Monica Allen

Broken-Symmetry States in Doubly Gated Suspended Bilayer Graphene

Broken Symmetries Bilayer graphene samples are expected exhibit quantum Hall states that are ferromagnetic with different types of spin ordering. Weitz et al. (p. 812, published online 14 October) studied the conductance of high-quality suspended bilayer graphene samples. They used an applied perpendicular electric field to induce transitions between the different broken-symmetry states that appear at low carrier densities and deduced their order parameters. These states appeared in both the absence of a magnetic field, as well as in the presence of a symmetry-breaking magnetic field. They also showed that, even in absence of both an applied magnetic or electric field, the bilayer exhibits an energy gap, which indicates that electron-electron interactions contribute to the band structure. Ferromagnetic quantum Hall states were observed in suspended bilayer graphene samples in both zero and high magnetic fields. The single-particle energy spectra of graphene and its bilayer counterpart exhibit multiple degeneracies that arise through inherent symmetries. Interactions among charge carriers should spontaneously break these symmetries and lead to ordered states that exhibit energy gaps. In the quantum Hall regime, these states are predicted to be ferromagnetic in nature, whereby the system becomes spin polarized, layer polarized, or both. The parabolic dispersion of bilayer graphene makes it susceptible to interaction-induced symmetry breaking even at zero magnetic field. We investigated the underlying order of the various broken-symmetry states in bilayer graphene suspended between top and bottom gate electrodes. We deduced the order parameter of the various quantum Hall ferromagnetic states by controllably breaking the spin and sublattice symmetries. At small carrier density, we identified three distinct broken-symmetry states, one of which is consistent with either spontaneously broken time-reversal symmetry or spontaneously broken rotational symmetry.

Gate defined quantum confinement in suspended bilayer graphene

Quantum-confined devices that manipulate single electrons in graphene are emerging as attractive candidates for nanoelectronics applications. Previous experiments have employed etched graphene nanostructures, but edge and substrate disorder severely limit device functionality. Here we present a technique that builds quantum-confined structures in suspended bilayer graphene with tunnel barriers defined by external electric fields that open a bandgap, thereby eliminating both edge and substrate disorder. We report clean quantum dot formation in two regimes: at zero magnetic field B using the energy gap induced by a perpendicular electric field and at B>0 using the quantum Hall ν=0 gap for confinement. Coulomb blockade oscillations exhibit periodicity consistent with electrostatic simulations based on local top-gate geometry, a direct demonstration of local control over the band structure of graphene. This technology integrates single electron transport with high device quality and access to vibrational modes, enabling broad applications from electromechanical sensors to quantum bits.

Spatially resolved edge currents and guided-wave electronic states in graphene

Experiments show that electron waves can be confined to and guided along the edges of monolayer and bilayer graphene sheets, analogous to the guiding of light waves in optical fibres.

Local Compressibility Measurements of Correlated States in Suspended Bilayer Graphene

Bilayer graphene has attracted considerable interest due to the important role played by many-body effects, particularly at low energies. Here we report local compressibility measurements of a suspended graphene bilayer. We find that the energy gaps at filling factors ν= ± 4 do not vanish at low fields, but instead merge into an incompressible region near the charge neutrality point at zero electric and magnetic field. These results indicate the existence of a zero-field ordered state and are consistent with the formation of either an anomalous quantum Hall state or a nematic phase with broken rotational symmetry. At higher fields, we measure the intrinsic energy gaps of broken-symmetry states at ν=0, ± 1, and ± 2, and find that they scale linearly with magnetic field, yet another manifestation of the strong Coulomb interactions in bilayer graphene.

Gyromagnetically induced transparency of metasurfaces.

We demonstrate that the presence of a (gyro) magnetic substrate can produce an analog of electromagnetically induced transparency in Fano-resonant metamolecules. The simplest implementation of such gyromagnetically induced transparency (GIT) in a metasurface, comprised of an array of resonant antenna pairs placed on a gyromagnetic substrate and illuminated by a normally incident electromagnetic wave, is analyzed. Time reversal and spatial inversion symmetry breaking introduced by the dc magnetization makes metamolecules bianisotropic. This causes Fano interference between the otherwise uncoupled symmetric and antisymmetric resonances of the metamolecules giving rise to a sharp transmission peak through the otherwise reflective metasurface. We show that, for an oblique wave incidence, one-way GIT can be achieved by the combination of spatial dispersion and gyromagnetic effect. These theoretically predicted phenomena pave the way to nonreciprocal switches and isolators that can be dynamically controlled by electric currents.

