Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session L01: Fractional Quantum Hall Effect: Composite Fermions |
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Sponsoring Units: DCMP Chair: Steven Simon, University of Oxford Room: BCEC 106 |
Wednesday, March 6, 2019 11:15AM - 11:27AM |
L01.00001: Fractional Quantum Hall Effect at ν=2+6/13: The Parton Paradigm for the Second Landau Level Ajit Coimbatore Balram, Sutirtha Mukherjee, Kwon Park, Maissam Barkeshli, Mark Rudner, Jainendra Jain The unexpected appearance of a fractional quantum Hall effect (FQHE) plateau at ν=2+6/13 [Kumar et al., Phys. Rev. Lett. 105, 246808 (2010)] offers a clue into the physical mechanism of the FQHE in the second Landau level (SLL). Here we propose a ``bar3bar2111'' parton wave function and demonstrate it to be a good candidate state for this phase. We make several predictions for experimentally measurable properties that can reveal the nature of this state and also distinguish it from the topologically distinct 6/13 state realized in the lowest Landau level. Taking these results together with the recent demonstration that the related ``bar2bar2111'' wave function is a good candidate for the ground state at ν=2+1/2 [Balram et al., Phys. Rev. B 98, 035127 (2018)], we propose that the ``bar{n}bar2111'' family of parton wave functions naturally describes the experimentally observed sequence of SLL FQHE plateaus at 2+2/3, 2+1/2 and 2+6/13, and their hole partners. |
Wednesday, March 6, 2019 11:27AM - 11:39AM |
L01.00002: On the Interpretation of Thermal Conductance of the nu=5/2 Edge Steven Simon Recent experiments [Banerjee et al, Nature 2018] have measured thermal conductance of the $\nu=5/2$ edge in a GaAs electron gas and found it to be quantized as $K \approx 5/2$ (in appropriate dimensionless units). This result is unexpected, as prior numerical work predicts that the $\nu=5/2$ state should be the Anti-Pfaffian phase of matter, which should have quantized $K=3/2$. The purpose of this paper is to propose a possible solution to this conflict: if the Majorana edge mode of the Anti-Pfaffian does not thermally equilibrate with the other edge modes, then $K=5/2$ is expected. I discuss several possible reasons for this nonequilibration, and discuss possible mechanisms in some detail. I further discuss what should be examined further to determine if this is the case. |
Wednesday, March 6, 2019 11:39AM - 11:51AM |
L01.00003: Dirac Composite Fermions and Emergent Reflection Symmetry about Even Denominator Filling Fractions Hart Goldman, Eduardo Hector Fradkin Motivated by the appearance of a “reflection symmetry” in transport experiments and the absence of statistical periodicity in relativistic quantum field theories, we propose a series of relativistic composite fermion theories for the compressible states appearing at filling fractions ν = 1/2n in quantum Hall systems. These theories consist of electrically neutral Dirac fermions attached to 2n flux quanta via an emergent Chern-Simons gauge field. While not possessing an explicit particle-hole symmetry, these theories reproduce the known Jain sequence states proximate to ν = 1/2n, and we show that such states can be related by the observed reflection symmetry, at least at mean field level. We further argue that the lowest Landau level limit requires that the Dirac fermions be tuned to criticality, whether or not this symmetry extends to the compressible states themselves. |
Wednesday, March 6, 2019 11:51AM - 12:03PM |
L01.00004: Partial Equilibration of Integer and Fractional Edge Channels in the Thermal Quantum Hall Effect Kwok Wai Ma, Dmitri Feldman Since the charged mode is much faster than the neutral modes on quantum Hall edges at large filling factors, the edge may remain out of equilibrium in thermal conductance experiments. This sheds light on the observed imperfect quantization of the thermal Hall conductance at ν=8/3 and can increase the observed thermal conductance by two quanta at ν=8/5. Under certain unlikely but not impossible assumptions, this might also reconcile the observed thermal conductance at ν=5/2 with not only the PH-Pfaffian order but also the anti-Pfaffian order. |
Wednesday, March 6, 2019 12:03PM - 12:15PM |
