Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session R27: Fractional Quantum Hall Effect IV. |
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Sponsoring Units: FIAP Chair: F.D.M. Haldane, Princeton University Room: 290 |
Thursday, March 16, 2017 8:00AM - 8:12AM |
R27.00001: Holomorphic state within a Landau level: a new discrete formulation in periodic (torus) geometry F. D. M. Haldane It is widely believed that the holomorphic character of model states of particles projected into a Landau level (e.g., the Laughlin state) results from their being ``lowest Landau level Schr\"{o}dinger wavefunctions''. In fact this ``common wisdom'' is incorrect, as should have been obvious after the observation of a Laughlin-type state in the second Landau level. Indeed, even the notion that these states are described by a ``wavefunction'' is misleading, because non-locality after projection into (any) Landau level removes the possibility of using a local basis that defines $\Psi(\bm x)$ = $\langle \bm x|\Psi\rangle$, and a Heisenberg formalism must be used. I have found this reinterpretation of the holomorphic states is not just a ``debating point'' but leads to powerful new identities on the torus that were previously missed. I present a new discretized and modular-invariant formulation based on a ``lattice'' of $(N_{\Phi})^2$ points in the fundamental region through which $N_{\Phi}$ flux quanta pass. This mathematically-exact reformulation allows a greatly-improved (faster) formulation for Monte-Carlo studies of model FQH states, as well as explicitly implementing the physical requirement of modular invariance, and expansions in an orthonormal Landau basis. [Preview Abstract] |
Thursday, March 16, 2017 8:12AM - 8:24AM |
R27.00002: Fractional Quantum Hall Plateau Transitions and Composite Fermi Liquids Gil Young Cho, Eun-Gook Moon, Eduardo Fradkin We will investigate relationship between the fractional quantum Hall plateau transition from Laughlin state at $\nu = \frac{1}{2n+1}$ to a trivial insulator, and composite Fermi liquid at $\nu = \frac{1}{2(2n+1)}$. We use the recently-developed quantum field theoretic technique, 3d dualities, in combinations with the coupled-wire descriptions for quantum Hall states. We will show that we can also access various other phases, including non-abelian paired states at $\nu = \frac{1}{2(2n+1)}$, from the plateau transition. [Preview Abstract] |
Thursday, March 16, 2017 8:24AM - 8:36AM |
R27.00003: Non-Abelian Bosonization and Fractional Quantum Hall Transitions Aaron Hui, Michael Mulligan, Eun-Ah Kim A fully satisfying theoretical description for the quantum phase transition between fractional quantum Hall plateaus remains an outstanding problem. Experiments indicate scaling exponents that are not readily obtained in conventional theories. Using insights from duality, we describe a class of quantum critical effective theories that produce qualitatively realistic scaling exponents for the transition. We discuss the implications of our results for the physically-relevant interactions controlling this broad class of quantum critical behavior. [Preview Abstract] |
Thursday, March 16, 2017 8:36AM - 8:48AM |
R27.00004: A DMRG study of topological domain walls in fractional quantum Hall states Abolhassan Vaezi, Mohammad-Sadegh Vaezi |
Thursday, March 16, 2017 8:48AM - 9:00AM |
R27.00005: Abstract Withdrawn We have studied a lattice model to provide exactly flat bands with non-trivial Chern numbers. These bands are formally identical with single particle Landau levels of continuum electrons with quenched kinetic energy. Our results generalize models that have been studied by Eliot Kapit and Erich Mueller [PRL 105, 215303 (2010)] to the case beyond the lowest Landau. In the presence of local bosonic interaction Hamiltonians and proper filling factor, ground states may be stabilized that have the exact same form as certain well known many-body fractional Hall trial state defined for the continuum case. For most cases, our results can be reproduced to good approximation with NN and NNN hopping only, which can be easily realized in experiment. Our model allows us to realize exactly quantum Hall model wave functions on a lattice that had not previously been considered in this context, notably states further down the hierarchy and new non-Abelian states. |
Thursday, March 16, 2017 9:00AM - 9:12AM |
R27.00006: Light-induced fractional quantum Hall phases in graphene Areg Ghazaryan, Michael Gullans, Pouyan Ghaemi, Mohammad Hafezi Graphene has a special property that, under a strong magnetic field, its Landau levels are not equidistant. This propety allows one to selectively couple only two Landau levels, using a laser field resonant with their spacing. Such light-matter coupling results in a new form of bilayer fractional quantum Hall system, where the role of the layer is played by Landau level index and hopping between the layers is controlled by light-matter interaction strenght. We present the realizable fractional quantum Hall phases in these systems for 2/3 filling, and analyze the special type of interaction responsible for these phases. We also show that the form of the interaction distinguishes these systems from previously studied bilayer systems. [Preview Abstract] |
Thursday, March 16, 2017 9:12AM - 9:24AM |
