Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session R01: Fractional Quantum Hall Effect: Novel States |
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Sponsoring Units: DCMP Chair: Ravindra Bhatt, Princeton University Room: BCEC 106 |
Thursday, March 7, 2019 8:00AM - 8:12AM |
R01.00001: Incompressible Even Denominator Fractional Quantum Hall States in the Zeroth Landau Level of Monolayer Graphene SUJIT NARAYANAN, Bitan Roy, Malcolm Kennett Incompressible fractional quantum Hall states at even denominator fractions (ν = 1/2, 1/4) have recently been observed in experiments in monolayer graphene. We use a Chern-Simons description of multicomponent fractional quantum Hall states in graphene to study these incompressible fractional quantum hall states in the zeroth Landau level and suggest variational wavefunctions that may describe them. We find that the experimentally observed even denominator fractions and standard odd fractions (such as ν = 1/3, 2/5, etc.) can be accommodated within the same flux attachment scheme and argue that they may arise from sublattice or chiral symmetry breaking orders (such as charge-density-wave and antiferromagnetism) of composite Dirac fermions. We also discuss possible experimental probes that can narrow down the candidate broken symmetry phases for the fractional quantum Hall states in the zeroth Landau level of monolayer graphene. |
Thursday, March 7, 2019 8:12AM - 8:24AM |
R01.00002: Pfaffian paired states at filling factor 5/2 Milica Milovanovic, Jaksa Vucicevic, Luka Antonic Within the Dirac composite fermion theory of fractional quantum Hall effect (FQHE), we investigate which Pfaffian paired state will dominate at a fixed value of a particle-hole (PH) symmetry breaking parameter - the mass of Dirac composite fermions. The Dirac mass mimics the presence of Landau level mixing in experiments. We demonstrate that the presence of mass stabilizes PH Pfaffian topological pairing contrary to our naive expectation that the PH Pfaffian will be relevant for the (zero-mass) PH symmetric case. Using only field theoretical means we show that, due to gauge field effects, there is a strong competition among Pfaffians; depending on the sign of mass, Pfaffian or anti-Pfaffian will dominate for small masses, consistent with numerical experiments at filling factor 5/2, and PH Pfaffian may be present for larger masses. L. Antonic, J. Vucicevic, and M.V. Milovanovic, Paired states at 5/2 : Particle-hole Pfaffian and particle-hole symmetry breaking, Physical Review B 98, 115107 (2018). |
Thursday, March 7, 2019 8:24AM - 8:36AM |
R01.00003: A Study of Reentrant Integer Quantum Hall States in High Landau Levels DOHYUNG RO, Nianpei Deng, Michael Manfra, Loren Pfeiffer, Kenneth West, Gabor Csathy Reentrant integer quantum Hall states are widely thought to be realizations of the so called electronic bubble phases, some of the most intricate electron solids forming in the two-dimensional electron gas. According to the predictions of the Hartree-Fock theory, different types of bubble phases may exist, as distinguished by the number of electrons per bubble. So far, in the third and higher Landau levels four reentrant integer quantum Hall states were seen. Here we report the observation of eight reentrant integer quantum Hall states developing in the fourth Landau level. Properties of these reentrant states will be discussed. Our observation highlights the development of correlated phases of increasing complexity in improved samples and support the bubble interpretation of the reentrant integer quantum Hall states. |
Thursday, March 7, 2019 8:36AM - 8:48AM |
R01.00004: Geometry of flux attachment in anisotropic fractional quantum Hall states Ravindra Bhatt, Matteo Ippoliti, Frederick D Haldane We study the internal metric of fractional quantum Hall (FQH) states, a degree of freedom which allows them to variationally optimize their energy in the presence of competing geometries. In particular, we focus on incompressible FQH states in the presence of isotropic Coulomb interaction and anisotropic band mass [1]. We use an infinite-cylinder density matrix renormalization group method [2] to numerically simulate these states and access their internal metric through the long-wavelength limit of their static guiding center structure factor. We find the response to band mass anisotropy is approximately the same for all states belonging to the first Jain sequence (ν = 1/3, 2/5, …). The ν = 1/5 state, on the other hand, exhibits markedly smaller anisotropy. The observed behavior is well captured by a two-body model of flux attachment. |
Thursday, March 7, 2019 8:48AM - 9:00AM |
R01.00005: Working principles of the short-period superlattice structure in GaAs quantum wells Edwin Chung, K. W. Baldwin, Kenneth West, Mansour Shayegan, Loren Pfeiffer We present the design rules of GaAs quantum wells that utilize the short-period superlattice (SPSL) structure to achieve a two dimensional electron system (2DES). By changing growth conditions such as doping density, barrier composition, and well width within the SPSL, we show that the density of the 2DES can be tuned from 2.0 x 10^{11} cm^{-2} to 4.5 x 10^{11} cm^{-2} even with a fixed spacer thickness. This implies we can prepare samples that have quite different 2DES density but rather similar scattering conditions. The magnetotransport is analyzed in detail and the influence of the change in 2DES density is discussed, with an emphasis on the strength of the fraction quantum Hall states. |
