Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session P45: Quantum Hall Physics |
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Sponsoring Units: DCMP Chair: David Parker, Oak Ridge National Laboratory Room: LACC 505 |
Wednesday, March 7, 2018 2:30PM - 2:42PM |
P45.00001: Entangled Pauli Principles: the DNA of Quantum Hall Fluids Sumanta Bandyopadhyay, Li Chen, Mostafa Ahari, Gerardo Ortiz, Zohar Nussinov, Alexander Seidel A formalism is developed for the rigorous study of solvable fractional quantum Hall parent Hamiltonians with Landau level mixing. The idea of organization through ``generalized Pauli principles'' |
Wednesday, March 7, 2018 2:42PM - 2:54PM |
P45.00002: Transport signatures of Hall viscosity Luca Delacretaz, Andrey Gromov Hall viscosity is a non-dissipative response function describing momentum transport in two-dimensional systems with broken parity. It is quantized in the quantum Hall regime, and contains information about the topological order of the quantum Hall state. Hall viscosity can distinguish different quantum Hall states with identical Hall conductances, but different topological order. To date, an experimentally accessible signature of Hall viscosity is lacking. We exploit the fact that Hall viscosity contributes to charge transport at finite wavelengths, and can therefore be extracted from non-local resistance measurements in inhomogeneous charge flows. We explain how to determine the Hall viscosity from such a transport experiment. In particular, we show that the profile of the electrochemical potential close to contacts where current is injected is sensitive to the value of the Hall viscosity. |
Wednesday, March 7, 2018 2:54PM - 3:06PM |
P45.00003: MBE Grown Bismuth Thin Films for Hydrodynamic Transport Studies Shuo-Ying Yang, Kai Chang, Kumari Gaurav Rana, Stuart S Parkin In quantum many-body systems, interactions between particles can lead to electron transport behaving as viscous liquid flow that is governed by hydrodynamic equations. The hydrodynamic regime is entered when the length scales are shorter than the electron mean-free path. Bi has long been known for its unusual electronic properties due to its low carrier concentration, small carrier effective mass, and long carrier mean free paths, making it a strong candidate to study for the hydrodynamic physics. In this work, we probe the signatures of hydrodynamic transport in MBE grown Bi films. Varying thickness of Bi films are grown epitaxially on Bi_{2}Te_{3} with Al_{2}O_{3} substrates. The few nanometer Bi_{2}Te_{3} buffer layer allows wetting of the Bi film which does not occur on the oxide substrate. The films are then patterned by electron beam lithography and etched by Ar plasma to channels as narrow as hundreds of nanometer wide. Because the channel width is narrower than the electron mean-free path, a shear force induced by viscosity is expected at the channel walls to make electron velocity profile of a Stokes flow and resistivity varies with the square of the channel width. The results of these experiments as well as analysis of the SdH oscillations of the Bi channels will be presented. |
Wednesday, March 7, 2018 3:06PM - 3:18PM |
P45.00004: Chaos Along the Edge of the 2/3 Fractional Quantum Hall State Hamed Asasi, Michael Mulligan Hierarchical fractional quantum Hall states, like that at filling fraction equal to 2/3, are believed to consist of several branches of chiral edge modes [Phys. Rev. Lett. 64, 220 (1990)]. In this picture, equilibration between edge modes is necessary to explain the universal (fractionally) quantized Hall conductance [Phys. Rev. Lett. 72, 4129 (1994)]. To probe this equilibration, we study out-of-time-ordered correlation functions in the theory for the 2/3 fractional quantum Hall edge. These correlation functions provide a diagnostic of chaotic behavior in classical systems. To study the interplay of these correlation functions with electrical transport, we calculate their dependence on (short-ranged) electron-electron interactions and the interaction with disorder. |
Wednesday, March 7, 2018 3:18PM - 3:30PM |
P45.00005: Time-reversal-symmetry-broken nematic insulators near quantum spin Hall phase transitions Fei Xue, Allan MacDonald Quantum spin Hall insulators have drawn attention in recent years because they support time-reversal symmetry protected helical edge states. We study the phase diagram of a model quantum spin Hall system as a function of band inversion and band-coupling strength, demonstrating that when the latter is weak, an interaction induced nematic insulator state emerges over a wide range of band inversion. This property is a consequence of the long-range Coulomb interaction, which favors interband phase coherence that is weakly dependent on momentum and is therefore frustrated by the single-particle Hamiltonian at the band inversion point. For weak band hybridization, interactions convert the continuous gap-closing topological phase transition at inversion into a pair of continuous phase transitions bounding a state with broken time-reversal and rotational symmetry, and no gap closing. At intermediate band hybridization the topological phase transition proceeds instead via a Chern insulator state, whereas at strong hybridization interactions play no essential role. We comment on the implications of our findings for InAs/GaSb quantum spin Hall systems. |
