Session B54: Fractional Excitations in the Quantum Hall Effect

Fermionic parity stability and interference measurements of non-Abelian e/4 and Abelian e/2 quasiparticle braiding at 7/2 and 5/2 filling factors

The 5/2 state is expected to have Abelian charge e/2 quasiparticles and non-Abelian charge e/4 quasiparticles; past interference measurements are consistent with this [1]. Recent [2] interferometer experiments present 3 new findings: 1) at 5/2 four dominant resistance oscillation periods are observed at the expected values for the full complement of braids of non-Abelian e/4 and Abelian e/2: e/2 braiding e/2, e/4 braiding e/2, and modulated oscillations specifically attributable to non-Abelian e/4 braiding e/4, the even-odd effect. Parameters controlling expression of these oscillations are delineated. 2) at 7/2 this full complement of e/4 and e/2 braiding oscillations is also observed, but at different periods as expected for that filling factor. 3) most importantly, the oscillations attributable to non-Abelian e/4 even-odd effect are stable against fermionic parity fluctuations over long times (hours) near 5/2 and 7/2; this observed stability strengthens the case for using non-Abelian e/4 quasiparticles for topological quantum computation.
[1] PNAS 106, 8853; & PRL.111,186401.
[2] Interference measurements of non-Abelian e/4 and Abelian e/2 quasiparticle braiding, arXiv:1905.10248.   

Non-Abelian braiding statistics via Aharonov–Bohm interferometry

One of the most striking consequences of the non-Abelian braiding statistics in the ν=5/2 quantum Hall state has been the so-called even–odd effect theoretically predicted over a decade ago. While signatures consistent with the theoretical prediction have been seen in quantum Hall Fabry–Pérot interferometers, the key ingredient – controlling the number of quaiparticles inside the interferometer – remains a challenging experimental problem. Fortunately, signatures of the non-Abelian statistics can emerge in a simpler setting, namely in Aharonov–Bohm-type experiments where interference patterns are produced solely by changing the magnetic field. This nucleates new quasiparticles inside the interferometer, and if those include non-Abelian particles, the Aharonov–Bohm oscillations are expected to have distinct spectral features that would be absent otherwise. This talk will focus on the theoretical predictions and their comparison with the recent observations [1], arguing that the preponderance of experimental evidence unmistakably points towards the non-Abelian nature of ν=5/2 and 7/2 quantum Hall states and provides strong evidence of non-Ableian braiding.

1. R. L. Willett, K. Shtengel, C. Nayak, L. N. Pfeiffer, Y. J. Chung, M. L. Peabody, K. W. Baldwin, K. W. West, arXiv:1905.10248   

Contacts and Equilibration in the ν=5/2 Quantum Hall Effect

The thermal Hall conductance K_T of the fractional quantum Hall state at ν=5/2 has recently been measured to be K_T≈2.5(π²k_B²T/3h)[1]. The half-integer value of this result provides strong evidence for the presence of a Majorana edge mode and a corresponding quantum Hall state hosting quasiparticles with non-Abelian statistics. Whether this measurement points to the realization of the PH-Pfaffian state or the anti-Pfaffian state has been the subject of debate [2][3]. Here we consider various edge-state scenarios which may explain the measured thermal conductance, paying close attention to the role of contacts and edge-state equilibration. Through a study of the kinetic equations describing the low-temperature transport in the anti-Pfaffian and PH Pfaffian edge states, we determine regimes of parameter space, controlling the interactions between the different edge modes, that agree with experiment. We also discuss how point-contact tunneling can distinguish various edge-state scenarios.

[1] M. Banerjee, M. Heiblum, V. Umansky, D. E. Feldman, Y. Oreg, and A. Stern. Nature, 559(7713):205–210, 2018.
[2] S. H. Simon. Phys. Rev. B, 97:121406, Mar 2018.
[3] D. E. Feldman. Phys. Rev. B, 98:167401, Oct 2018.   

Patterns in paired electron additions to fractional quantum Hall edge states in large GaAs quantum dots

In vertical tunneling into a large and low disorder 2D GaAs quantum dot, we observe electrons entering edge states and an unusual and unpredicted pair tunneling of electrons into the dot’s quantum Hall edge states, with double-height capacitance peaks and a coincident h/2e periodicity in magnetic flux through the dot. Remarkably, results from interferometry experiments[1] at similar Landau level filling fractions also show this h/2e periodicity over the nearly the same filling factor range where it is observed in these dot experiments. Thus, in increasing the magnetic field through the dot by one flux quantum, we observe that 4 electrons are added to the edge (2 double height peaks). While we observe such pairing everywhere in the filling factor range from v = 2 to v = 5, the h/2e periodicity applies near filling factor 5/2. Away from 5/2, the double-height peaks are not uniformly spaced in magnetic field but instead themselves group into pairs. Fourier transforms of the data reveal different unusual periodicities other than h/e and h/2e, particularly in the tunneling rates for the peaks.
[1]Choi et al. Nat. Comm. 6, 7435 (2015)   

