Local Noise Spectroscopy of Wigner Crystals in Two-Dimensional Materials.

We propose local electromagnetic noise spectroscopy as a versatile and noninvasive tool to study Wigner crystal phases of strongly interacting two-dimensional electronic systems. In-plane imaging of the local noise is predicted to enable single-site resolution of the electron crystal when the sample-probe distance is less than the interelectron separation. At larger sample-probe distances, noise spectroscopy encodes information about the low-energy Wigner crystal phonons, including the dispersion of the transverse shear mode, the pinning resonance due to disorder, and optical modes emerging, for instance, in bilayer crystals. We discuss the potential utility of local noise probes in analyzing the rich set of phenomena expected to occur in the vicinity of the melting transition.

Cascade of Multielectron Bubble Phases in Monolayer Graphene at High Landau Level Filling.

The phase diagram of an interacting two-dimensional electron system in a high magnetic field is enriched by the varying form of the effective Coulomb interaction, which depends strongly on the Landau level index. While the fractional quantum Hall states that dominate in the lower-energy Landau levels have been explored experimentally in a variety of two-dimensional systems, much less work has been done to explore electron solids owing to their subtle transport signatures and extreme sensitivity to disorder. Here, we use chemical potential measurements to map the phase diagram of electron solid states in N=2, N=3, and N=4 Landau levels in monolayer graphene. Direct comparison between our data and theoretical calculations reveals a cascade of density-tuned phase transitions between electron bubble phases up to two, three, or four electrons per bubble in the N=2, 3, and 4 Landau levels, respectively. Finite-temperature measurements are consistent with melting of the solids for T≈1 K.

Experimental Determination of the Energy per Particle in Partially Filled Landau Levels.

We describe an experimental technique to measure the chemical potential µ in atomically thin layered materials with high sensitivity and in the static limit. We apply the technique to a high quality graphene monolayer to map out the evolution of µ with carrier density throughout the N=0 and N=1 Landau levels at high magnetic field. By integrating µ over filling factor ν, we obtain the ground state energy per particle, which can be directly compared to numerical calculations. In the N=0 Landau level, our data show exceptional agreement with numerical calculations over the whole Landau level without adjustable parameters as long as the screening of the Coulomb interaction by the filled Landau levels is accounted for. In the N=1 Landau level, a comparison between experimental and numerical data suggests the importance of valley anisotropic interactions and reveals a possible presence of valley-textured electron solids near odd filling.

Beam steering at the nanosecond time scale with an atomically thin reflector.

Techniques to mold the flow of light on subwavelength scales enable fundamentally new optical systems and device applications. The realization of programmable, active optical systems with fast, tunable components is among the outstanding challenges in the field. Here, we experimentally demonstrate a few-pixel beam steering device based on electrostatic gate control of excitons in an atomically thin semiconductor with strong light-matter interactions. By combining the high reflectivity of a MoSe2 monolayer with a graphene split-gate geometry, we shape the wavefront phase profile to achieve continuously tunable beam deflection with a range of 10°, two-dimensional beam steering, and switching times down to 1.6 nanoseconds. Our approach opens the door for a new class of atomically thin optical systems, such as rapidly switchable beam arrays and quantum metasurfaces operating at their fundamental thickness limit.

Observation of fractional Chern insulators in a van der Waals heterostructure.

Topologically ordered phases are characterized by long-range quantum entanglement and fractional statistics rather than by symmetry breaking. First observed in a fractionally filled continuum Landau level, topological order has since been proposed to arise more generally at fractional fillings of topologically nontrivial Chern bands. Here we report the observation of gapped states at fractional fillings of Harper-Hofstadter bands arising from the interplay of a magnetic field and a superlattice potential in a bilayer graphene-hexagonal boron nitride heterostructure. We observed phases at fractional filling of bands with Chern indices [Formula: see text] Some of these phases, in [Formula: see text] and [Formula: see text] bands, are characterized by fractional Hall conductance-that is, they are known as fractional Chern insulators and constitute an example of topological order beyond Landau levels.