Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session P51: Fractional QHE: Level Mixing & Transitions |
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Sponsoring Units: FIAP Chair: John Cumings, University of Maryland Room: Hilton Baltimore Holiday Ballroom 2 |
Wednesday, March 16, 2016 2:30PM - 2:42PM |
P51.00001: Heterostructure Symmetry and the Orientation of the Quantum Hall Nematic Phases J.P. Eisenstein, J. Pollanen, K.B. Cooper, S. Brandsen, L.N. Pfeiffer, K.W. West The native symmetry-breaking potential which consistently orients the quantum Hall nematic phases in high mobility 2D electron systems relative to the host semiconductor crystal axes remains unknown. Here we report an extensive set of measurements examining the role of the structural symmetries of the potential confining the 2D system in determining the orientation of the nematics [1]. In single quantum well samples we find that neither the local symmetry of the confinement potential nor the depth of the 2D electron system beneath the sample surface dictates the orientation of the nematic. In contrast, for 2D electrons confined at a single heterointerface between GaAs and AlGaAs, the nematic orientation does depends on the depth of the 2D electron system beneath the sample surface. We relate these results to various theoretical models of the symmetry-breaking potential. [1] J. Pollanen et al., Phys. Rev B 92, 115410 (2015). [Preview Abstract] |
Wednesday, March 16, 2016 2:42PM - 2:54PM |
P51.00002: Nematic quantum phase transition of composite Fermi liquids in half-filled Landau levels and their geometric response Yizhi You, Gil Young Cho, Eduardo Fradkin We present a theory of isotropic-nematic quantum phase transition in the composite Fermi liquid arising in the half-filled Landau levels. We show that the quantum phase transition is triggered by the attractive quadrupolar interaction. By performing flux attachment, system turns into a composite Fermi liquid. The nematic order parameters act as the dynamical metric interplaying with the underlying topology, the Chern-Simons theory. Here both the fluctuations of the gauge field and the nematic order parameter can soften the Fermi surface and thus the fermions form a non-Fermi liquid. The effective field theory for the isotropic-nematic phase transition has z = 3 dynamical exponent due to the Landau damping due to the finite density of the fermions. We show that there is a Berry phase term of the nematic order parameter, which can be interpreted as the “Hall viscosity” of the dynamical metric. We also find the Wen-Zee-like term, which effectively dresses the nematic vortex with the electric charge. Both of the terms are originated from the time reversal breaking fluctuation of the Chern-Simons gauge fields. This indicates the fluctuations of the gauge fields modify the Hall viscosity and orbital spin of the compressible half-filled Landau level. [Preview Abstract] |
Wednesday, March 16, 2016 2:54PM - 3:06PM |
P51.00003: Phase Transition between Fermionic IQHE and Bosonic FQHE Via Feshbach Resonance Shiuan-Fan Liou, Kun Yang, Zi-Xiang Hu We study an integer quantum Hall system with two species of fermions with total Landau filling factor two (or one per kind of fermions) on disk geometry. Via Feshbach resonance fermions interact with each other such that two different species of fermions become a boson as coupling strength increases. Through exact diagonalization method, we see that fermions undergo a phase transition from fermionic integer quantum Hall phase to bosonic fractional quantum Hall phase with $\nu = \frac{1}{2}$. Besides, it seems to be a second order phase transition by investigating the expectation value of particle number of bosons. [Preview Abstract] |
Wednesday, March 16, 2016 3:06PM - 3:18PM |
P51.00004: The effect of Landau level mixing on spin polarization of composite fermions: a non-perturbative study Yuhe Zhang, Jainendra K. Jain The spin polarization transitions enable precise tests of the fractional quantum Hall (FQH) theory. Possible factors responsible for the deviations between theories and experiments include Landau level (LL) mixing and finite quantum well width. Previous works generally treat LL mixing perturbatively. Following [1], we perform a “fixed-phase” diffusion Monte Carlo study to solve the many-body Schrodinger equation within the approximation of fixing the phase of the wave function. We calculate the critical Zeeman energy ($E_z$) needed to fully spin polarize several FQH states, and find that $E_z$ depends less sensitively on LL mixing than previously thought. We also take into account the effect of finite quantum well width by using an effective two-dimensional interaction based on the realistic charge distribution. We compare our results with experiments and make further predictions. [1] G. Ortiz, D. M. Ceperley, and R.M. Martin, Phys. Rev. Lett. 71, 2777 (1993). [Preview Abstract] |
Wednesday, March 16, 2016 3:18PM - 3:30PM |
