Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session M56: Fractional Quantum Hall and Non-Fermi Liquids |
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Sponsoring Units: DCMP Chair: Andres Felipe Schlief Raether, Max Planck Institute for the Physics of Complex Systems Room: Mile High Ballroom 2C |
Wednesday, March 4, 2020 11:15AM - 11:27AM |
M56.00001: Fractional Quantum Hall Effect from Hilbert Space Algebra and New Approaches for Experimental Realisation Bo Yang, Ying-Hai Wu, Zlatko Papic We show that model states of fractional quantum Hall (FQH) fluids for many topological phases can be uniquely determined by the Hilbert space algebra manifested as the classical reduced density matrix constraints, or the local exclusion constraint (LEC). The scheme allows us to identify filling factors, topological shifts and clustering of topological quantum fluids universally without resorting to microscopic Hamiltonians. Elementary excitations of the FQH phases can also be characterised by the LECs. More interestingly, the LEC formalism leads to a new perspective for the FQH model Hamiltonians, which can now be understood as a the von Neumann lattice of local potentials. This suggests a completely new way of experimentally realising the FQH states, including the coveted non-Abelian states (e.g the Moore-Read and Fibonacci states). We show that by tuning the local one-body potential profile, one can effectively tune the individual pseudopotentials (not just two-body, but few-body pseudopotentials) independently, and this can be done in experiments in principle. (related arXiv papers: Bo Yang, arXiv: 1901.00047, Bo Yang, Ajit Balram, arXiv:1907.09493, Bo Yang, Ying-Hai Wu, Zlatko Papic, arXiv:1907.12572) |
Wednesday, March 4, 2020 11:27AM - 11:39AM |
M56.00002: Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states Ajit Coimbatore Balram, Maissam Barkeshli, Mark Rudner The fractional quantum Hall (FQH) effect encompasses a wide range of quantum many-body phases which are characterized by exotic topological orders. Among these, the Read-Rezayi (RR) states harbor parafermionic excitations, whose non-Abelian braiding properties could potentially be used to carry out fault-tolerant quantum computation. Recent intriguing numerical results indicate that the 12/5 FQH state realized in GaAs could be described by the particle-hole conjugate of an RR state. However, numerically constructing the RR states for large systems, which is necessary for their characterization and for the demonstration of the exotic properties of their excitations, is computationally prohibitive. In this work, we use the parton framework to construct states that lie in the same phases as the particle-hole conjugates of the RR states. A nice feature of our parton states is that their wave functions can be evaluated for very large system sizes, thus, paving the way for the numerical investigation of parafermions. |
Wednesday, March 4, 2020 11:39AM - 11:51AM |
M56.00003: Bosonic Integer and Fractional Quantum Hall effect in an interacting lattice model Gaurav Kumar Gupta, Krishnamurthy H. R., Subhro Bhattacharjee We explore the presence of bosonic integer, as well as the fractional quantum Hall effect in an interacting lattice model. Our model is defined over the bipartite honeycomb lattice with $\pi$ magnetic flux per unit cell and is populated by bosons with hardcore constraint. The bosons can hop to the nearest neighbor (simple hopping) and to the next nearest neighbor (correlated hopping). We use the Lanczos algorithm (Exact Diagonalization (ED)) to find the ground state as well as a few excited states of the system with an aim to characterize the different phases of the system. We have performed calculations for two different fillings and provide evidence for the presence of the bosonic integer quantum Hall effect (BIQHE) and the bosonic fractional quantum Hall effect (BFQHE). We also show the phase transition from the bosonic quantum Hall state to the superfluid (SF) state. We have also performed the adiabatic flux threading to confirm the presence of quantum Hall states. |
Wednesday, March 4, 2020 11:51AM - 12:03PM |