R27.00007: Ground state of the 5/2 fractional quantum Hall effect in the presence of Landau level mixing Edward Rezayi By now there is widespread agreement that the leading candidates for the quantized Hall states at $\nu=5/2$ is either the Moore-Read (Pfaffian) state or its particle-hole (PH) conjugate, the anti-Pfaffian. These represent distinct phases of topological matter. In the presence of PH symmetry both are equally valid candidates for the generic Coulomb Hamiltonian; the system will choose one of them by spontaneously breaking the PH symmetry. If, on the other hand, PH symmetry is broken externally one of the two will be selected and an extensive gap will separate the two states. In experiment PH symmetry is broken by inter Landau level (LL) transitions. Previously, in a 3-Landau-level (3-LL) model using exact diagonalization and iDMRG, it was found that the anti-Pfaffian is favored irrespective of the strength of the LL-mixing parameter $\kappa=k e^2/\ell/\hbar\omega$. In a separate approach, Pakrousky et. al.(PRX 5, 2015), using a 2 and 3-body effective Hamiltonian that accounts for LL-mixing to the lowest order in $\kappa$, found the opposite, casting doubt on the validity of the 3-LL model. In this talk the source of the discrepancy will be addressed by finite-size calculations for both spherical and toroidal geometries. It will be shown that the two approaches are in agreement. [Preview Abstract] |
Thursday, March 16, 2017 9:24AM - 9:36AM |
R27.00008: Stripe phase in half-filled N=0 Landau level of 2D hole systems Po Zhang, Rui-Rui Du, Loren Pfeiffer, Ken West 2D electron gas (2DEG) and 2D hole gas (2DHG) exhibit rich phases when subjected to strong magnetic fields and low temperatures, including the fractional quantum Hall (FQH) states, Wigner crystal, stripe phase, and bubble phase. It has been well established that in GaAs 2DEG the stripe phases prevail in half-filled Landau level (LL) whose index N$>$1 ($\ge$1), under a perpendicular (tilt) magnetic field. The FQH states are more favored in N=1 and N=0 LLs. The ground states at half-fillings vary from LL to LL because in each LL the pseudo potential is different. 2DHG differs from 2DEG due to the former’s stronger LL mixing and inverted LL index, hence one may expect a different pattern of phase competition in 2DHG. Here we report an observation of stripe phase at filling factor v = 3/2 in N=0 Landau level of GaAs 2DHG (arXiv:1607.07858). The widths of quantum wells involved are 17.5nm and 20nm. Similar observation was reported by Y. Liu et al., Phys. Rev. B 94, 155312 (2016), in wider (30 and 35nm) quantum wells. [Preview Abstract] |
Thursday, March 16, 2017 9:36AM - 9:48AM |
R27.00009: Composite Fermi surface in the half-filled Landau level with anisotropic electron mass Matteo Ippoliti, Scott Geraedts, Ravindra Bhatt We study the problem of interacting electrons in the lowest Landau level at half filling in the quantum Hall regime, when the electron dispersion is given by an anisotropic mass tensor. Based on experimental observations\footnote{D. A. Kamburov et al., Phys. Rev. B 89, 085304 (2014)} and theoretical arguments\footnote{K. Yang, Phys. Rev. B 88, 241105 (2013)}, the ground state of the system is expected to consist of composite Fermions filling an elliptical Fermi sea, with the anisotropy of the ellipse determined by the competing effects of the isotropic Coulomb interaction and anisotropic electron mass tensor. We test this idea quantitatively by using a numerical density matrix renormalization group method for quantum Hall systems on an infinitely long cylinder\footnote{M. P. Zaletel et al., Phys. Rev. B 91, 045115 (2015)}. Singularities in the structure factor allow us to map the Fermi surface of the composite Fermions\footnote{S. D. Geraedts et al., Science 352 (6282), 197 (2016)}. We compute the composite Fermi surface anisotropy for several values of the electron mass anisotropy which allow us to deduce the functional dependence of the former on the latter. [Preview Abstract] |
Thursday, March 16, 2017 9:48AM - 10:00AM |
R27.00010: Weiss oscillations and particle-hole symmetry at the half-filled Landau level Alfred Cheung, S. Raghu, Michael Mulligan Unbroken particle-hole symmetry with respect to a filled Landau level $n$ of the two-dimensional electron gas requires the electrical Hall conductivity to equal $\frac{2n - 1}{2} \frac{e^2}{h}$ at half-filling. In this note, we study the consequences of weakly broken particle-hole symmetry for magnetoresistance oscillations about half-filling when there is a one-dimensional (approximately) electrostatic potential present. We find an approximate sum rule obeyed for all pairs of oscillation minima that can be tested in experiment. We discuss the implications of our results and approximations for the description of the half-filled Landau level. [Preview Abstract] |
Thursday, March 16, 2017 10:00AM - 10:12AM |
R27.00011: Broken translation symmetry in the half-filled lowest Landau level Prashant Kumar, Srinivas Raghu We present a Hartree-Fock theory of electrons in a half-filled lowest Landau level interacting with Coulomb forces. With the assumptions of a gapless Fermi sea and particle-hole symmetry, we find a charge density wave state in the form of a square crystal. The Fermi sea wavefunction is built from a Slater determinant of single particle wavefunctions that reside strictly within the lowest Landau level. It possesses a $\pi$ Berry phase upon encircling the Fermi surface. Furthermore, the deviations from a half-filled Landau level in our theory produce cyclotron orbits that are sensitive to the effective magnetic field rather than the absolute value of the field. We discuss the relevance of our theory to the phenomenology of the half-filled Landau level. [Preview Abstract] |
