Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session G54: Fractional Quantum Hall Effect and Composite Fermions 
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Sponsoring Units: DCMP Chair: Yaroslaw Bazaliy, Univ of South Carolina Room: Mile High Ballroom 2A 
Tuesday, March 3, 2020 11:15AM  11:27AM 
G54.00001: Bloch Ferromagnetism of Composite Fermions Md. Shafayat Hossain, Tongzhou Zhao, Songyang Pu, M A Mueed, Meng Ma, Kevin Villegas Rosales, Edwin Chung, Loren Pfeiffer, Kenneth West, K. W. Baldwin, Jainendra Jain, Mansour Shayegan The magnetic properties of the ground state of a lowdensity, 2D electron system (2DES) have been a topic of intense theoretical and experimental speculation and controversy, because the physics here is governed by strong correlations. Bloch predicted a fully spinpolarized ground state for a dilute fermionic system in 1929. However, such a state has eluded experimental realization for the last nine decades. Here we present an experimental realization of the elusive interactiondriven spin polarization in a dilute, 2D fermionic system, namely composite fermions (CFs). CFs are exotic quasiparticles, each composed of an electron and two flux quanta, formed in the halffilled Landau level of a 2DES. We determine the spinpolarization of these CFs via direct measurements of the CFs’ Fermi wavevector. We find that at high electron densities (n_{e}), the CFs are fully spinpolarized, consistent with previous experiments. As we lower n_{e}, the CFs lose their magnetization, also as expected. Remarkably, however, as n_{e} is further reduced, the CFs make a sudden transition and become fully spinpolarized. This spontaneous magnetization of CFs closely resembles the Bloch ferromagnetism. We also performed theoretical calculations that provide a semiquantitative understanding of the phenomenon. 
Tuesday, March 3, 2020 11:27AM  11:39AM 
G54.00002: Hall viscosity of composite fermions Songyang Pu, Mikael Fremling, Jainendra Jain Hall viscosity, also known as the Lorentz shear modulus, has been proposed as a topological property of a quantum Hall fluid. Using a recent formulation of the composite fermion theory on the torus [1], we evaluate the Hall viscosities for a large number of fractional quantum Hall states at filling factors of the form ν=n/(2pn±1) [2], where n and p are integers. The calculated Hall viscosities η^{A} agree with the expression η^{A} =hSρ/8π, where ρ is the density and S is the ``shift'' in the spherical geometry [3]. We show that the Hall viscosity for ν=n/(2pn+1) may be derived analytically from the microscopic wave functions providing some assumption. This derivation is applicable to a class of states in the parton construction, which are products of integer quantum Hall states with magnetic fields pointing in the same direction [4]. 
Tuesday, March 3, 2020 11:39AM  11:51AM 
G54.00003: Fractional Chern insulators in magicangle twisted bilayer graphene in the Hofstadter regime Bartholomew Andrews, Alexey Soluyanov We apply a perpendicular magnetic field to the minimal effective twoorbital FermiHubbard 
Tuesday, March 3, 2020 11:51AM  12:03PM 
G54.00004: Quantum Well Width Dependence of the Fractional Quantum Hall Energy Gaps Kevin Villegas Rosales, Pranav T Madathil, Edwin Chung, K. W. Baldwin, Kenneth West, Loren Pfeiffer, Mansour Shayegan The fractional quantum Hall effect (FQHE) stems from the strong shortrange Coulomb interaction in a twodimensional (2D) electron system at high magnetic fields. However, the Coulomb interaction is softened in realistic samples which contain quasi2D systems with a finite (nonzero) electron layer thickness. This softening leads to a weakening of the FQHE states, as manifested in a lowering of their energy gaps in both experiments [1] and calculations [2,3]. Here we present measurements of the energy gaps, from the temperature dependence of the magnetoresistance minima, of several fractional states in the lowest Landau level as a function of the width of the confining square quantum well. Our samples have a fixed density (n ≈ 1x10^{11} cm^{2}) while the width of the confining GaAs well varies between 20 and 80 nm. This is in contrast to measurements reported in [1] where the electrons were confined to parabolic Al_{x}Ga_{1x}As quantum wells. The gaps in our measurements change in magnitude when plotted versus the GaAs well width. We contrast our results with numerical calculations that include the role of finite layer thickness [2,3]. 