Wednesday, March 7, 2018 3:30PM - 3:42PM |
P45.00006: Hall Viscosity in the Chern-Simons Matrix Model of the Laughlin Fractional Quantum Hall States Matthew Lapa, Taylor Hughes We compute the Hall viscosity in the Chern-Simons matrix model (CSMM) of the Laughlin fractional quantum Hall (FQH) states. The CSMM is a matrix quantum mechanics model proposed by Polychronakos as a regularization of the noncommutative Chern-Simons theory of the Laughlin states proposed by Susskind. Both models can be understood as describing the electrons in a FQH state as forming a noncommutative fluid, i.e., a fluid occupying a noncommutative space. Here we revisit the CSMM in light of recent work on geometric response in the FQH effect, with the goal of determining whether the CSMM captures this aspect of the physics of the Laughlin states. To compute the Hall viscosity in the CSMM we first identify the quantum operators which generate area-preserving deformations of the noncommutative fluid coordinates, and then compute the Hall viscosity using standard methods (e.g., the Kubo formula) from previous works. We find that the Hall viscosity in the CSMM with level m is exactly equal to the guiding center Hall viscosity of the Laughlin state with filling fraction 1/m as computed by Park and Haldane. Thus, our result confirms that these noncommutative models accurately describe (at least some aspects of) the geometric response of the Laughlin states. |
Wednesday, March 7, 2018 3:42PM - 3:54PM |
P45.00007: Multi-flavor QED3 as the Quantum Plateau Transitions of Fractional Chern Insulators Yin-Chen He, Jong Yeon Lee, Chong Wang, Michael Zaletel, Ashvin Vishwanath Recent experiments in graphene hetro-structures have revealed the existence of Chern Insulators - integer and fractional Quantum Hall states made possible by the presence of a periodic substrate potential. Here we show that the new kinds of quantum critical points are enabled by the interplay of magnetic fields, interactions and the periodic potential. We discuss transitions between distinct quantized Hall states using both microscopic models and effective field theories, and highlight two important differences from the well studied disorder driven plateau transition. (i) First, the periodic potential, rather than disorder, enables a change in the Hall conductance at a fixed magnetic field and electron density and (ii) the presence of translation symmetry allows for direct transitions between quantum Hall states that otherwise require fine tuning. Transitions between particle-hole conjugate Jain states take the form of `pure' QED3 with multiple flavors of Dirac fermions. |
Wednesday, March 7, 2018 3:54PM - 4:06PM |
P45.00008: Evolution of the optimal trial wave function of fractional Chern insulators with interactions Yumin Luan, Yinhan Zhang, Junren Shi We demonstrate the evolution of the optimal trial wave function of fractional Chern insulators(FCI) with interactions in checkerboard model. The gauge of the single particle Bloch states for constructing the optimal wave function is obtained by applying the interaction energy variational principle proposed by Zhang et al.. We consider the short-range interaction, coulomb interaction, and an interpolation between them. We find that the optimal gauge critically depends on the forms of interaction. In particular, we compare the optimal gauge with those proposed by Qi and Wu et al., and find that Wu et al.'s gauge can be close to the optimal gauge when interaction is close to coulomb interaction, while Qi's gauge is qualitatively different from the optimal gauge in all the cases. |
Wednesday, March 7, 2018 4:06PM - 4:18PM |