P51.00005: Competing states for the fractional quantum Hall effect in the 1/3-filled second Landau level Jae-Seung Jeong, Hantao Lu, Kenji Hashimoto, Suk Bum Chung, Kwon Park We study the nature of the fractional quantum Hall state in the 1/3-filled second Landau level at filling factor 7/3 via exact diagonalization. We show a series of transitions in the energy spectrum from a Laughlin-type spectrum, to an intermediate compressible spectrum, to a reentrant incompressible spectrum, and to a compressible spectrum with decrease of the Haldane pseudopotential. To search for a trial state describing the 7/3 state, we compute the overlap of the exact 7/3 ground state with various competing states including the Laughlin state, the particle-hole conjugate of the ${\mathrm Z}_4$ parafermion state, the fermionic Haffnian state, the antisymmetrized product state of two composite fermion seas (CFSs) at 1/6 filling, and the antisymmetrized correlated state of two CFSs at 1/4 filling, which are obtained as an antisymmetrized projection of the bilayer quantum Hall states. Specifically, we prove that the fermionic Haffnian state is equivalent to the antisymmetrized projection of the Halperin (551) state. [Preview Abstract] |
Wednesday, March 16, 2016 3:30PM - 3:42PM |
P51.00006: SU(3) and SU(4) singlet quantum Hall states at $\nu=2/3$ Fengcheng Wu, Inti Sodemann, Allan H. MacDonald, Thierry Jolicoeur We report on an exact diagonalization study of fractional quantum Hall states at a filling factor $\nu=2/3$ in a system with a four-fold degenerate $n$=0 Landau level and SU(4) symmetric Coulomb interactions. Our investigation reveals previously unidentified SU(3) and SU(4) singlet ground states which appear at flux quantum shift 2 when a spherical geometry is employed, and lie outside the established composite-fermion or multicomponent Halperin state patterns. We will present the pair correlation functions of these states, and describe similar singlets at another filling factor 2/5. Strategies to construct trial wave functions will be discussed. [Preview Abstract] |
Wednesday, March 16, 2016 3:42PM - 3:54PM |
P51.00007: Adiabatic Transport of Geometric Singularities in the Quantum Hall Effect Michael Laskin, Yu Hung Chu, Tankut Can, Paul Wiegmann We present a framework for studying the fractional Quantum Hall Effect (FQHE) on singular surfaces - in particular surfaces with multiple geometric singularities. It is now known that, aside from the Hall conductance and viscosity, there exists a third universal transport coefficient of the FQHE - the gravitational anomaly. This coefficient is difficult to measure since it usually appears as a higher order correction to observable quantities, such as the particle density. Singular surfaces are the first setting where the gravitational anomaly appears as a leading order effect. These surfaces are therefore ideal for studying geometric response and the gravitational anomaly within the FQHE. We expand the generating functional in the large $N$ limit on such surfaces. From there, we braid the conical singularities of the surface and find a remarkable result - the gravitational anomaly determines the braiding statistics of the transported conical singularities. [Preview Abstract] |
Wednesday, March 16, 2016 3:54PM - 4:06PM |
P51.00008: Quantum Hall State on Singular Surfaces Yu Hung Chiu, Tankut Can, Michael Laskin, Paul B. Wiegmann We propose a framework to study the response towards geometry with FQHE state on singular surfaces. Such study on singular surface provides a path to measure the gravitational anomaly, the third universal transport coefficient of FQHE, in leading order. The large $N$ expansion of generating functional is computed via two independent methods: a Ward Identity and a field theory approach. Meanwhile the second moment of the density is also obtained via Ward Identity. We observe that the generating functional on singular surfaces can be viewed as vertex operators at the cone tips. Divergence in the Liouville functional due to singularities is, as expected, a source for the modification, but not the sole source. From both methods, we are able to obtain the charge and conformal dimension $h_\alpha$ of such a vertex operator. The talk will concentrate on the one cone result obtained via both approaches. [Preview Abstract] |
Wednesday, March 16, 2016 4:06PM - 4:18PM |
P51.00009: 12/5 and 13/5 fractional quantum Hall states and Landau level mixing Kiryl Pakrouski, Michael Peterson, Yang-Le Wu, Matthias Troyer We use exact diagonalization to study the way Landau level mixing breaks the particle-hole symmetry between the 12/5 and 13/5 fractional quantum Hall states in GaAs. We discuss the possible relationship between our observations and the absence of the 13/5 state in experiment. [Preview Abstract] |
Wednesday, March 16, 2016 4:18PM - 4:30PM |