M56.00004: Parafermions in Hierarchical Fractional Quantum Hall States Luiz Santos Non-Abelian quasiparticles are sought-after building blocks of fault-tolerant quantum computation. These quasiparticles can occur as extrinsic defects on interfaces and edges of two-dimensional Abelian topological phases, of which the Fractional quantum Hall (FQH) effect provides the most abundant realization. In this talk, we will discuss the properties of parafermion zero modes that arise as extrinsic non-Abelian defects in domain walls formed on interfaces of hierarchical FQH Jain states with filling fraction p/(2mp+1) of the lowest Landau level, where m and p are positive integers. Exploring the condensation of bulk Abelian anyons, we use Abelian bosonization to construct local interactions that gap modes with opposite chirality at the interface of two Jain states with the same filling fraction. We identify a class of such local interactions that breaks charge conservation and gives rise to an interface anyon condensate supporting parafermion zero modes whose quantum dimension reflects the topological order and the hierarchy of the bulk FQH Jain state. Our results shed light on the hierarchy of non-Abelian defects in two-dimensional Abelian topological phases. Reference: arXiv:1906.07188 |
Wednesday, March 4, 2020 12:03PM - 12:15PM |
M56.00005: Josephson frequency of fractional charges from Shot Noise measurements Maëlle Kapfer, Preden Roulleau, Matthieu Santin, Ian Farrer, David A Ritchie, Christian Glattli The determination of the quasiparticles charge e* is crucial to understand the Fractional Quantum Hall Effect (FQHE) phases occurring at fractional filling factors ν. Among various attempts to measure e*, the most reliable were based on the tiny shot noise produces by their granularity1,2. However, for complex FQHE states such as ν=2/5 or 2/3, noise measurements may give unexpected charges depending on experimental conditions3,4. Here, we present a novel fractional charge measurement based on the Josephson frequency fj=e*V/h which manifests as singularities in the Photo-Assisted Shot Noise (PASN) when fj matches the microwave irradiation frequency f. Measurements are done on a QPC realized on high mobility GaAs/AlGaAs heterojunctions. Cross-correlated and auto-correlated current fluctuations are recorded to provide the shot noise. The Josephson frequency gives e*=e/5 for v=2/5, while for v=1/3 fj gives e*=e/3 even at low temperature. |
Wednesday, March 4, 2020 12:15PM - 12:27PM |
M56.00006: Absence of diffusion on the edge Luca Delacretaz, Paolo Glorioso The edge of a FQH droplet supports gapless excitations that are protected by a U(1) anomaly. At small but finite temperature, diffusive spreading is expected to occur around the chiral ballistic front. We show that this chiral diffusive fixed point is never stable. Hydrodynamic long-time tails give large corrections to dissipative transport on the edge, leading to a breakdown of diffusion. We comment on the connection to a possible lack of thermalization in the nu=5/2 state. |
Wednesday, March 4, 2020 12:27PM - 12:39PM |
M56.00007: Consequences of Chern bands in twisted bilayer graphene Shubhayu Chatterjee, Nick Bultinck, Michael Zaletel In magic angle twisted bilayer graphene (TBG), alignment of hexagonal Boron Nitride (h-BN) substrate with one or both graphene monolayers can lead to nearly flat Chern bands labeled by valley and spin indices. At odd-fillings, we discuss how interaction effects in topologically non-trivial bands lead to a ferromagnetic Chern insulator with an anomalous Hall conductance that has been recently observed [1,2]. At the even filling of 2 of 4 conduction bands, we argue that charged skyrmions (allowed by Chern bands) offer a natural explanation of the magnetoresistance [1]. Finally, we discuss how the Chern character of the bands also places strong constraints on superconductivity in TBG. |
Wednesday, March 4, 2020 12:39PM - 12:51PM |