Flux superperiods and periodicity transitions in quantum Hall interferometers

For strongly screened Coulomb interactions, quantum Hall interferometers can operate in a novel regime: the intrinsic energy gap can be larger than the charging energy, and addition of flux quanta can occur without adding quasi-particles. We show that flux superperiods are possible, and reconcile their appearance with the Byers-Yang theorem. We explain that the observation of anyonic statistical phases is possible by tuning to the transition from a regime with constant chemical potential to a regime with constant particle density, where a flux superperiod changes to a periodicity with one flux quantum at a critical magnetic field strength.   

Probing the photon-assisted processes of anyons of charge e/3 and e/5 in the FQHE regime

Recently, the microwave excitation of fractional edge channels at GHz frequency f have demonstrated time domain manipulation of e*=e/3 and e*=e/5 charged anyons in the FQHE regime [1]. The signature of anyons absorbing a single photon was observed a shot noise ingularity when the applied voltage obeying the fractional Josephson relation e*V=hf. Going beyond these observations we analyze the amplitude of the microwave field propagating from the excited contact to a Quantum Point Contact. Using photon-assisted current, the microwave amplitude is shown to display interference when sweeping the frequency from 2 to 18GHz. We attribute these interference features to different propagation velocities of neutral and charged electron (or anyon) modes when several integer or fractional edge propagates in parallel. This study provide the necessary information to realize single anyon sources similar to Leviton [2] sources.
[1] A Josephson relation for fractionnally charged anyons, M. Kapfer et al. ( SCIENCE (2019) https://doi.org/10.1126/science.aau3539 )
[2] Minimal-excitation states for electron quantum optics using levitons, J. Dubois et al., NATURE 502, 659-663 (2013   

Sublattice resolved spin wave transport through graphene fractional quantum Hall states as a probe of isospin order

High quality graphene heterostructures host an array of fractional quantum Hall isospin ferromagnets with diverse spin and valley orders. While a variety of phase transitions have been observed, disentangling the isospin phase diagram of these states is hampered by the absence of direct probes of spin and valley order. I will describe nonlocal transport measurements based on launching spin waves from a gate defined lateral heterojunction, performed in ultra-clean Corbino geometry graphene devices. At high magnetic fields, we find that the spin-wave transport signal is detected in all FQH states between ν = 0 and 1; however, between ν = 1 and 2 only odd numerator FQH states show finite nonlocal transport, despite the identical ground state spin polarizations in odd- and even numerator states. The results reveal that the neutral spin-waves are both spin and sublattice polarized making them a sensitive probe of ground state sublattice structure. Armed with this understanding, we use nonlocal transport signal to a magnetic field tuned isospin phase transition, showing that the emergent even denominator state at ν = 1/2 in monolayer graphene is indeed a multicomponent state featuring equal populations on each sublattice.   

Microscopic theory of fractional excitations in gapless bilayer quantum Hall states: semi-quantized quantum Hall states

Recent experiments in quantum Hall bilayer systems have revealed a new strongly correlated state: the semi-quantized quantum Hall state. This state arises in a bilayer quantum Hall system with strong interlayer-interactions, has a quantized Hall resistance and vanishing longitudinal resistance, while at the same time featuring a gapless sector that allows this state to exist for a continuum of filling factors. In this talk, I will explain what a semi-quantized quantum Hall state is, and use a coupled-wire construction to predict possible future experiments in the already existing experimental platforms.   

Non-linear transport and noise measurements in reentrant integer quantum Hall states

Two-dimensional electron gas (2DEG) system in strong magnetic field is an ideal platform to explore interesting physics such as reentrant integer quantum Hall (RIQH) effect in second and higher Landau levels. We have carried out non-linear transport and noise measurements in ultra-high mobility GaAs/AlGaAs 2DEG to study RIQH states in Corbino-geometry samples. By increasing the DC bias gradually, we found the insulating phase of RIQH states disappeared, and the depinning trace can be divided into three regions according to different DC bias values. The narrow-band noise only appears in the middle region.   

Edge Mode Engineering and Interferometry in the Quantum Hall Regime

The interference of fractional charges is a much sought after goal in a variety of electronic interferometers. It has been shown before in an electronic Mach-Zehnder interferometer that neutral modes, topological or non-topological (via edge-reconstruction), cause dephasing in the fractional quantum Hall effect regime [1]. Recently interference of fractional charges has been observed in an electronic Fabry-Perot interferometer [2], though anionic statistics was not revealed. Here, we have adapted a novel route of engineering edge channels away from the physical boundary in order to minimize edge reconstruction. First, we show that these engineered edge channels, especially fractional ones, can have different edge structures (with a different thermal conductance) compared to ubiquitous edge channels that have the same electrical conductance. We then used a modified Mach-Zehnder interferometer to interfere such synthetic edge modes, with initial promising results.


