Session E07: Fractional Quantum Hall 1

Quantitative comparisons between theory and experiment in fractional quantum Hall effect

Comparisons with exact computer experiments have demonstrated the composite fermion theory to be quantitatively accurate at the level of a few percent, but the discrepancy with actual experiments is much larger because of corrections due to finite quantum well width, Landau level mixing and disorder. We carry out detailed calculations for spin phase transitions [1] including the effect Landau level mixing through a non-perturbative fixed phase diffusion Monte Carlo method [2], and find excellent agreement with experimental results. In particular, we explain a substantial difference between spin phase transitions for states at $\nu=n/(2n+1)$ and $\nu=2-n/(2n+1)$ which are related by an exact particle hole symmetry in the absence of Landau level mixing. We also study [3] the competition between the fractional quantum Hall liquid and the crystal phases in the presence of Landau level mixing and explain the re-entrant transitions between FQHE and insulator in the vicinity of $nu=1/3$ in low density hole type samples.

[1] Y. Zhang et al. PRL 117, 116803 (2016); PRB 95, 195105 (2017).
[2] G. Ortiz, D.M. Cepterley, R.M. Martin, PRL 71, 2777 (1993); V. Melik-Alaverdian et al. PRL 79, 5286 (1997); A. D. Guclu and C. J. Umrigar, PRB 71, 045309 (2005).
[3] J. Zhano et al. unpublished.   

Loop Models, Modular Symmetry and Duality

We will discuss the connection between loop mopdels of particle-hole invariant theories of anyons to field theoreric dualities. We will discuss both systems in two space dimensions and boundaries of 3D systems, and the role of quantum anomalies. We will discuss the signifcance of our results to theories of quantum phase transitions in fractional quantum Hall fluids and other two and three-dimensional topological fluids.   

Studies of Localization in a Fraction of the Lowest Landau Level

The problem of localization in the lowest Landau level has been studied extensively and is known to exhibit a diverging localization length due to the presence of topological extended states. In the presence of interactions, these states were shown to delocalize the entire spectrum [1]. We consider the case of a disordered two-dimensional electron system in a high magnetic field with a periodic delta-function potential, which splits the lowest Landau level into Hofstadter subbands. Our particular choice of potential allows us to isolate a set of subbands with vanishing total Chern number and with tunable bandwidth-to-bandgap ratio. By projecting the system into one such set of bands, we are able to investigate the nature of localization in a topologically trivial fraction of the lowest Landau level. We study the projected problem by numerical exact diagonalization and compare the results to those obtained without the projection procedure, thus shedding light on the role of topological extended states in hindering localization. The stability of the localized phase to interactions and the possibility of a many-body localized regime is also studied.
[1] S. D. Geraedts and R. N. Bhatt, Phys. Rev. B 95, 054303 (2017)   

Bimetric Theory of Fractional Quantum Hall States

I will describe the recently developed bimetric theory of fractional quantum Hall states. This effective theory includes the Chern-Simons theory that describes the topological properties of the fractional quantum Hall states and a la quantum bimetric gravity theory that describes the massive Girvin-MacDonald-Platzman mode at long wavelengths. The theory reproduces universal features of the chiral lowest Landau level (LLL) FQH states that lie beyond the reach of pure Chern-Simons theory, such as the projected static structure factor and the GMP algebra. The LLL projection and particle-hole ``symmetry'' of the theory are particularly transparent. Familiar quantum Hall observables acquire a curious geometric interpretation in the bimetric language.   

The 16-fold Way and the Quantum Hall Effect at ν=5/2

Numerous topological orders were proposed in the QHE at the filling factor ν=5/2. We show that the popular Pfaffian, SU(2)₂, 113, K=8, 331, PH-Pfaffian orders, and their particle-hole conjugates can be classified in terms of Kitaev's 16-fold way. The experimental evidence for composite fermions at ν=5/2 suggests that only the topological orders of the 16-fold way are viable 5/2 states. We use a coupled QHE strip construction to generate Hamiltonians for all 16 orders from the parent Hamiltonians for the Pfaffian and K=8 states. We address the signatures of the 16 orders in Mach-Zehnder and Fabry-Pérot interferometry, and electrical and thermal transport. Only the PH-Pfaffian order is compatible with the existing data in GaAs at charge densities n∼3×10¹¹cm⁻².   

Imaging electron density variations in a high mobility GaAs modulation-doped quantum well

We use micro-photoluminescence (micro-PL) to measure the local electron density in a GaAs MBE quantum well under a 40 µm diameter laser excitation spot^[1]. When the laser excitation spot is raster-scanned across the sample, we observe in the PL signal, local variations in the Fermi filling that correspond to spatial variations in the electron density of the 2D system.
We find we can control the amplitude of these density fluctuations by varying the thickness of an insulating buffer layer located between the GaAs substrate and the quantum well. For a 200 nm buffer thickness the peak amplitudes of the density fluctuations are typically about 5% of the 2.6 x 10¹¹/cm² nominal electron density. Moreover, these fluctuation amplitudes decrease by a factor of ten when the buffer thickness increases by a factor of ten to 2000 nm. This suggests that the fluctuations are due to charged disorder patches located at the substrate/MBE interface. We believe these charged patches locally gate the 2D system in the nearby quantum well. The length-scale of these density fluctuations ranges from smaller than our 40 µm laser spot size to lengths as large as 700 µm.
[1] Appl. Phys. Lett. 110, 262104 (2017)
  

Effect of low-temperature illumination on quantum lifetime in GaAs quantum wells

It is well known that low temperature illumination of a high-mobility two-dimensional electron gas hosted in GaAs quantum wells can greatly improve the quality of magnetotransport data even when the carrier density and mobility remain essentially unchanged. In high magnetic fields, this improvement is evident from the appearance or better development of fractional quantum Hall states as well as stripe and bubble phases. However, what exactly drives this improvement remain unclear. Here, we investigate the effect of illumination on microwave photoresistance in low magnetic fields. We find that the amplitude of microwave-induced resistance oscillations increases dramatically after low-temperature illumination. Dingle analysis reveals that illumination leads to a substantial increase in the single particle lifetime.   