L01.00005: Finite-thickness effect of the fractional quantum Hall states in the second Landau level Pengjie Wang, Jian Sun, Yijia Wu, Hua Chen, Loren Pfeiffer, Kenneth West, Xincheng Xie, Xi Lin Given the finite thickness of the samples in experiments, the in-plane magnetic field will squeeze the single-particle electron wave function in the direction perpendicular to the plane, effectively decrease the quantum well (QW) width and modify the electron interaction. However, this effect has only been reported in the non-Abelian candidate, 5/2 fractional quantum Hall (FQH) state, while other FQH states in the second Landau level (SLL), including the particle-hole conjugate of 5/2 FQH state, i.e. 7/2 FQH state, remain uninvestigated. We will present our energy gap measurements of the FQH states (7/3, 5/2, 8/3 and 7/2) in the SLL under tilted magnetic fields. A universal critical in-plane magnetic field of around 1.0 T is observed at different fillings, which corresponds to an in-plane magnetic length of around 26 nm. This critical value is comparable with the QW width of 28 nm in our sample, indicating the finite-thickness effect in the SLL. At higher in-plane magnetic fields, we found that the FQH states deviated from its strengthening tendency with in-plane field, further demonstrating the finite-thickness effect. |
Wednesday, March 6, 2019 12:15PM - 12:27PM |
L01.00006: Strain-induced resistance anisotropy near the FQHE v=5/2 in two-dimensional GaAs single quantum wells Alexander Stern, Brian Casas, Johannes Pollanen, James Eisenstein, Kenneth West, Loren Pfeiffer, Jing Xia We report strain-dependent low temperature magnetotransport measurements of a two-dimensional electrons gas confined in GaAs single quantum wells. The samples are mounted to a piezoelectric-based strain device with which we can apply, and vary, tensile strain in the quantum well in situ. With this apparatus we have achieved strain as large as ~0.5% in GaAs quantum wells at cryogenic temperatures. We find that with increasing strain with a high magnetic field applied causes the magnetoresistance of the two-dimensional electron system confined in the quantum well to develop anisotropic resistance near the FQHE v = 5/2. Additionally, we find that this strain and field induced resistance anisotropy is caused by a meta-stable phase that has a temperature dependent decay back to its isotropic state. |
Wednesday, March 6, 2019 12:27PM - 12:39PM |
L01.00007: Principal component analysis of quantum Hall wave functions Na Jiang, Siyao Ke, Xin Wan The fractional quantum Hall effect demonstrates the robustness of topological properties in many-body systems. The effect of mass and interaction anisotropy can be understood in terms of a geometrical description. We present a study of the evolution of quantum Hall wave functions with interaction anisotropy by a statistical learning technique known as the principal component analysis (PCA). We show that the topological and geometrical aspects of a family of wave functions can be readily separated by the PCA. We discuss how to use the PCA to extract wave function metric and to determine the stability of a fractional quantum Hall phase. |
Wednesday, March 6, 2019 12:39PM - 12:51PM |
L01.00008: Hamiltonian theory for Quantum Hall systems in a tilted magnetic field: composite
fermion geometry and robustness of activation gaps Kang Yang, Mark Oliver Goerbig, Benoît Douçot In 2011, Haldane showed the existence of an internal geometric degree of freedom in the description of incompressible fractional quantum Hall states. The static value of this metric tells us how the quantum Hall system reacts in the presence of anisotropy, e.g. in the electron-electron interaction. We implement this geometry into Shankar and Murthy's Hamiltonian theory, which provides an analytical framework for Jain's composite fermion (CF) picture according to which the fractional quantum Hall effect arises from an integer number of fully filled CF Landau levels. Here, we study a quantum Hall system in a tilted magnetic field. With a finite width of the system in the z-direction, the parallel component of the magnetic field induces anisotropy into the effective two-dimensional interactions. We find that this anisotropy introduces mixing of CF Landau levels and thus perturbs the Hartree-Fock CF state of the Hamiltonian theory. By changing the internal geometry of the CF, such a perturbation can be minimized by optimizing the underlying metric, and we calculate the corresponding activation gaps for different tilt angles. Our results show that the activation gaps are remarkably robust against the in-plane magnetic field in the lowest and first Landau levels. |