P51.00010: Exactly Solvable Model for Impurity Scattering at the Edge of the $\nu=2/3$ FQH State Chris Heinrich, Michael Levin We present an exactly solvable model for impurity scattering on the edge of a $\nu=2/3$ FQH state that is valid in the strong scattering limit. For this model we obtain exact mode expansions for the charge density and current operators, as well as the exact low energy spectrum. Importantly, we find that the low energy theory of the model consists of decoupled and counterpropagating charge and neutral modes, agreeing with the earlier work of Kane, Fisher, and Polchinski. Unlike the previous derivation, which relied on perturbative renormalization group arguments, our approach allows us to derive the emergence of decoupled charge and neutral modes from a microscopic model which is initially far from the decoupled fixed point. [Preview Abstract] |
Wednesday, March 16, 2016 4:30PM - 4:42PM |
P51.00011: Fragile Fractional Quantum Hall States in the Lowest and the Second Landau Level Gabor Csathy, Ethan Kleinbaum, Ashwani Kumar, Nodar Samkharadze, Loren Pfeiffer, Ken West Ultra-low temperature measurements of the two-dimensional electron gas have revealed some of the most fragile fractional quantum Hall states. In these experiments electron thermalization was achieved using a He-3 immersion cell and the temperature of the bath is monitored using a quartz tuning fork viscometer. We will review the recently discovered fractional quantum Hall state at filling factor $\nu=3+1/3$ observed in the second Landau level and those at the filling factor $\nu=4/11$ and $5/13$ in the lowest Landau level. The work at Purdue was supported by NSF DMR 1207375 and 1505866 grants. The work at Princeton University was funded by the Gordon and Betty Moore Foundation through the EPiQS initiative Grant GBMF4420, and by the National Science Foundation MRSEC Grant DMR-1420541. [Preview Abstract] |
Wednesday, March 16, 2016 4:42PM - 4:54PM |
P51.00012: Band geometry of higher Landau levels Rahul Roy, Fenner Harper, Thomas Jackson A set of recent results have shown that the quantum geometry of bands as encoded in quantities such as the mean fluctuations of the Berry curvature and the quantum metric provide a useful way of analyzing the stability of FQHE phases in Chern bands. These quantum geometric quantities measure the closeness of Chern bands to the lowest Landau level. Here, we find a more complete set of criteria for the stability of FQHE phases which incorporate a distance measure to an arbitrary Landau level. [Preview Abstract] |
Wednesday, March 16, 2016 4:54PM - 5:06PM |
P51.00013: Fractional Chiral metal from the wire construction Adolfo Grushin, Tobias Meng, Kirill Shtengel, Jens Bardarson In this work we use the wire construction to build integer and fractional phases of the 4+1 dimensional quantum Hall effect by coupling 3+1 dimensional Weyl semimetals in an extra dimension. In the presence of an external magnetic field, each Weyl species reduces to a (degenerate) chiral wire, the zeroth Landau level, which, upon coupling, delivers a consistent response to an external electromagnetic field in terms of a 4+1 dimensional Chern Simons field theory. Going one step beyond, we show that the theory at the boundary is gapless and explicitly write the quantum field theory that represents and defines this novel state of matter, the fractional chiral metal. We end by discussing the construction in the absence of external magnetic fields. [Preview Abstract] |
Wednesday, March 16, 2016 5:06PM - 5:18PM |
P51.00014: Mapping a fractional quantum Hall state to a fractional Chern insulator Yinhan Zhang, Junren Shi We establish a variational principle for properly mapping a fractional quantum Hall (FQH) state to a fractional Chern insulator (FCI). We find that the mapping has a gauge freedom which could generate a class of FCI ground state wave functions appropriate for different forms of interactions. Therefore, the gauge should be fixed by a variational principle that minimizes the interaction energy of the FCI model. For a soft and isotropic electron-electron interaction, the principle leads to a gauge coinciding with that for maximally localized two-dimensional projected Wannier functions of a Landau level. [Preview Abstract] |
Wednesday, March 16, 2016 5:18PM - 5:30PM |
P51.00015: Suppression of interference in quantum Hall Mach-Zehnder geometry by upstream neutral modes Yuval Gefen, Moshe Goldstein Mach-Zehnder interferometry has been suggested as a probe for anyonic quasiparticles in fractional quantum Hall states. However, all experimental attempts to measure such an interference signal have failed to date, despite the high visibility of interference fringes in the integer quantum Hall case. In our work we have studied the relation between this null result and another recent surprising experimental finding, namely the detection of upstream neutral modes in virtually all fractional quantum Hall states (including, e.g., filling 1/3), not only in hole-like filling factors (such as 2/3). We have found that the excitation of upstream modes makes the interference visibility in the Mach-Zehnder geometry decay exponentially with the total length of the interferometer arms, even when the lengths are exactly equal. We also suggest ways to overcome this suppression. [Preview Abstract] |
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