Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session W25: Fractional Quantum Hall Effect 1: Theory and Experiment |
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Sponsoring Units: DCMP Chair: Adbhut Gupta, Princeton University Room: Room 217/218 |
Thursday, March 9, 2023 3:00PM - 3:12PM |
W25.00001: Quantum Hall valley Ferromagnets as a platform for topologically protected quantum memory Kartiek Agarwal Materials hosting topologically protected non-Abelian zero modes offer the exciting possibility of storing and manipulating quantum information in a manner that is protected from decoherence at the hardware level. In this work, we study the possibility of realizing such excitations along line defects in certain fractional quantum Hall states in multi-valley systems. Such line defects have been recently observed experimentally between valley polarized Hall states on the surface of Bi(111), and excitations near these defects appear to be gapped (gapless) depending on the presence (absence) of interaction-induced gapping perturbations constrained by momentum selection rules, while the position of defects is determined by strain. In this work, we use these selection rules to show that a hybrid structure involving a superlattice imposed on such a multi-valley quantum Hall surface realizes non-Abelian anyons which can then be braided by modulating strain locally to move line defects. Specifically, we explore such defects in Abelian fractional quantum Hall states of the form { u} = 2/m using a K-matrix approach, and identify relevant gapping perturbations. Charged modes on these line defects remain gapped, while charge netural valley pseudospin modes may be gapped with the aid of two (mutually orthogonal) superlattices which pin non-commuting fields. When these superlattices are alternated along the line defect, non-Abelian zero modes result at points where the gapping perturbation changes. Given that these pseudospin modes carry no net physical charge or spin, the setup eschews utilizing superconducting and magnetic elements to engineer gapping perturbations. We provide a scheme to braid these modes using strain modulation, and confirm that the resulting unitaries satisfy a representation of the braid group. |
Thursday, March 9, 2023 3:12PM - 3:24PM |
W25.00002: Two-particle time-domain interferometry in the Fractional Quantum Hall Effect regime Christian D Glattli, Imen Taktak, Maëlle A Kapfer, Matteo ACCIAI, Janine SPLETTSTOESSER, Preden Roulleau, Ian Farrer, David A Ritchie Quasi-particles are elementary excitations of the ground state of condensed matter quantum phases. Demonstrating that they keep quantum coherence while propagating is a fundamental issue for their manipulation for quantum information tasks. This is particularly the case for the quasi-particles called anyons of the Fractional Quantum Hall Effect (FQHE). These fractionally charged quasi-particles obey anyonic statistics intermediate between fermionic and bosonic. Their quantum coherence has been observed by their transmission through the localized states of electronic Fabry-Pérot interferometers. Surprisingly, no or very weak quantum interference of anyons was observed in electronic Mach-Zehnder interferometers for which the quasi-particle transmission occurs via propagating states. Here, we show that FQHE anyons do keep a finite quantum coherence while propagating by using a novel kind of interferometry, namely two-particle time-domain interference [1] using an electronic beam-splitter. By varying the time delay between photo-created electron-hole pairs and measuring cross-correlated noise sensitive to the two-particle Hanbury Brown Twiss (HBT) phase [1], we observe strong quasiparticle interference [2]. At bulk filling factor 2/5, visibilities as high as 53% and 60% are observed for e/5 and e/3 charged propagating anyons, probably limited by co-propagating channel mixing [3]. At bulk filling factor 2/3 a similar large quantum coherence is observed for the 2/3 edge channel. |
Thursday, March 9, 2023 3:24PM - 3:36PM |
W25.00003: Quasiparticles Andreev scattering in the ν=1/3 fractional quantum Hall regime Pierre GLIDIC The scattering of exotic quasiparticles may follow different rules than electrons. In the fractional quantum Hall regime, a quantum point contact (QPC) provides a source of quasiparticles with selectable charges and statistics. These can then be scattered on a downstream ‘analyzer’ QPC to investigate these rules. Remarkably, for incident quasiparticles dissimilar to those naturally transmitted across the analyzer, electrical conduction conserves neither their nature nor their number. Indeed, theory predicts the emergence of a mechanism akin to the Andreev reflection, but without interface with a superconductor or a different quantum Hall state. |