Wednesday, March 6, 2019 12:51PM - 1:03PM |
L01.00009: A Josephson relation for fractionally charged anyons. Maelle Kapfer, Preden Roulleau, Ian Farrer, David A Ritchie, Christian Glattli Anyons (intermediate between bosons and fermions) occur in two-dimensional electron systems in high magnetic field as fractional excitations with charge e*=e/q in the topological ordered states of the Fractional Quantum Hall Effect (FQHE). Owing to their importance for topological quantum phases and possible decoherence free quantum information approaches, understanding anyons is of utmost importance. However, experiments probing their dynamics are lacking. Here we report on a dynamical property of anyons: the long predicted Josephson relation f_{J}=e*V/h for charge e*=e/3 and e/5. It manifests as marked signatures in the Photo Assisted Shot Noise (PASN) versus voltage V when irradiating contacts at microwaves frequency f=f_{J}. The validation of FQHE PASN models opens the way to realize time-resolved anyon sources based on levitons to perform time-domain anyon braiding. |
Wednesday, March 6, 2019 1:03PM - 1:15PM |
L01.00010: Non-Magnetic Fractionally Quantized Conductance in Quasi-One Dimensional Semiconductor Structures Michael Pepper, Sanjeev Kumar, Yilmaz Gul, Maksym Myronov, David A Ritchie, Ian Farrer, Henry Montagu We have investigated quasi-one dimensional carrier transport using holes, (electrons), in Ge-SiGe, (GaAs-AlGaAs), heterostructures in the ballistic regime. At values of carrier concentration below about 5.1010 cm-2 the integer ground state disappears to be replaced by fractional values of conductance. This occurs when the confinement of the carriers is relaxed to be on the verge of two-dimensionality. For holes in Ge we find that, in units of e2/h, the fractional values of conductance are 1/2, spin degenerate, dropping to 1/4 in the presence of a parallel magnetic field and 1/16 which is spin polarized at zero field, (1). The accuracy of the quantization was 0.5%, possibly corresponding to fractional charges of e/2 and e/4. |
Wednesday, March 6, 2019 1:15PM - 1:27PM |
L01.00011: Melting of interference in the fractional quantum Hall regime: Appearance of neutral modes Mitali Banerjee, R Bhattacharyya, Moty Heiblum, Diana Mahalu, Vladimir Umansky The core reason for the absence of interference of fractional charges (in the lowest Landau level) has long been a subject of discussions. Certainly there is dephasing of quasiparticles, but the agent behind this havoc was never singled out experimentally. While interference of electrons has been routinely observed in the integer regime, it gradually reduced as the filling was reduced towards ν=1, where it fully quenched, not to recover in the fractional regime. Here, we have systematically studied the Aharonov-Bohm interference in a Mach-Zehnder interferometer (MZI) and correlated it with the appearance of upstream neutral modes. The latter were determined by an appearance of a conductance plateau of ν=1/3 in a quantum point contact (QPC), which carried shot-noise. As the bulk filling approached ν=1 a substantial drop in the visibility was observed, concomitantly with the appearance ν=1/3 noisy conductance plateau in the QPC (of the MZI) - pointing at the birth of neutral modes at the QPC. Such ν=1/3 conductance plateau persisted throughout the hole-conjugate regime, where interference was absent. We believe that unexpected edge reconstruction, favored in a rather soft edge potential at 2>ν≥1 gives birth to upstream neutral modes that dephase the interference. |
Wednesday, March 6, 2019 1:27PM - 1:39PM |
