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We demonstrate operation of a small Fabry-Perot interferometer in which highly coherent Aharonov-Bohm oscillations are observed in the integer and fractional quantum Hall regimes. Using a novel heterostructure design, Coulomb effects are drastically suppressed. Coherency of edge mode interference is characterized by the energy scale for thermal damping, T0 = 206mK at ν = 1. Selective backscattering of edge modes originating in the N = 0, 1, 2 Landau levels allows for independent determination of inner and outer edge mode velocities. Clear Aharonov-Bohm oscillations are observed at fractional filling factors ν = 2/3 and ν = 1/3. Our device architecture provides a platform for measurement of anyonic braiding statistics. arXiv:1901.08452v1 [cond-mat.mes-hall]

The so-called zigzag edge of graphenes has localized and strongly spin-polarized electrons. However, magnetoresistance (MR) behavior associated with the edge electrons has not been reported in graphenes. Here, we measure MR of graphene antidot-lattices, honeycomb-like arrays of hexagonal antidots with a large ensemble of hydrogen-terminated and low-defect antidot edges, prepared by a nonlithographic method using nanoporous alumina templates. We find anomalous MR oscillations arising from localized electron spins existing at the antidot edges. These are promising for realization of spintronic devices.

We consider quantum lifetime derived from low-field Shubnikov-de Haas oscillations as a metric of quality of the two-dimensional electron gas in GaAs quantum wells that expresses large excitation gaps of the ⌫ = 5 2 fractional quantum Hall state in the N=1 Landau level. In high quality samples small density inhomogeneities dramatically impact the amplitude of Shubnikov-de Haas oscillations such that the canonical method (cf. Coleridge, Phys. Rev. B 44, 3793) for determination of quantum lifetime substantially underestimates ⌧ q unless density inhomogeneity is explicitly considered. We have developed a method which can be used to determine density inhomogeneity and extract the intrinsic ⌧ q by analyzing the Shubnikov-de Haas oscillations. However, even after accounting for inhomogeneity, ⌧ q does not correlate well with sample quality as measured by 5/2 , the excitation gap of the fractional quantum Hall state at 5/2 filling.

Liquid crystalline phases of matter permeate nature and technology, with examples ranging from cell membranes to liquid-crystal displays. Remarkably, electronic liquid-crystal phases can exist in two-dimensional electron systems (2DES) at half Landau-level filling in the quantum Hall regime. Theory has predicted the existence of a liquid-crystal smectic phase that breaks both rotational and translational symmetries. However, previous experiments in 2DES are most consistent with an anisotropic nematic phase breaking only rotational symmetry. Here we report three transport phenomena at half-filling in ultra-low disorder 2DES: a non-monotonic temperature dependence of the sample resistance, dramatic onset of large time-dependent resistance fluctuations, and a sharp feature in the differential resistance suggestive of depinning. These data suggest that a sequence of symmetry-breaking phase transitions occurs as temperature is lowered: first a transition from an isotropic liquid to a nematic phase and finally to a liquid-crystal smectic phase.

Observation of interference in the quantum Hall regime may be hampered by a small edge state velocity due to finite phase coherence time. Therefore designing two quantum point contact (QPCs) interferometers having a high edge state velocity is desirable. Here, we present a new simulation method for realistically modeling edge states near QPCs in the integer quantum Hall effect (IQHE) regime. We calculate the filling fraction in the center of the QPC and the velocity of the edge states, and predict structures with high edge state velocity. The 3D Schrödinger equation is split into 1D and 2D parts. Quasi-1D Schrödinger and Poisson equations are solved self-consistently in the IQHE regime to obtain the potential profile near the edges, and quantum transport is used to solve for the edge state wavefunctions. The velocity of edge states is found to be E /B, where E is the expectation value of the electric field for the edge state. Anisotropically etched trench gated heterostructures with double sided delta doping have the highest edge state velocity among the structures considered.

Quantum Hall interferometers have been used to probe fractional charge and statistics of quasiparticles. We present measurements of a small Fabry–Perot interferometer in which the electrostatic coupling constants which affect interferometer behavior can be determined experimentally. Near the center of the ν = 1/3 state this device exhibits Aharonov–Bohm interference interrupted by a few discrete phase jumps, and Φ0 oscillations at higher and lower magnetic fields, consistent with theoretical predictions for detection of anyonic statistics. We estimate the electrostatic parameters KI and KIL by two methods: using the ratio of oscillation periods in compressible versus incompressible regions, and from finite-bias conductance measurements. We find that the extracted KI and KIL can account for the deviation of the phase jumps from the theoretical anyonic phase θa = 2π/3. At integer states, we find that KI and KIL can account for the Aharonov–Bohm and Coulomb-dominated behavior of different edge states.

We study low-frequency charge noise in shallow GaAs/AlGaAs heterostructures using quantum point contacts as charge sensors. We observe that devices with an Al2O3 dielectric between the metal gates and semiconductor exhibit significantly lower charge noise than devices with only Schottky gates and no dielectric. Additionally, the devices with Schottky gates exhibit drift over time toward lower conductance, while the devices with the dielectric drift toward higher conductance. Temperature-dependent measurements suggest that in devices with Schottky gates, noise is dominated by tunneling from the gates to trap sites in the semiconductor, and when this mechanism is suppressed by inclusion of a dielectric, thermally activated hopping between trap sites becomes the dominant source of noise.