Thursday, March 9, 2023 3:36PM - 3:48PM |
W25.00004: Fractional Hall Conductivity and Spin-c Structure in Solvable Lattice Hamiltonians Zhaoyu Han, Jing-Yuan Chen The Kapustin-Fidkowski no-go theorem forbids U(1) symmetric topological orders with non-trivial Hall conductivity in (2+1)d from admitting commuting projector Hamiltonians, where the latter is the paradigmatic method to construct exactly solvable lattice models for topological orders. Even if a topological order would intrinsically have admitted commuting projector Hamiltonians, the theorem forbids so once its interplay with U(1) global symmetry which generates Hall conductivity is taken into consideration. Nonetheless, in this work, we show that for all (2+1)d U(1) symmetric abelian topological orders of such kind, we can construct a lattice Hamiltonian that is controllably solvable at low energies, even though not "exactly" solvable; hence, this no-go theorem does not lead to significant difficulty in the lattice study of these topological orders. Moreover, for the fermionic topological orders in our construction, we introduce the lattice notion of spin-c structure – a concept important in the continuum that has previously not been adequately introduced in the lattice context. |
Thursday, March 9, 2023 3:48PM - 4:00PM |
W25.00005: Exact Hamiltonian for non-Abelian quasiparticle states Koji Kudo, Anirban Sharma, G. J. Sreejith, Jainendra K Jain Non-Abelian anyons have been predicted to emerge in the 5/2 fractional quantum Hall effect. Here, we propose a model Hamiltonian that is exactly solvable for non-Abelian quasiparticles (QPs) as well as quasiholes (QHs). Motivated by the bipartite composite fermion theory [1,2], we construct interactions in terms of two- and three-body Haldane's pseudopotentials. The QP and QH states exhibit the same counting for edge excitations, implying that they obey the same non-Abelian statistics. Our model provides exact solutions for neutral excitations as well. We demonstrate adiabatic continuity for the neutral excited states as we deform our Hamiltonian into the lowest Landau level Hamiltonian with a three-body interaction. |
Thursday, March 9, 2023 4:00PM - 4:12PM |
W25.00006: GaAs/AlGaAs heterostructures for interference experiments at the v = 5/2 fractional quantum Hall state James R Nakamura, Shuang Liang, Tanmay Maiti, Geoffrey C Gardner, Michael J Manfra The quantum Hall state at filling factor 5/2 has been predicted to have non-Abelian excitations. The non-Abelian character of these quasiparticle excitations can be probed through interferometry; however, there are challenges to developing a heterostructure which is suitable for these experiments. The heterostructure must be extremely low disorder, support stable gating, and provide a sharp confining potential. We present details of a heterostructure that achieves these requirements and exhibits high quality magnetotransport. This heterostructure design will be useful for fabricating quantum Hall interferometers. |
Thursday, March 9, 2023 4:12PM - 4:24PM |
W25.00007: The partially-filled bosonic E8 quantum Hall state Pak Kau Lim, Michael Mulligan, Jeffrey Teo We study chiral bosonic topological phases constructed from electrons. In addition to a bulk excitation energy gap, these bosonic phases also have a fermion energy gap below which all local excitations in the bulk and on the edge are bosonic even combinations of electrons. We focus on phases that can arise from the short-range entangled E8 quantum Hall state, the bosonic analogue of the filled lowest Landau level of electrons. We present families of long-range entangled bosonic fractional states that "partially fill" the E8 state and are pairwise related by a generalized particle-hole symmetry. We construct exactly solvable coupled-wire model Hamiltonians of these phases and observe the emergence of non-local fermions and gauge theories. |
Thursday, March 9, 2023 4:24PM - 4:36PM |