The Fractional Quantum Hall to Nematic Phase transition at ν = 7/2

Recently, we observed the hydrostatic pressure-driven transition from the fractional quantum Hall state to the quantum Hall nematic phase at ν = 5/2 in the GaAs two dimensional electron system. This discovery breaks expectations about the half filled Landau level, despite thirty years of research on these filling factors. The data we obtain is consistent with a quantum phase transition from the topologically ordered fractional quantum Hall state to the broken rotational symmetry quantum Hall nematic phase. Many aspects of this transition are still unknown, however.

To study the transition in greater detail, we report now on the ν = 7/2 state under pressure. The ν = 7/2 state is the particle-hole conjugate state of ν = 5/2, and is expected to share much of the same physics. Indeed, we observe the same transition from fractional quantum Hall state to quantum Hall nematic phase at ν = 7/2. The data we obtain at ν = 7/2 is also consistent with a quantum phase transition. However, the transitions from fractional quantum Hall to quantum Hall nematic phase occur at different pressures at ν = 5/2 and ν = 7/2. We discuss the implications of this finding. This work is funded by DOE Grant DE-SC0006671.

  

Phase transitions at filling ν = 5/2 in ZnO heterostructures

Half-filled Landau levels (LL) elicit competing phases which intimately depend on the nature of inter-particle interaction effects. The competition between emergent Fermi-surfaces, the fractional quantum Hall (FQH) effect and broken symmetry nematic ground states is now well documented. Here we report a complex cascade of phases which exist at filling ν = 5/2 in high mobility ZnO heterostructures and the ability to tune between them by selectively enhancing the Zeeman energy through sample rotation. We are able to induce a series of phase transitions between an incompressible FQH state, a compressible ground state, an anisotropic nematic state and an isotropic insulating state. These occur in the vicinity of the coincidence of the N = 1 and 0 LL as electrons are transferred between opposing spin branches. The even denominator FQH incompressibility only occurs when significant population of N = 1 exists, reinforcing the role of the orbital character of carriers for the development of this ground state. The anisotropic transport shows B-field sweep direction dependent hysteresis, suggesting the underlying nematic texture may be from magnetic domains of electrons of differing spin and orbital character close to the level crossing.   

Tunability of Landau Level Crossings and Fractional Quantum Hall Phases in Few Layer Ballistic Graphene

Bernal stacked trilayer graphene (TLG) has four low energy mirror symmetric bands. These bands are very electric field sensitive because electric field breaks the original mirror symmetry with respect to the middle layer of TLG. Electric field hybridizes the bands and consequently the Landau level (LL) spectrum in presence of magnetic field gets modified. We study the dependence of the LLs in TLG on electric field. TLG has many naturally occurring LL crossings due to its differently dispersing bands. This provides a great platform for studying electric field effect in terms of its LL crossing locations in phase space. Electric field couples only a specific set of LLs which led to the observation of mostly crossings rather than avoided crossing at the degeneracy points. However, interestingly, we see signatures of valley coupling due to short range electronic interaction at the crossing point of two opposite valleys of zeroth LL (N_M=0). These opposite valleys are brought into degeneracy by an electric field. We also observe some signatures of fractional quantum Hall effect in TLG.   

Observation of new collective mode in the partially populated second Landau level

We present the observation of a new collective mode in the partially populated second Landau level. The mode is measured in experiments of resonant inelastic light scattering (RILS) at temperature of 40mK. Its energy is proportional to the square root of the filling factor of quasiholes for electron filling factors v equal or greater than v= 5/2 or quasiparticles for v equal or less than v= 5/2. This collective mode exists in the range 2.1 < v < 2.8. While the mode coexists with the fractional quantum Hall state at v= 7/3, it is absent at v= 5/2. Possible interpretations of this intriguing observation will be considered.   

Berry Phase and Anomalous Transport of the Composite Fermions at the Half-Filled Landau Level

Recent developments in the theory of composite fermions (CFs) have led to a prediction of a π Berry phase for the CFs circling around the Fermi surface at half-filling ν=1/2 (where ν is the Landau level filling factor). In this talk, we provide the first experimental evidence for the detection of the Berry phase of CFs in the fractional quantum Hall effect by studying their density-dependent magnetotransport in heterojunction insulated-gate field-effect transistors (HIGFETs), in which the electron density can be tuned over a large range. Our measurements of the Shubnikov-de Haas oscillations of CFs as a function carrier density at a fixed magnetic field provide a strong support for an existence of a π Berry phase at ν = 1/2. We also discover that the conductivity of composite fermions at ν = 1/2 displays an anomalous linear density dependence, whose origin remains mysterious yet tantalizing.   

3/2 fractional quantum Hall plateau in a single layer two-dimensional electron gas

In a single layer two-dimensional electron gas, we observed a new even-denominator fractional quantum Hall plateau quantized at (h/e^2 )/(3/2) under confinement, at a bulk filling factor of 5/3. This unexpected plateau develops below 300 mK with a quantization of 0.02%. The conductance transmitting through the confined region is also quantized at 3/2 e^2/h, and the conductance of 1/6 e^2/h is backscattered. A new elemental excitation with e/6 effective charge, the further fractionalization of the e/3 quasi-particles, through topological soliton and topological phase transition is proposed as a tentative explanation.