Carlos Forsythe

Tunable fractional quantum Hall phases in bilayer graphene

Breaking down graphene degeneracy Bilayer graphene has two layers of hexagonally arranged carbon atoms stacked on top of each other in a staggered configuration. This spatial arrangement results in degenerate electronic states: distinct states that have the same energy. Interaction between electrons can cause the states to separate in energy, and so can external fields (see the Perspective by LeRoy and Yankowitz). Kou et al., Lee et al., and Maher et al. used three distinct experimental setups that clarify different parameter regimes of bilayer graphene. Science, this issue p. 55, p. 58, p. 61; see also p. 31 The influence of the electric field on electronic properties is studied in dual-gated bilayer graphene. [Also see Perspective by LeRoy and Yankowitz] Symmetry-breaking in a quantum system often leads to complex emergent behavior. In bilayer graphene (BLG), an electric field applied perpendicular to the basal plane breaks the inversion symmetry of the lattice, opening a band gap at the charge neutrality point. In a quantizing magnetic field, electron interactions can cause spontaneous symmetry-breaking within the spin and valley degrees of freedom, resulting in quantum Hall effect (QHE) states with complex order. Here, we report fractional QHE states in BLG that show phase transitions that can be tuned by a transverse electric field. This result provides a model platform with which to study the role of symmetry-breaking in emergent states with topological order.

Landau Level Spectroscopy of Electron-Electron Interactions in Graphene

We present magneto-Raman scattering studies of electronic inter-Landau level excitations in quasineutral graphene samples with different strengths of Coulomb interaction. The band velocity associated with these excitations is found to depend on the dielectric environment, on the index of Landau level involved, and to vary as a function of the magnetic field. This contradicts the single-particle picture of noninteracting massless Dirac electrons but is accounted for by theory when the effect of electron-electron interaction is taken into account. Raman active, zero-momentum inter-Landau level excitations in graphene are sensitive to electron-electron interactions due to the nonapplicability of the Kohn theorem in this system, with a clearly nonparabolic dispersion relation.

Measurement of collective dynamical mass of Dirac fermions in graphene

Individual electrons in graphene behave as massless quasiparticles. Unexpectedly, it is inferred from plasmonic investigations that electrons in graphene must exhibit a non-zero mass when collectively excited. The inertial acceleration of the electron collective mass is essential to explain the behaviour of plasmons in this material, and may be directly measured by accelerating it with a time-varying voltage and quantifying the phase delay of the resulting current. This voltage-current phase relation would manifest as a kinetic inductance, representing the reluctance of the collective mass to accelerate. However, at optical (infrared) frequencies, phase measurements of current are generally difficult, and, at microwave frequencies, the inertial phase delay has been buried under electron scattering. Therefore, to date, the collective mass in graphene has defied unequivocal measurement. Here, we directly and precisely measure the kinetic inductance, and therefore the collective mass, by combining device engineering that reduces electron scattering and sensitive microwave phase measurements. Specifically, the encapsulation of graphene between hexagonal boron nitride layers, one-dimensional edge contacts and a proximate top gate configured as microwave ground together enable the inertial phase delay to be resolved from the electron scattering. Beside its fundamental importance, the kinetic inductance is found to be orders of magnitude larger than the magnetic inductance, which may be utilized to miniaturize radiofrequency integrated circuits. Moreover, its bias dependency heralds a solid-state voltage-controlled inductor to complement the prevalent voltage-controlled capacitor.

Ambipolar Landau levels and strong band-selective carrier interactions in monolayer WSe 2

Monolayers (MLs) of transition-metal dichalcogenides (TMDs) exhibit unusual electrical behaviour under magnetic fields due to their intrinsic spin–orbit coupling and lack of inversion symmetry1–15. Although recent experiments have also identified the critical role of carrier interactions within these materials11,15, a complete mapping of the ambipolar Landau level (LL) sequence has remained elusive. Here we use single-electron transistors (SETs)16,17 to perform LL spectroscopy in ML WSe2, and provide a comprehensive picture of the electronic structure of a ML TMD for both electrons and holes. We find that the LLs differ notably between the two bands, and follow a unique sequence in the valence band (VB) that is dominated by strong Zeeman effects. The Zeeman splitting in the VB is several times higher than the cyclotron energy, far exceeding the predictions of a single-particle model and, moreover, tunes significantly with doping15. This implies exceptionally strong many-body interactions, and suggests that ML WSe2 can serve as a host for new correlated-electron phenomena.Measurements of the chemical potential in a monolayer of WSe2 using a single electron transistor sensing scheme allows for the exact mapping of the level spacing of Landau levels of monolayer WSe2 in the conductance and valence bands.

Band structure engineering of 2D materials using patterned dielectric superlattices

The ability to manipulate electrons in two-dimensional materials with external electric fields provides a route to synthetic band engineering. By imposing artificially designed and spatially periodic superlattice potentials, electronic properties can be further altered beyond the constraints of naturally occurring atomic crystals1–5. Here, we report a new approach to fabricate high-mobility superlattice devices by integrating surface dielectric patterning with atomically thin van der Waals materials. By separating the device assembly and superlattice fabrication processes, we address the intractable trade-off between device processing and mobility degradation that constrains superlattice engineering in conventional systems. The improved electrostatics of atomically thin materials allows smaller wavelength superlattice patterns relative to previous demonstrations. Moreover, we observe the formation of replica Dirac cones in ballistic graphene devices with sub-40 nm wavelength superlattices and report fractal Hofstadter spectra6–8 under large magnetic fields from superlattices with designed lattice symmetries that differ from that of the host crystal. Our results establish a robust and versatile technique for band structure engineering of graphene and related van der Waals materials with dynamic tunability.A new superlattice fabrication process on 2D material heterostructures enables the observation of replica Dirac cones in graphene as well as Hofstadter’s fractal magnetic spectrum under triangular and square superlattice symmetries.