Observation of Electron Coherence and Fabry–Perot Standing Waves at a Graphene Edge

Electron surface states in solids are typically confined to the outermost atomic layers and, due to surface disorder, have negligible impact on electronic transport. Here, we demonstrate a very different behavior for surface states in graphene. We probe the wavelike character of these states by Fabry-Perot (FP) interferometry and find that, in contrast to theoretical predictions, these states can propagate ballistically over micron-scale distances. This is achieved by embedding a graphene resonator formed by gate-defined p-n junctions within a graphene superconductor-normal-superconductor structure. By combining superconducting Aharanov-Bohm interferometry with Fourier methods, we visualize spatially resolved current flow and image FP resonances due to p-n-p cavity modes. The coherence of the standing-wave edge states is revealed by observing a new family of FP resonances, which coexist with the bulk resonances. The edge resonances have periodicity distinct from that of the bulk states manifest in a repeated spatial redistribution of current on and off the FP resonances. This behavior is accompanied by a modulation of the multiple Andreev reflection amplitude on-and-off resonance, indicating that electrons propagate ballistically in a fully coherent fashion. These results, which were not anticipated by theory, provide a practical route to developing electron analog of optical FP resonators at the graphene edge.Abstract: Interference of standing waves in electromagnetic resonators forms thebasisofmanytechnologies, fromtelecommunications[1]andspectroscopy[2]tode-tection of gravitational waves [3]. However, unlike the connement of light wavesin vacuum, the interference of electronic waves in solids is complicated by boundaryproperties of the crystal, notably leading to electron guiding by atomic-scale poten-tials at the edges [4x967]. Understanding the microscopic role of boundaries on co-herent wave interference is an unresolved question due to the challenge of detectingcharge ow with submicron resolution. Here we employ Fraunhofer interferometryto achieve real-space imaging of cavity modes in a graphene Fabry-P erot (FP) res-´onator, embedded between two superconductors to form a Josephson junction [8].By directly visualizing current ow using Fourier methods [9], our measurements re-veal surprising redistribution of current on and off resonance. These ndings providedirect evidence of separate interference conditions for edge and bulk currents andreveal the ballistic nature of guided edge states. Beyond equilibrium, our measure-mentsshowstrongmodulationofthemultipleAndreevreectionamplitudeonanoffresonance, a direct measure of the gate-tunable change of cavity transparency. Theseresults demonstrate that, contrary to the common belief, electron interactions withrealistic disordered edges facilitate electron wave interference and ballistic transport.Graphene provides an appealing platform to explore x93electron-opticsx94 due to the ballistic nature ofwavelike carriers and ability to engineer transmission of electronic waves in real space using electro-static potentials [10x9617]. In particular, the electronic analog to refractive index is the Fermi energy,which is tunable via electrostatic gating [11,18]. Because the gapless spectrum of Dirac materialsenables continuous tunability of carrier polarity, positive and negative index of refraction regions canbe combined in bipolar structures that form the building blocks of Veselago x93electronic lensesx94 [15],Fabry-P ´erot (FP) interferometers [11x9615,17], and whispering gallery mode cavities [19]. Electronicanalogs to optical interferometers attract attention because relativistic effects such as hyperlensingand phase-coherent Klein transmission provide capabilities beyond conventional optics [10x9617,20].Here we investigate the simplest analog to an optical interferometer, the electron FP resonator, whichconsists of standing electron waves conned between two reective interfaces [21,22]. Despite ex-tensiveexplorationinthemomentumdomain,inwhichFermimomentumissimplytunedwithagate,little information is available about the real-space distribution of current ow due to the challenge ofimaging current paths with submicron resolution. Furthermore, in real devices, atomically sharp po-tentialsattheedgesofgraphenecanconneelectronwavesintoguidededgemodes,inanalogytotheguidingoflightinopticalbers[4x967],aswehavedemonstratedexperimentallyinpriorwork[23]. Toinvestigate the nature of these boundary currents, we measure the interference of standing waves in agraphene Josephson junction and image the real space distribution of supercurrent ow using Fraun-hofer interferometry [9]. By visualizing the spatial structure of current-carrying states in the cavityusing Fourier methods, our measurements disentangle edge from bulk current ow and highlight thesurprising role of the crystal boundaries.In a coherent electron cavity, quantum interference of electron waves replaces classical diffusionas a key feature of electronic transport [21,22]. In our system, a pair of superconducting electrodesis coupled to a graphene membrane, dening a ballistic cavity between the two graphene-electrodeinterfaces. As the Fermi wavelength in the cavity is tuned with a gate, the quantized energy levels ofthe cavity are moved on and off resonance with the Fermi energy of the superconducting leads, thusinducing an oscillatory critical current whose period satises the FP interference conditions. Due