M56.00008: Microscopic theory for the nematic fractional quantum Hall effect Bo Yang We analyse various properties of the nematic fractional quantum Hall effect (FQHE) in the thermodynamic limit, and present necessary conditions required of the microscopic Hamiltonians for the nematic FQHE to be robust. Analytical expressions of the degenerate ground state manifold, ground state energies, and gapless Goldstone modes are given in compact forms with the input interaction and the corresponding ground state structure factors. We relate the long wavelength limit of the neutral excitations (serving as the nematic FQHE ground state from spontaneous symmetry breaking) to the guiding center metric deformation, and show explicitly the family of trial wavefunctions for the Goldstone modes with spatially varying nematic order. We show for short range interactions, the dynamics of the nematic FQH is completely determined by the long wavelength part of the ground state structure factor. This is the only part that requires numerical studies in the future work, which is potentially more tractable than the conventional numerical approaches. |
Wednesday, March 4, 2020 12:51PM - 1:03PM |
M56.00009: Probing Nonlinear Luttinger liquid Physics in Semiconducting Single Walled Carbon Nanotubes Sheng Wang, Sihan Zhao, Zhiwen Shi, Fanqi Wu, Zhiyuan Zhao, Lili Jiang, Kenji Watanabe, Takashi Taniguchi, Alex Zettl, Chongwu Zhou, Feng Wang Quantum-confined electrons in one dimension (1D) constitute a Luttinger liquid, which features charge spin separation and other intriguing properties distinctly different from the Fermi liquid. Single walled carbon nanotubes (SWNTs) provide the ideal platform to explore such Luttinger liquid physics due to strong lateral quantum confinement and the presence of nanotubes of different species. But in many 1D materials including semiconducting SWNTs, the deviation from linear dispersion can greatly alter the electron behaviors. In order to describe the high-energy electron behaviors in 1D materials with nonlinear band structures, novel theoretical approaches have been employed to replace the linear dispersion with a generic one, which is known as the nonlinear Luttinger liquid theory. Here we probe the nonlinear Luttinger liquid physics in semiconducting SWNTs by combining electronic transport and infrared nano-imaging methods. The electron behaviors in semiconducting SWNTs are well captured by the nonlinear Luttinger liquid theory and are in strong contrast to the linear Luttinger liquid as in metallic SWNTs. Our findings provide novel insight into 1D systems beyond the conventional linear Luttinger liquid paradigm. |
Wednesday, March 4, 2020 1:03PM - 1:15PM |
M56.00010: Observing a Hierarchy of Modes in a Finite-Length Nonlinear Luttinger Liquid Pedro Vianez, Wooi Kiat Tan, Oleksandr Tsyplyatyev, Yiqing Jin, Ankita Anirban, Anne Anthore, Ian Farrer, David A Ritchie, Jonathan Griffiths, Leonid Glazman, Christopher J B Ford It is notoriously hard to study theoretically interacting quantum systems outside the Luttinger-liquid regime, particularly when considering higher-energy excitations in finite 1D systems. Recent theoretical work has focused on extending this theory to include such regimes [1,2], where it is predicted that, for higher-order excitations, length-dependent 'replica' parabolic dispersions with higher momenta or negative effective mass should be observed. Our work focuses on the experimental detection and quantification of these higher-order modes. We measure momentum-resolved tunnelling of electrons to and from an array of 1D wires to a 2D electron system formed within a GaAs heterostructure, and map their dispersion both in the equilibrium and nonequilibrium regimes [3,4]. We present recent experimental data obtained for a variety of wire lengths where both first- and second-order replica modes can be observed. We also observe these features even when multiple subbands are occupied, beyond the regime of the models. |
Wednesday, March 4, 2020 1:15PM - 1:27PM |
M56.00011: Competing phases and critical phenomena in three coupled spinless Luttinger liquids Sarbajaya Kundu, Vikram Tripathi Coupled one-dimensional systems of interacting fermions appear in diverse contexts, and bosonization, along with a scaling treatment, is the usual method for studying low-energy properties of such systems. If three or more fermionic species are present, the scaling procedure generically introduces off-diagonal corrections to the stiffness matrix in the quadratic part of the bosonized Hamiltonian, requiring both rescaling as well as large rotations of the fields. In this talk, I will discuss phase competition in a system of three coupled spinless Luttinger liquids, using bosonization, along with a renormalization group analysis which takes into account these rotations, generating a coupling between different interaction channels even at the tree-level order in the coupling constants. I will further discuss the different instabilities in the particle-particle and particle-hole channels, the nature of the phase transitions, and the conditions under which valley symmetry breaking and intervalley orders may appear. These results may be directly relevant for systems with multiple small Fermi pockets (like graphite intercalates and bismuth) subject to quantizing magnetic fields, and cylindrical nanotubes at high fields. |