W25.00008: Observation of a G = ½ e2/h quantized conductance plateau in a quantum point contact at the v = 2/3 fractional quantum Hall state James R Nakamura, Shuang Liang, Geoffrey C Gardner, Michael J Manfra Quantum point contacts (QPCs) can be used to reflect quantum Hall edge states and probe the properties of fractional quasiparticles. We have investigated the v = 2/3 state in QPCs on a GaAs/AlGaAs heterostructure designed to achieve sharp confinement. When measuring conductance as a function of gate voltage and applying a small finite bias, we observe an intermediate conductance plateau with G = ½ e2/h. This plateau is a robust feature, being observed in multiple QPCs, and exists over a significant range of magnetic field, gate voltage, and source-drain bias. Using a simple model which considers scattering and equilibration between counterpropagating edge modes, we have found that this half-integer plateau is consistent with full reflection of an inner counterpropagating -1/3 edge mode while the outer integer mode is fully transmitted. In a QPC fabricated on a standard structure which is expected to have a soft confining potential, we instead observe an intermediate plateau at G = 1/3 e2/h, which is consistent with a theoretically predicted transition to an edge reconstructed state when the confining potential becomes soft. |
Thursday, March 9, 2023 4:36PM - 4:48PM |
W25.00009: Interference of higher-order fractional quantum Hall states in Fabry-Perot interferometers James R Nakamura, Shuang Liang, Geoffrey C Gardner, Michael J Manfra Fabry Perot interferometry can be used to probe the fractional charge and statistics of quasiparticles in the fractional quantum Hall regime. We have measured interference at the v = 2/3 fractional quantum Hall state, which is the hole-conjugate to the Laughlin v = 1/3 state. Measurements at different quantum point contact operating points indicate that two different edge states are present. The dominant frequencies present in FFTs of the conductance oscillations are consistent with the edge structure proposed by Macdonald consisting of an outer integer mode and an inner counterpropagating fractional mode. However, the fine structure in the data shows additional features which have not been seen at other quantum Hall states, and require additional investigation to interpret. |
Thursday, March 9, 2023 4:48PM - 5:00PM |
W25.00010: Anyon statistics through conductance measurements of time-domain interferometery Noam Schiller, Yuval Oreg, Ady Stern, Yotam Shapira We propose a method to extract the mutual exchange statistics of the anyonic excitations of a general Abelian fractional quantum Hall state, by comparing the tunneling characteristics of a quantum point contact in two different experimental conditions. In the first, the tunneling current between two edges at different chemical potentials is measured. In the second, one of these edges is strongly diluted by an earlier point contact. We describe the case of the dilute beam in terms of a time-domain interferometer between the anyons flowing along the edge and quasiparticle-quasihole excitations created at the tunneling quantum point contact. Remarkably, our proposal does not require the measurement of current correlations, and allows us to carefully separate effects of the fractional charge and statistics from effects of intra- and inter-edge interactions. |
Thursday, March 9, 2023 5:00PM - 5:12PM |
W25.00011: Non-abelian bosonization and the quantum Hall states at $
u=5/2$ Jun Ho Son, Srinivas Raghu The quantum Hall plateau at the filling fraction $
u=5/2$ has garnered attention due to the proposal that it hosts non-abelian anyons. Historically, there have been two major candidates for the quantum Hall state at $
u=5/2$ – the Pfaffian state and the anti-Pfaffian state. A more recent series of theoretical works, to match the theory with thermal Hall conductance experimentally measured for the $
u=5/2$ plateau, proposed a picture akin to the Chalker-Coddington network model in which the quantum Hall state at $
u=5/2$ are composed of puddles of Pfaffian and anti-Pfaffian states induced by disorder. In this work, we apply field-theoretical methods to study the Pfaffian-anti-Pfaffian network and show how the strong-disorder fixed point obtained from non-abelian bosonization can be employed to access both the insulating phase of the network consistent with the quantum Hall plateau at $
u=5/2$ and the thermal metal phase. While these two phases were previously known to appear in the network of Pfaffian and anti-Pfaffian states, non-abelian bosonization provides a unified framework to understand how the two different phases can emerge in the same network. We support our analytical insight with numerical simulations as well. |
Thursday, March 9, 2023 5:12PM - 5:24PM |