[1] Rajarshi Bhattacharyya, Mitali Banerjee, Moty Heiblum, Diana Mahalu, Vladimir Umansky, Phys. Rev. Lett. 122, 246801 (2019)
[2] J. Nakamura, S. Fallahi, H. Sahasrabuddhe, R. Rahman, S. Liang, G.C. Gardner, M.J. Manfra, Nature Physics 15, 563-569(2019)   

Paired Electron Additions to Fractional Quantum Hall Edge States in Large GaAs Quantum Dots

We measure capacitance signals from additions of single electrons to a large (0.8 μm) 2D GaAs quantum dot and thereby determine the energies required to add electrons to the dot. The dot is sandwiched inside of a “tunnel capacitor” in which electrons can tunnel from the dot to a nearby capacitor electrode. We observe single electron capacitance peaks to edge states over a wide range of filling factors. As a function of magnetic flux through the dot, between filling factors v = 1 and v = 2, these edge state peaks are regularly spaced, with periodicity h/e. Surprisingly, over the range v = 2 to v = 5, the peaks have double-height, and the periodicity is halved to h/2e. The pairing cannot be explained in the Coulomb blockade picture, in which the two electrons in a pair would instead be separated by a charging energy, and models involving electron rearrangements fail because they predict a suppression of tunneling rates that we do not observe. Instead the sequence of successive paired tunneling events behaves in the same way as tunneling of electrons into superconducting quantum dots.   

Fabry-Perot interferometry of fractional quantum Hall edge states

Electronic interferometry has been proposed as an experimental probe of the braiding statistics and quasiparticle charge in quantum Hall states. Two significant challenges in Fabry-Perot interferometers are Coulomb charging effects and poor phase coherence. We have overcome these challenges using a novel GaAs/AlGaAs heterostructure which utilizes auxiliary GaAs screening wells in addition to the primary quantum well in order to screen and suppress Coulomb charging effects. This heterostructure design has enabled measurements of robust Aharonov-Bohm interfere at the ν = 1/3 fractional quantum Hall state. A recent theoretical work has predicted a shift in the interference pattern at ν = 1/3 when the magnetic field is varied from the center of the plateau. We present experimental measurements of Aharonov-Bohm interference across the 1/3 plateau. These results represent progress towards direct observation of anyonic braiding statistics.   

Phase Diagram of Majorana Island

Scalable topological qubit proposals based on semiconductor-superconductor systems are built on Majorana islands hosting pairs of Majorana zero modes. Here, by systematically measuring the periodicity of Coulomb blockade oscillations of InSb/Al island, we reconstruct the ground state parity of the island over large ranges of magnetic field and plunger gate voltage (Vpg). The resulting phase diagram can be divided into three regimes compared with numerical simulations. For negative Vpg, sub-gap states are absent due to strong proximity effect, so the 2e to 1e-periodic transition happens at high B-fields, indicating the poisoning of the superconducting state. For positive Vpg, the 2e-1e transition happens instead at a constant but small B-field. The reason is un-proximitized states quickly disperse below the charging energy due to the orbital effect of the magnetic field. The two regimes are separated by an intermediate regime where the 2e-1e transition field varies smoothly with Vpg, which is the most promising for locating a robust topological phase according to simulations. In this regime, we observe correlated oscillating peak spacing and heights. This complete phase diagram of Majorana island can lead to a guideline to set up a topological qubit in more complicated devices.   

Wigner Crystal Melting Phase Diagram of GaAs Two-dimensional Holes

In a strongly interacting two-dimensional (2D) electron system, when the Coulomb energy dominates over the kinetic energy, the electrons tend to arrange periodically and form a so-called Wigner crystal (WC) ground state. In a GaAs 2D electron system, a magnetic-field-induced quantum WC forms at very low temperature and high magnetic field near filling factor v = 1/5 when the kinetic (Fermi) energy is quenched and the Coulomb energy dominates. In an GaAs 2D hole system, on the other hand, the WC phase forms near v = 1/3 because of the significant Landau level mixing caused by the large hole effective mass. Despite the fact that the 2D hole system has been a subject of intense interest for many years, a WC melting temperature vs filling factor phase diagram has been missing. In this work, we map out such phase diagram using a newly developed technique which probes the melting of the WC via its screening efficiency. The phase diagram shows rich features of the WC phases at low fillings and a clear reentrant behavior around v = 1/3.