Thursday, March 16, 2017 10:12AM - 10:24AM |
R27.00012: Non-Abelian Fracton Topological Order and New Constructions of Fracton Phases S. Vijay, Liang Fu We present recent progress in the study of fracton topological phases, 3D topologically-ordered states of matter with gapped, fractionalized excitations that are immobile (termed “fractons”), and cannot be moved by acting with any local operator without creating other gapped excitations. We present an isotropic construction of a fracton topological phase, starting from inter-penetrating layers of a 2D topological phase. Condensation of excitations that are created in adjacent layers can lead to a fracton topological phase or a more conventional 3D topological order. This construction leads to a new perspective on the emergence of the immobile fracton excitations, as well as an understanding of the wavefunction for certain fracton phases. We then introduce a model that realizes a new ``non-Abelian” fracton topological phase, where the fracton excitations have quantum dimension $d > 1$. Bound-states of the fractons can behave as mobile, non-Abelian anyons with well-defined statistics and fusion rules. This provides an example of a truly 3D phase of matter with non-Abelian anyons. Finally, we describe a lattice model of interacting bosons with a local $U(1)$ symmetry that realizes a stable, gapless phase with emergent fracton excitations. [Preview Abstract] |
Thursday, March 16, 2017 10:24AM - 10:36AM |
R27.00013: Braiding statistics of strings with general linking in 3$+$1D topological order Chao-Ming Jian, Xiao-Liang Qi In contrast to topological orders in 2$+$1D, the unifying structure of 3$+$1D topological phases is not yet well understood. In order to shed light on such a unifying structure, we study a large set of topological states given by the Dijkgraaf-Witten gauge theories. In particular, we are interested in the fusion and the braiding statistics of the string excitations in such theories. Previous studies of the string braiding statistics only focused on a specific type of string configurations that enables a dimensional reduction of the problem from 3$+$1D to 2$+$1D. In this work, we focus on more general string configurations that do not generally admit a dimensional reduction picture. We show how the fusion and braiding statistics depends on the linking of the strings in these configurations. We also derive several consistency conditions of the string braiding statistics, which we conjecture to be true for the most general 3$+$1D topological states. [Preview Abstract] |
Thursday, March 16, 2017 10:36AM - 10:48AM |
R27.00014: Thermopower and Nernst measurements in a half-filled lowest Landau level Xiaoxue Liu, Po Zhang, Chi Zhang, RuiRui Du, Loren Pfeiffer, Ken West Recently Son presented a particle-hole symmetric (PHS) fermionic quasiparticle theory for half-filled lowest Landau level - massless Dirac composite fermions (DCF) [1]，which is different from the PHS broken HLR theory [2]. Subsequently, thermoelectric transport experiments were proposed to differentiate the DCF and HLR. Motivated by this we systematically study the electronic and thermoelectric properties of v = 1/2 and 3/2 in high-mobility GaAs/AlGaAs 2DEGs. In this talk，preliminary results and a brief discussion will be presented. [1] Dam Thanh Son, Phys. Rev. X 5, 031027 (2015). [2] B. I. Halperin, P. A. Lee, and N. Read, Phys. Rev. B 47, 7312 (1993). [3] Andrew C. Potter, Maksym Serbyn, and Ashvin Vishwanath, Phys. Rev. X 6, 031026 (2016). [Preview Abstract] |
Thursday, March 16, 2017 10:48AM - 11:00AM |
R27.00015: Interacting composite fermions: Nature of the 4/5, 5/7, 6/7, and 6/17 fractional quantum Hall states Ajit Coimbatore Balram Numerical studies by W\'ojs, Yi and Quinn have suggested that an unconventional fractional quantum Hall effect is plausible at filling factors $\nu=$ 1/3 and 1/5, provided the interparticle interaction has an unusual form for which the energy of two fermions in the relative angular momentum three channel dominates. The interaction between composite fermions in the second $\Lambda$ level (composite fermion Landau level) satisfies this property, and recent studies have supported unconventional fractional quantum Hall effect of composite fermions at $\nu^*=$ 4/3 and 5/3, which manifests as fractional quantum Hall effect of electrons at $\nu=$ 4/11, 4/13, 5/13, and 5/17. I investigate the nature of the fractional quantum Hall states at $\nu=$ 4/5, 5/7, 6/17, and 6/7, which correspond to composite fermions at $\nu^*=$ 4/3, 5/3 and 6/5, and find that all these fractional quantum Hall states are conventional. The underlying reason is that the interaction between composite fermions depends substantially on both the number and the direction of the vortices attached to the electrons. I also study in detail the states with different spin polarizations at 6/17 and 6/7 and predict the critical Zeeman energies for the spin phase transitions between them. [Preview Abstract] |
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