Tuesday, March 3, 2020 12:03PM  12:15PM 
G54.00005: Achievement of Systematically Higher Transport Mobilities for a Large Range of Twodimensional Electron Densities in GaAs Quantum Wells Loren Pfeiffer, Edwin Chung, K. A. VillegasRosales, K. W. Baldwin, Kenneth West, Mansour Shayegan For the range of twodimensional (2D) electron densities between 1.5 x 10^{10} cm^{2} and 1.4 x 10^{11} cm^{2}, we report measurements that confirm a ~60 to 70 % increase in the transport mobility of remotelydoped GaAs quantum wells compared to all previous GaAs material. A characteristic example of this development is the 2D transport mobility at an electron density of 1 x 10^{11} cm^{2} in a 50 nm quantum well. Previously, in this type of sample the electron mobilities were limited to ~ 1.8 x 10^{7} cm^{2}V^{1}s^{1}; now we have grown several with transport mobilities reaching ~3.0 x 10^{7} cm^{2}V^{1}s^{1}. We attribute these results to our program of hightemperature insitu bakes that have cleaned our AlGaAs barrier material of oxygen impurities, and to the use of largearea cryogenic coldplates operating at 17 K in the vacuum sump of our molecular beam epitaxy chamber. When cooled to temperatures below 100 mK, the magnetotransport data of the 1 x 10^{11} cm^{2} samples described above are remarkable, displaying clear quantum Hall features at the Landau level filling factors ν = 11/23, 12/25, and even 13/27. 
Tuesday, March 3, 2020 12:15PM  12:27PM 
G54.00006: Renormalization Group Flow of Dirac Composite Fermions at Half Filling Jonathan San Miguel, Hart Goldman, Prashant Kumar, Srinivas Raghu We compare the effects of gauge field fluctuations between different composite fermion descriptions of the halffilled Landau level: the HalperinLeeRead (HLR) theory of nonrelativistic composite fermions and the theory of Dirac composite fermions recently proposed by Son. While the Dirac theory is explicitly particlehole symmetric, the HLR theory contains a fluctuating statistical gauge field which appears to break particlehole symmetry. To better characterize this distinction, we present a renormalization group study of these theories in the presence of Coulomb interactions, using a controlled expansion both in the number of fermion species and the width of the Coulomb potential. In particular, we pay close attention to the effects in the HLR theory that break particlehole symmetry. We find that both theories are described by marginal Fermi liquid fixed points and compare their universal features. 
Tuesday, March 3, 2020 12:27PM  12:39PM 
G54.00007: Heterostructure Design for High Twodimensional Electron Density in GaAs/AlGaAs Quantum Wells at Large Hydrostatic Pressures Edwin Chung, Shuai Yuan, Yang Liu, K. W. Baldwin, Kenneth West, Mansour Shayegan, Loren Pfeiffer The application of hydrostatic pressure to GaAs/AlGaAs heterostructures has been a topic of great interest due to the possibility of achieving a gfactor ≈ 0 in highquality, twodimensional electron systems (2DESs). Despite the exciting prospect of studying electronelectron interactions in the absence of spin splitting, there are very few experimental reports on this subject. This is because in standard modulationdoped GaAs/AlGaAs heterostructures, the 2DES density decreases significantly as the magnitude of hydrostatic pressure applied to the system is increased. Here, we present a heterostructure design that circumvents such density degradation, so that highdensity, highquality 2DESs can be obtained at large hydrostatic pressures. We show that by implementing this scheme, the 2DES density only decreases by ~ 4 x 10^{10} cm^{2} even at a hydrostatic pressure of 8.2 kbar. This is a factor of ~4 improvement compared to conventional structures. We will also present lowtemperature magnetotransport data that demonstrate the high quality of our samples at large hydrostatic pressures. 
Tuesday, March 3, 2020 12:39PM  12:51PM 
G54.00008: Diagnosis of universal geometric responses of fractional quantum Hall liquids Wei Zhu, Donna Sheng, Zhao Liu, Liangdong Hu Geometric response of topological quantum liquids is expected to reveal rich phenomenon. However, explicit demonstration or identification of the geometric response in a microscopic model is very challenging. Here, we demonstrate that Dehntwist deformation is able to reveal both the universal modular properties and the microscopic features. We provide numerical evidences for various fractional quantum Hall (FQH) states, including fermionic and bosonic Laughlin states, Hierarchy states, Halperin states and MooreRead states, by means of exact diagonalization calculations. We conclusively show, geometric transformation applied on torus geometry gives rise to a viscosity related Berry phase, which reflects the geometric metric of elementary FQH droplets. It also captures intrinsic modular information like topological spin and chiral central charge. These findings not only provide a unified description of Berry phase induced by geometric deformation, but also provide a systematical way to inspect the incompressibility of a gapped topological order in the projected Landau level. 
Tuesday, March 3, 2020 12:51PM  1:03PM 
G54.00009: Particlehole symmetry of the fractional quantum Hall effect in the lowest Landau level Eduardo Palacios, Michael R Peterson Electrons confined to twodimensions experience the fractional quantum Hall effect (FQHE) at low electron densities, high magnetic fields, and low temperatures. FQHE states are topologically ordered phases characterized by the electron filling factor ν which is the electron number divided by the Landau level degeneracy. Alternatively, under particlehole conjugation of a spinpolarized system confined to a single Landau level one can consider the system in terms of holes (the absence of an electron) with a hole filling factor of νh = 1  ν. Naively, if the system maintains particlehole symmetry, then the FQHE at filling factor ν will also occur at 1 ν with all the same properties. However, realistic effects such as Landau level mixing can break particlehole symmetry at the level of the Hamiltonian through the inclusion of threebody terms. We study the nature of particlehole symmetry on the FQHE in the lowest Landau level under realistic conditions numerically using exact diagonalization. 