Wednesday, March 4, 2020 1:27PM - 1:39PM |
M56.00012: Confinement Tuning of Non Magnetic Fractional Quantized Conductance Sanjeev Kumar, Michael Pepper, David A Ritchie, Ian Farrer There has been considerable interest in the possibility of fractional quantization of conductance in the absence of a magnetic field [1]. In the absence of spin-orbit coupling, appropriate systems have been modelled as 2D lattice site with a flat potential. In this work, we have investigated electron transport of a weakly confined quasi-1D quantum wire formed in a GaAs/AlGaAs heterostructure. The conductance measured almost on the verge of the 2D transition, resulted in conductance plateaux (in units of e2/h) dependent on confinement conditions. Thus flat plateau can be observed with both even and odd denominators such as 1/6, 1/2 and 2/5.. On the application of a fixed in-plane magnetic field of 10T, additional plateaux at 2/5 and 2/7 appeared as a function of increasing asymmetry in confinement potential. We suggest that the Coulomb interactions between electrons create correlated motion and formation of a zigzag array of electrons with a consequent emergence of fractional behavior [2,3]. |
Wednesday, March 4, 2020 1:39PM - 1:51PM |
M56.00013: Super van Hove singularities in graphene-like materials Baokai Wang, Bahadur Singh, Robert Markiewicz, Arun Bansil We discuss the crossover from weak to strong correlations in Dirac materials by analyzing the excitonic insulator (EI) transition in a paradigmatic family of ‘slow’ graphenes. We consider the exciton modes at Q = (0, 0) and (π, 0), and show that pristine graphene is free of an excitonic instability. When the band structure is compressed, a gap opens first in a Q = (π, 0) EI phase before a Q = (0, 0) EI phase is triggered when the bands are further compressed. The gap in the Q = (π, 0) phase dominates over that in the the Q = (0, 0) phase throughout the band compression process. Interestingly, we find the presence of high order van Hove singularities1 in both the EI phases driven by the interaction-induced changes in the band structure. Our study suggests that two-dimensional slow graphenes could provide a novel platform for exploring the physics of EI phases and high order van Hove singularities. |
Wednesday, March 4, 2020 1:51PM - 2:03PM |
M56.00014: Topological Orders and Phase Transitions in Hofstadter-Chern Bands Jian Wang, Luiz Santos The quantum Hall effect provides a realization of topological phases of matter in the presence of an external magnetic field. In conventional semiconductors, the achieved magnetic flux per unit cell is orders of magnitude smaller than the magnetic flux quantum h/e, giving rise to degenerate Landau levels enabling strong electronic correlations. Motivated by the realization of two-dimensional moiré superlattices with unit cell of few to hundreds of nanometers in linear size, we discuss a lattice composite fermion theory that accounts for topological states in the opposite regime where the magnetic flux per unit cell is of the order of the magnetic flux quantum, which gives rise to Hofstadter-Chern bands that can be partially filled by electrons. Through analytical and numerical methods, we uncover classes of candidate topological states beyond the Landau level regime, which are characterized by strong coupling of electronic states with the lattice. We explore this setting to establish the existence of topological phase transitions mediated by modulations of the lattice potential. Our study, therefore, identifies new topological orders and how to manipulate them in two-dimensional Hofstadter-Chern lattices. |
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