kirk W Baldwin, Ken West, Mansour Shayegan 2D electron systems subjected to a strong perpendicular magnetic field display rich, many-body phases like the fractional quantum Hall states (FQHSs). A description of these strongly interacting states can be mapped exactly onto the Landau levels of weakly-interacting quasi-particles each composed of an electron and two flux quanta, the so-called Composite Fermions (CFs) [1]. The FQHSs of electrons can then be thought of as the Integer quantum Hall states of CFs. The effective mass of the CF is inversely proportional to the energy gap of the FQHSs, a fundamental parameter of the many-body state. In addition, the mass is also largely robust to disorder and thus, more relevant to comparisons with theoretical calculations. Experimentally, we extracted the mass by performing standard transport measurements on ultra-high-quality GaAs quantum wells [2] with varying well width and analyzing the temperature dependence of the Shubnikov de Haas oscillations in the FQHSs. Our data reveal that the CF mass increases with increasing well width, reflecting a decrease in the energy gap as the electron layer becomes thicker and the in-plane Coulomb energy softens. Our data also show significant quantitative discrepancies between the theoretical [3,4] and measured masses, suggesting the need for more rigorous and accurate calculations. |
Friday, March 10, 2023 10:36AM - 10:48AM |
Y25.00014: Atypical edge current interference in high quality 2D electron systems: both Ising and Fibonacci anyons? Robert L Willett, Loren N Pfeiffer, Edwin Y Chung, Kirk W Baldwin, Milton Peabody In the highest quality 2D heterostructures produced to date Fabry-Perot interferometry has shown elaborate oscillation sets at 7/2 and 5/2 consistent in detail with non-Abelian properties expected for Ising anyons. The foundation of these results are the interference periods, consistent with addition of two e/4 charges on B-field sweep and respectfully corresponding to addition of 1/7 and 1/5 of a single flux to the interferometer: the even-odd effect. These oscillations are striking in their stability, amplitude, and packet form. Even more striking are oscillations that occur centered around 12/5 and 17/5, candidate filling factors for Fibonacci anyons. These oscillations are of comparable or even greater amplitude than those at 7/2 and 5/2, are equally stable in time and B-field sweeps, but have more elaborate packet formation: 12/5 and 17/5 oscillations display distinct multiple frequency spectral peaks. Importantly, these spectra have central frequencies corresponding roughly to addition of three e/5 quasiparticles for both 12/5 and 17/5. Presented here will be B-field sweep resistance measurements across the interferometers in different devices and samples with focus on the oscillation features and periods, comparison to other oscillation measurements from filling factors 2 to 4, and exhibited induced phase shifts of 1/3 period. While these particular results show potential consistency with non-Abelian Fibonacci anyons, alternative explanations are presently under study. |
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