Thursday, March 7, 2019 9:00AM - 9:12AM |
R01.00006: A recursion approach to thin cylinder approximants for fractional quantum Hall states Matheus Schossler, Sumanta Bandyopadhyay, Alexander Seidel Aside from the beautiful many-body wave functions that have defined the field, recursive and/or second-quantized presentations of fractional quantum Hall states have played an increasingly important role in the past. Examples include the recent discovery of the MPS structure of many quantum Hall states, but also a recursion for the Laughlin state related to the “non-local order parameter’’ defined by Read, originally defined in a mixed first/second quantized manner. Such recursions have recently been generalized to all composite fermion states, and put into a purely second-quantized, “all guiding-center’’ form. Here we observe that these recursions commute with the expansion of cylinder fractional quantum hall states in a “thin-cylinder parameter’’. This allows one to define not only the full quantum Hall state recursively, but also any “thin cylinder approximant’’, to any order. Relations/differences with the MPS are discussed, and we speculate on broader implications for DMRG approaches to quantum Hall states, in particular the efficient evaluation of non-local order parameters. |
Thursday, March 7, 2019 9:12AM - 9:24AM |
R01.00007: Evidence for an even-denominator fractional quantum Hall state in the ground Landau level of an anisotropic system Md. Shafayat Hossain, Meng Ma, Edwin Chung, Loren Pfeiffer, Kenneth West, K. W. Baldwin, Mansour Shayegan Even-denominator fractional quantum Hall states (FQHSs) are widely believed to host a novel class of matter that obey non-Abelian statistics and could be of potential use in topological quantum computing. Examples of such states include the ν = 5/2 FQHS in GaAs two-dimensional (2D) electron systems. Even-denominator FQHSs have also been reported in both 2D electron and 2D hole systems confined to wide GaAs quantum wells, in bilayer GaAs 2D electron systems and, more recently, in 2D electrons in ZnO and in graphene. We report here the observation of an even-denominator FQHS at filling factor ν = 1/2 in a 2D electron system confined to a wide AlAs quantum well where the electrons can occupy multiple conduction-band valleys with an anisotropic effective mass. We observe phase transitions from a compressible Fermi liquid to an incompressible FQHS and then to an insulating phase as we tilt the sample in the magnetic field, thus rendering the electron charge distribution more bilayer-like. |
Thursday, March 7, 2019 9:24AM - 9:36AM |
R01.00008: Hall viscosity of manifestly modular invariant composite fermion wave functions Songyang Pu, Jainendra Jain The Hall viscosity has been proposed to be robust within a topological phase [1]. We perform a numerical calculation of the Hall viscosity of general fractional quantum Hall states by deforming the modular parameter $\tau$ on a torus. For this purpose, we follow the approach in [2] to construct composite fermion wave functions on a torus in terms of Haldane’s modified sigma function [3] to achieve a manifestly modular invariant form. (Numerical calculations show that the wave functions in this new form are identical to those in Ref. [2], therefore proving modular invariance for the latter wave functions as well.) We compare our Hall viscosities with the orbital spins for various fractional quantum Hall states in a broad region of the modular parameter $\tau$. |
Thursday, March 7, 2019 9:36AM - 9:48AM |
R01.00009: Kohn-Sham Theory of the Fractional Quantum Hall Effect Yayun Hu, Jainendra Jain The Kohn-Sham (KS) formulation of the density functional theory (DFT) fails for FQHE because the FQHE state cannot be mapped into a system of non-interacting electrons. We instead map the FQHE system into a system of non-interacting composite fermions, which experience an effective magnetic field that depends on density. We generalize the Hohenberg-Kohn theorem to systems with a density-dependent kinetic energy operator, and formulate the KS equations for the FQHE. We also show the equivalence of our formulation with the generalized Kohn-Sham scheme. Numerical results show that our method produces densities that are good approximations to those obtained from many-body wave functions for states with general occupation configurations. As two applications of our method, we (i) obtain the density profile at the edge of fractional quantum Hall states, finding edge reconstruction as the confinement potential becomes softer; and (ii) show how an external charge produces a screening cloud with a fractionally quantized charge accumulation. We speculate on the implications of our method for general strongly correlated systems. |
Thursday, March 7, 2019 9:48AM - 10:00AM |
R01.00010: Fixed phase diffusion Monte Carlo study of finite width effect in FQHE Tongzhou Zhao, Jainendra Jain In FQHE, it is customary to include finite width effects by calculating the transverse wave function at zero magnetic field in LDA, and assuming that it does not change as a high perpendicular magnetic field is applied. We instead determine the transverse density profile directly at a high magnetic field through the fixed phase diffusion Monte Carlo method, where the phase is fixed by the in-plane FQHE state. While the results are in qualitative agreement with those obtained from zero-field LDA, there are interesting quantitative deviations. We will discuss the implications of our study to experiments. |