Tuesday, March 3, 2020 1:03PM  1:15PM 
G54.00010: Identification of topological orders in fractional quantum Hall state at ν=1/4 Kwok Wai Ma The nature of the fractional quantum Hall state at quarter filling in a wide quantum well is still under debate. Both onecomponent nonAbelian and twocomponent Abelian orders have been proposed to describe the system. Interestingly, these candidates received support from different experiments under disparate conditions. In this article, we focus on nonAbelian orders from Cooper pairing between composite fermions and the Abelian Halperin(5,5,3) order. We discuss and predict systematically different experimental signatures to identify them in future experiment. In particular, we address the MachZehnder interferometry experiment and show that it can identify the recently proposed 22111 parton order. 
Tuesday, March 3, 2020 1:15PM  1:27PM 
G54.00011: Anomalous nematic states in halffilled high Landau levels Xiaojun Fu, Qianhui Shi, Michael Zudov, Geoff C Gardner, John Watson, Michael Manfra, K. W. Baldwin, Loren Pfeiffer, Kenneth West It is well established that the ground states of a twodimensional electron gas with halffilled high (N ≥ 2) Landau levels are compressible chargeordered states, known as quantum Hall stripe (QHS) phases. The generic features of QHSs are a maximum (minimum) in a longitudinal resistance R_{xx} (R_{yy}) and a nonquantized Hall resistance R_{H}. This talk will report on emergent minima (maxima) in R_{xx} (R_{yy}) and plateaulike features in R_{H} in halffilled N ≥ 3 Landau levels. Remarkably, these unexpected features emerge at temperatures considerably lower than the onset temperature of QHSs, suggestive of a new ground state. 
Tuesday, March 3, 2020 1:27PM  1:39PM 
G54.00012: Straininduced resistance anisotropy near the FQHE v=5/2 in twodimensional GaAs single quantum wells Alexander Stern, Brian Casas, Johannes Pollanen, James Eisenstein, Kenneth West, Loren Pfeiffer, Jing Xia We report straindependent low temperature magnetotransport measurements of a twodimensional electron gas (2DEG) confined in GaAs single quantum wells. The samples are mounted to a piezoelectricbased strain device with which we can, in situ, apply and vary tensile strain. With this apparatus, we have achieved strain as large as ~0.5% in GaAs quantum wells at cryogenic temperatures. We find that increasing strain causes the magnetoresistance of the 2DEG confined in the quantum well to become anisotropic near the filling factor v = 5/2. Additionally, we find that the effects of strain are highly dependent on the magnitude of the magnetic field applied. These anisotropic states are metastable and resume an isotopic state after a temperature dependent decay. 
Tuesday, March 3, 2020 1:39PM  1:51PM 
G54.00013: Density Functional Theory of the Abelian Anyon Gas Yayun Hu, Ganpathy Murthy, Sumathi Rao, Jainendra Jain A KohnSham density functional theory of composite fermions takes into account the flux attached to composite fermions in a selfconsistent fashion [1]. We extend this method to treat a system of many anyons. We construct a series of states that do not involve the center of mass excitations, and explore behavior in the vicinity of the fermionic statistics. We compare the energy obtained from our DFT calculation with exact energies known for small systems and find a qualitative and semiquantitative agreement. Our method provides an understanding of the existing exact result and also a selfconsistent way to calculate the ground state properties of the anyon gas in the thermodynamic limit. 
Tuesday, March 3, 2020 1:51PM  2:03PM 
G54.00014: From CFT matrix product states to parent Hamiltonians Matheus Schossler, Sumanta Bandyopadhyay, Alexander Seidel


G54.00015: Manifestations of the Uniform Berry Curvature in the Physics of Composite Fermions GUANGYUE JI, Junren Shi It was proposed that the composite fermion is subject to a uniform Berry curvature in the momentum space [1]. Based on the picture, we theoretically consider a number of possible manifestations of the uniform Berry curvature. We show that the presence of the Berry curvature induces a shift in the commensurability condition of the geometrical resonance experiments. We argue that the shift had actually been observed in experiments. We further show that an electrostatic modulation, which is equivalent to a modulation of the ChernSimons field of composite fermions, and the modulation of an externally applied magnetic field, yield different commensurability conditions. Moreover, we determine the lowfrequency and long wavelength electromagnetic responses of a composite fermion system, and find results different from both the HalperinLeeRead theory and Son's Dirac theory. 
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