P45.00009: Symmetries and Fractionalization in Fractional Chern Insulators via a Composite Fermion Theory Ramanjit Sohal, Luiz Santos, Eduardo Fradkin Fractional Chern Insulators (FCIs) are two dimensional interacting lattice systems which realize analogues of the Fractional Quantum Hall Effect (FQHE). Like FQH states, FCIs possess anyonic excitations and so can exhibit symmetry fractionalization, a phenomenon in which the anyons transform projectively under the symmetries of the system. For instance, fractionalization of the U(1) symmetry of FQH states and FCIs leads to the anyons carrying fractional charge. FCIs also possess additional lattice symmetries; in particular, the lattice translational symmetry may be fractionalized resulting in anyons carrying fractional momenta. Previously, we developed a composite fermion theory of FCIs on a Kagome lattice model (wherein fermions are mapped to composite fermions coupled to a lattice Chern-Simons gauge field). We illustrate how, using this approach, a Kagome lattice model can support FCIs realizing a large range of translational symmetry fractionalization classes. Our formalism also opens the possibility of investigating the competition and coexistence of FCIs with symmetry-broken states. |
Wednesday, March 7, 2018 4:18PM - 4:30PM |
P45.00010: The Single-Mode Approximation for Chern Bands David Bauer, Fenner Harper, T.S. Jackson, Rahul Roy The single-mode approximation (SMA) provides a tool for studying the collective excitations and the stability of the many-body gap in fractional quantum Hall (FQH) systems. In the SMA, one considers trial excitations in the form of density operators projected to the relevant single-particle bands, which for FQH systems are Landau levels. We extend this analysis by considering projection to more general Chern bands. We find that the structure factor of a Chern band factors into universal/Landau level and non-universal/lattice pieces. This allows analytical study of collective excitation gap in fractional Chern insulator (FCI) states when perturbative expansion of the Chern bands is possible. We discuss connections between the SMA and quantum geometry of single-particle bands. |
Wednesday, March 7, 2018 4:30PM - 4:42PM |
P45.00011: From tensor categories of conformal field theories to membrane models and topological phases in three dimensions Akin Morrison, Meng Hua, Alexander Sirota, Jeffrey Teo Topological phases in two dimensions, such as quantum Hall states and chiral spin liquids, and their low-energy edge degrees of freedom are related by a bulk-boundary correspondence. It relates the topological structure of gapped anyonic quasiparticle excitations in the (2+1)D bulk to the emergent conformal field theory (CFT) that describes the gapless modes along the (1+1)D edge. There has been recent theoretical discussions on relationships, such as anyon condensation and gauging, between (2+1)D topological phases and correspondingly between their (1+1)D CFTs. A collection of CFTs, equipped with a closed tensor product structure relative to these relationships, forms a tensor category. We establish the general framework of such categories of CFTs, and discuss its prospects in describing (3+1)D topological phases. |
Wednesday, March 7, 2018 4:42PM - 4:54PM |
P45.00012: Edge Waves in Odd Fluids Tankut Can, Alexandre Abanov, Sriram Ganeshan, Gustavo Monteiro In a fluid of chiral particles, the explicit breaking of parity symmetry allows for the existence of a non-dissipative viscosity coefficient, known as the odd (a.k.a. Hall) viscosity. In many cases, the bulk fluid flow remains unaffected by this coefficient. However, the existence of odd viscosity has striking consequences on boundary flows. In this talk, I will discuss the phenomenology of edge waves in 2+1d non-relativistic fluids with odd (aka Hall) viscosity. In particular, we study free surface waves under the condition of vanishing stress. We find that the propagating edge waves at wave vector k are characterized by a universal dispersion 2 η k│k│ proportional to the odd viscosity . Furthermore, we find that the fluid flow exhibits a boundary layer which leads to singular flow solutions in the incompressible inviscid limit. Finally, we connect this phenomenology to electronic fluids in a magnetic field, in particular the quantum Hall effect, and discuss experimental signatures of the odd flow. |
Wednesday, March 7, 2018 4:54PM - 5:06PM |
P45.00013: Quantum Impurities in Interacting Environments Colin Rylands, Natan Andrei Quantum impurities were traditionally studied in metal which are typically modeled as Fermi Liquids in 3-d. A canonical example is the Kondo problem. Recently, however, new devices probe impurities in such interactingenvironments as carbon nanotubes, edges of QHE samples or of 2-d topological insulator. Now theoretical modeling and study of such systems reveals rich physics. This talk will present new exact results on the thermodynamic properties of several of these systems, study their critical properties and relate them to experimental data. |
Wednesday, March 7, 2018 5:06PM - 5:18PM |
P45.00014: Edge Reconstruction in Monolayer Graphene at and near ν=0 Amartya Saha, Ganpathy Murthy Monolayer graphene in a magnetic field at ν=0 theoretically displays a variety of phases, |
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