L01.00012: Landau level subbands as a platform for many-body localization Akshay Krishna, Matteo Ippoliti, Ravindra Bhatt Previous numerical results [1] have confirmed the theoretical argument [2] that many-body localization is not possible in a Landau level in the presence of interactions and arbitrary disorder. We examine the possibility of many-body localization in subbands (both topological and non-topological) derived from the lowest Landau level. In particular, we use two specific models – a suitably engineered flat band potential, and randomly placed point-like impurities, to create subbands into which we project the problem, including both ineractions and disorder. We use exact diagonalization to compute the level spacing ratio as a diagnostic of localization. The results show the absence of localization in topological subbands and the possibility of a finite-disorder many-body localization transition in non-topological subbands. This represents a novel setting for the study of many-body localization in one and two dimensions. |
Wednesday, March 6, 2019 1:39PM - 1:51PM |
L01.00013: Bulk properties of the 5/2 fractional quantum Hall state with Corbino geometry Jian Sun, Pengjie Wang, Zheyi Zhu, Jiasen Niu, Loren Pfeiffer, Kenneth West, Xi Lin The nature of the ground state of the fractional quantum Hall (FQH) effects at half-filling in the second Landau level has been an interesting problem. In high-quality GaAs samples, the exact quantization of the 5/2 FQH state has been observed in van der Pauw geometry, but the fully bulk insulation of the 5/2 FQH state remains unrevealed. Corbino geometry, known for its edge-free nature, has been applied in studying the bulk physics of FQH states and charge density wave states recently. We will show our observation of bulk insulation in the 5/2 FQH state with Corbino geometry at an estimated low electron temperature of 12 mK. With in-plane electrical field, the stability of the 5/2 FQH state was explored. In our measurement, the 5/2 FQH state wasn’t enhanced by a weak in-plane electrical field as suggested. Our observation indicates a fully charge insulating nature of the bulk at filling factor 5/2 and could be informative for the proposed thermal conductivity measurements to search the striped Pfaffian and anti-Pfaffian state. |
Wednesday, March 6, 2019 1:51PM - 2:03PM |
L01.00014: Half-filled Landau levels: a continuum and sign-free regularization of 3D quantum critical points Matteo Ippoliti, Roger Mong, Fakher Assaad, Michael Zaletel We propose a method to regulate (2+1)-dimensional quantum critical points in which the ultraviolet cutoff is implemented by Landau level quantization, rather than by a lattice [1]. This allows numerical computations on arbitrary manifolds without introducing lattice defects. We focus on N=4 flavors (corresponding to the spin and valley degrees of freedom of electrons in graphene) at half filling, and introduce appropriate interaction anisotropies in flavor space to drive different types of magnetic order. We thus obtain a continuum regularization of the O(5) nonlinear sigma model (NLSM) with a topological term, which has been conjectured to flow to a deconfined critical point. We perform infinite-cylinder DMRG [2] simulations of this model and estimate the dimension of the O(5) vector to be Δ_{V }≈ 0.55 - 0.70, depending on the NLSM stiffness. This dependence may be a finite-size effect or further evidence of a weakly discontinuous transition. As the model is sign-problem-free, forthcoming quantum Monte Carlo simulations may be able to discriminate between these cases. |
Wednesday, March 6, 2019 2:03PM - 2:15PM |
L01.00015: Superconducting correlations in a fractional quantum Hall bilayer interface Jukka Vayrynen, Moshe Goldstein, Yuval Gefen We consider a fractional quantum Hall bilayer system with an interface between quantum Hall states of filling fractions (0,1) and (1,1/3), motivated by recently fabricated systems by the Heiblum group (Weizmann). We show that disordered tunneling within one of the layers will drive the system to a stable fixed point with two counterpropagating charge modes which have attractive interactions. As a result, superconducting correlations on the edge become slowly-decaying. We discuss the observable effects of the phenomenon and derive general requirements for electron attraction in Abelian quantum Hall states. |
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