W25.00012: Even-Denominator Fractional Quantum Hall State at Filling Factor ν = 3/4 Chengyu Wang, Adbhut Gupta, Siddharth Kumar Singh, Edwin Y Chung, Loren N Pfeiffer, Ken West, Kirk W Baldwin, Roland Winkler, Mansour Shayegan Fractional quantum Hall states (FQHSs) exemplify exotic phases of low-disorder two-dimensional (2D) electron systems when electron-electron interaction dominates over the thermal and kinetic energies. Particularly intriguing among the FQHSs are those observed at even-denominator Landau level filling factors, as their quasiparticles are generally believed to obey non-Abelian statistics and be of potential use in topological quantum computing. Such states, however, are very rare and fragile, and are typically observed in the excited Landau level of 2D electron systems with the lowest amount of disorder. Here we report the observation of a new and unexpected even-denominator FQHS at filling factor ν = 3/4 in a GaAs 2D hole system with an exceptionally high quality (mobility) [1]. Our magnetotransport measurements reveal a strong minimum in the longitudinal resistance at ν = 3/4, accompanied by a developing Hall plateau centered at (h/e2)/(3/4). This even-denominator FQHS is very unusual as it is observed in the lowest Landau level and in a 2D hole system. While its origin is not entirely not entirely clear, it is likely a non-Abelian state, emerging from the residual interaction between composite fermions. |
Thursday, March 9, 2023 5:24PM - 5:36PM |
W25.00013: Low-Temperature Phases of Dissipative Superconductor--Fractional Quantum Hall Junctions Evgenii Zheltonozhskii, Barak A Katzir, Netanel Lindner Fractional quantum Hall (FQH) edges with proximity-induced superconductivity can host parafermionic zero modes (PZMs), a promising platform for topological quantum computing. Recent experiments measured the edge conductance due to crossed Andreev reflection (CAR) between counterpropagating FQH edges separated by a narrow superconducting finger. The observed conductance was small and non-quantized, with two distinct behaviors: some FQH states exhibit temperature-independent conductance, while in others, it grows as the temperature decreases. We show that these observations can be explained by dissipation to sub-gap modes in the superconductor. We find that temperature-independent non-quantized conductance occurs only in the presence of an integer mode strongly coupled to the dissipative channel. The most notable example of states hosting such modes are ν=(p±1)/p states. |
Thursday, March 9, 2023 5:36PM - 5:48PM |
W25.00014: Realizing Z3 parafermionic edge modes in 1D fermionic lattices. Luis G Dias Da Silva, Raphael Levy Ruscio Castro Teixeira Parafermionic bound states, Zn-symmetric generalizations of Majorana zero modes, can emerge as edge states in strongly correlated systems displaying fractionalized excitations. The non-trivial fractional nature of Z3 parafermions, in particular, can be used to produce Fibonacci anyons, a key ingredient in a universal topological quantum computer. Due to their fractional nature, much of the theoretical work on Z3 parafermions has relied on bosonization methods or parafermionic quasiparticles. In this contribution, we introduce a representation of Z3 parafermions in terms of purely fermionic operators. We establish the equivalency of a family of lattice fermionic models written in the basis of the t−J model with a Kitaev-like chain supporting free Z3 parafermionic modes at its ends. By using density matrix renormalization group calculations, we are able to characterize the topological phase transition and study the effect of local operators (doping and magnetic fields) on the spatial localization of the parafermionic modes and their stability. Moreover, we discuss the necessary ingredients for realizing Z3 parafermions in strongly interacting electronic systems. |
Thursday, March 9, 2023 5:48PM - 6:00PM |
W25.00015: Overlap of parafermionic zero modes at a finite distance Raphael Levy Ruscio Castro Teixeira, Andreas O Haller, Edvin G Idrisov, Roshni Singh, Amal Mathew, Luis G Dias Da Silva, Thomas L Schmidt Parafermion bound states (PBSs) can be regarded as generalizations of Majorana bound states (MBSs) and have been predicted to exist as zero-energy eigenstates in proximitized fractional quantum Hall edge states. Similarly to MBSs, a finite distance between the PBS can split the ground state degeneracy. However, the underlying Z2n symmetry of parafermionic modes allows several distinct interaction terms, rendering the effective Hamiltonian governing a pair of PBSs at a finite distance nontrivial. In this contribution, we employ a combination of semiclassical instanton approximation and quantum Monte Carlo simulations. We determine the effective parafermion Hamiltonian and its ground state splitting. For this purpose, we go beyond the dilute one-instanton gas approximation and show how finite-size effects can give rise to higher-order parafermion interactions. We find excellent agreement between the analytical results and Monte Carlo simulations. We estimate these finite-size corrections in current experimental setups and argue that these results are non-negligible in the experimental regime. |
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