Thursday, March 7, 2019 10:00AM - 10:12AM |
R01.00011: Composite fermions with quenched disorder at the half-filled Landau level Prashant Kumar, Kevin Shengyi Huang, Michael C Mulligan, Srinivas Raghu The gapless state at the half-filled Landau level is approximately described in terms of nearly-free composite fermions. Within the mean-field approximation, it has recently been shown that the composite fermions describe a quantum phase transition between an insulator and an integer quantum Hall state when the effects of a quenched disorder are included. Here, we further characterize this random quantum critical point using the non-linear sigma model and network model approaches to disordered fermions. |
Thursday, March 7, 2019 10:12AM - 10:24AM |
R01.00012: Observation of new plasmons in the fractional quantum Hall effect: interplay of topological and nematic orders(*) Lingjie Du, Ursula Wurstbauer, Saeed Fallahi, Geoffrey Gardner, Michael Manfra, Loren Pfeiffer, Kenneth West, Aron Pinczuk Collective modes of exotic quantum fluids reveal underlying physical mechanisms responsible for emerging ground states. We observe unexpected collective modes in the fractional quantum Hall (FQH) regime of the second Landau level (LL): intra-Landau-level plasmons measured by resonant inelastic light scattering. The plasmons herald nematic phases in the second LL and uncover the nature of long-range translational invariance in these phases. The fascinating dependence of plasmon features on filling factor provides new insights on interplays between topological quantum Hall order and nematic electronic liquid crystal phases. At LL filling factor v = 7/3, a sharp and strong plasmon peak that links to emerging macroscopic coherence supports the proposed model of a FQH nematic state at this filling factor. A marked intensity minimum in the plasmon spectrum at v = 5/2 strongly suggests that the paired state overwhelms competing nematic phases, unveiling the robustness of the superfluid state. |
Thursday, March 7, 2019 10:24AM - 10:36AM |
R01.00013: Half-filled Landau level in a honeycomb lattice: Chern insulator of composite fermions Saurabh Maiti, Tigran Sedrakyan The study of electronic correlations in half-filled Landau level presents a challenge due to the massive degeneracy in the single-particle spectrum. The most successful description of this exotic state has been in terms of field theory of composite fermions: either the Halperin-Lee-Read (HLR) version where the composite fermions are the original electrons bound to some fluxes; or the Dirac composite fermion which exploits the duality of the field strength and density. In this work we demonstrate the construction of a lattice version of the long-wavelength field theories. We show that for a honeycomb lattice, a HLR type construction of composite fermions leads to a Chern insulator which reduces to the Haldane model at half-filling. As a result, the K and K’ points are gapped out which can be measured in tunneling experiments. |
Thursday, March 7, 2019 10:36AM - 10:48AM |
R01.00014: Probing the Melting of Two-dimensional Quantum Wigner Crystal via its Screening Efficiency Hao Deng, Meng Ma, Loren Pfeiffer, Kenneth West, K. W. Baldwin, Mansour Shayegan One of the most fundamental and yet elusive collective phases of an interacting electron system is the quantum Wigner crystal (WC), an ordered array of electrons dominated by Coulomb repulsion energy. In low-disorder, two-dimensional (2D) electron systems, the quantum WC is known to be favored at very low temperatures (T) and small Landau level filling factors (ν). Pinned by the disorder potential, the WC phase exhibits an insulating behavior. An experimental determination of a T vs ν phase diagram for the melting of the WC, however, has proved to be challenging. Here we use capacitance measurements to probe the 2D WC thorough its effective screening as a function of T and ν. We find that, as expected, the screening efficiency of the pinned WC is very poor at very low T and improves at higher T once the WC melts. Surprisingly, the screening efficiency shows a well-defined maximum at a T which is close to the previously-reported melting temperature of the WC. Our experimental results suggest a new method to map out the T vs ν phase diagram of the magnetic-field-induced WC precisely. |
Thursday, March 7, 2019 10:48AM - 11:00AM |
R01.00015: Aharonov-Bohm interference of integer and fractional quantum Hall edge modes in small electronic Fabry-Perot interferometers James Nakamura, Saeed Fallahi, Shuang Liang, Geoffrey Gardner, Michael Manfra Electronic Fabry-Perot interferometers may be used to probe quantum Hall edge states; however, Coulomb charging effects complicate the operation of small devices. We implement a novel GaAs/AlGaAs heterostructure design in which Coulomb charging effects are suppressed, enabling operation of small interferometers in the Aharonov-Bohm regime with high quantum coherence. We present measurements of the selective interference of inner and outer edge states in the integer quantum Hall regime. Aharonov-Bohm oscillations are observed at the fractional quantum Hall states ν = 2/3 and ν = 1/3. |
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