A van der Waals heterostructure is a type of metamaterial that consists of vertically stacked two-dimensional building blocks held together by the van der Waals forces between the layers. This design means that the properties of van der Waals heterostructures can be engineered precisely, even more so than those of two-dimensional materials. One such property is the 'twist' angle between different layers in the heterostructure. This angle has a crucial role in the electronic properties of van der Waals heterostructures, but does not have a direct analogue in other types of heterostructure, such as semiconductors grown using molecular beam epitaxy. For small twist angles, the moiré pattern that is produced by the lattice misorientation between the two-dimensional layers creates long-range modulation of the stacking order. So far, studies of the effects of the twist angle in van der Waals heterostructures have concentrated mostly on heterostructures consisting of monolayer graphene on top of hexagonal boron nitride, which exhibit relatively weak interlayer interaction owing to the large bandgap in hexagonal boron nitride. Here we study a heterostructure consisting of bilayer graphene, in which the two graphene layers are twisted relative to each other by a certain angle. We show experimentally that, as predicted theoretically, when this angle is close to the 'magic' angle the electronic band structure near zero Fermi energy becomes flat, owing to strong interlayer coupling. These flat bands exhibit insulating states at half-filling, which are not expected in the absence of correlations between electrons. We show that these correlated states at half-filling are consistent with Mott-like insulator states, which can arise from electrons being localized in the superlattice that is induced by the moiré pattern. These properties of magic-angle-twisted bilayer graphene heterostructures suggest that these materials could be used to study other exotic many-body quantum phases in two dimensions in the absence of a magnetic field. The accessibility of the flat bands through electrical tunability and the bandwidth tunability through the twist angle could pave the way towards more exotic correlated systems, such as unconventional superconductors and quantum spin liquids.

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Twisted bilayer graphene (TBLG) is one of the simplest van der Waals heterostructures, yet it yields a complex electronic system with intricate interplay between moiré physics and interlayer hybridization effects. We report on electronic transport measurements of high mobility small angle TBLG devices showing clear evidence for insulating states at the superlattice band edges, with thermal activation gaps several times larger than theoretically predicted. Moreover, Shubnikov-de Haas oscillations and tight binding calculations reveal that the band structure consists of two intersecting Fermi contours whose crossing points are effectively unhybridized. We attribute this to exponentially suppressed interlayer hopping amplitudes for momentum transfers larger than the moiré wave vector.

†These authors contributed equally to this work. AbstractA quantum Hall edge state provides a rich foundation to study electrons in 1-dimension (1d) but is limited to chiral propagation along a single direction. Here, we demonstrate a versatile platform to realize new 1d systems made by combining quantum Hall edge states of opposite chiralities in a graphene electron-hole bilayer. Using this approach, we engineer helical 1d edge conductors where the counterpropagating modes are localized in separate electron and hole layers by a tunable electric field. These helical conductors exhibit strong nonlocal transport signals and suppressed backscattering due to the opposite spin polarizations of the counterpropagating modes. Moreover, we investigate these electron-hole bilayers in the fractional quantum Hall regime, where we observe conduction through fractional and integer edge states of opposite chiralities, paving the way towards the realization of 1d helical systems with fractional quantum statistics.A helical 1d conductor is an unusual electronic system where forward and backward moving electrons have opposite spin polarizations. Theoretically, a helical state can be realized by combining two quantum Hall edge states with opposite chiralities and opposite spin polarizations (1,2). Most experimental efforts though have focused on materials with strong spin-orbit coupling(3-5), which avoids the need for magnetic fields. However, an approach based on quantum Hall edge states offers greater flexibility in system design with less dependence on material parameters. Moreover, a quantum Hall platform could harness the unique statistics of fractional quantum Hall states. Recent proposals have predicted that such a system, in the form of a fractional quantum spin Hall state(6-8), could host fractional generalizations of Majorana bound states.To simultaneously realize two quantum Hall states with opposite chiralities, it is necessary to have coexisting electron-like and hole-like bands. Such electron-hole quantum Hall states are observed in semi-metals but suffer from low hole-mobilities (9, 10). In this respect, graphene is an attractive system because it has high carrier mobilities and is electron-hole symmetric. In fact, the graphene electron and hole bands can be inverted by the Zeeman effect to realize helical states (11,12), but requires very large magnetic fields (13,14). A similar outcome could be realized more easily in a bilayer system, where an electric field can dope one layer into the electron band and the other into the hole band. In a moderate magnetic field, this electronhole bilayer will develop quantum Hall edge states with opposite chiralities in each layer. Here, we demonstrate a graphene electron-hole bilayer, which we use to realize a helical 1-dimensional conductor made from quantum Hall edge states.All studied devices consist of two monolayer graphene flakes stacked together using a dry transfer process (15,16). The stacking results in a rotational misalignment, or twist, between the layers. The domin...

We report the development and results of a two-step method for sorting cells and small particles in a microfluidic device. This approach uses a single microfluidic channel that has (1) a microfabricated sieve which efficiently focuses particles into a thin stream, followed by (2) a dielectrophoresis (DEP) section consisting of electrodes along the channel walls for efficient continuous sorting based on dielectric properties of the particles. For our demonstration, the device was constructed of polydimethylsiloxane, bonded to a glass surface, and conductive agarose gel electrodes. Gold traces were used to make electrical connections to the conductive gel. The device had several novel features that aided performance of the sorting. These included a sieving structure that performed continuous displacement of particles into a single stream within the microfluidic channel (improving the performance of downstream DEP, and avoiding the need for additional focusing flow inlets), and DEP electrodes that were the full height of the microfluidic walls ("vertical electrodes"), allowing for improved formation and control of electric field gradients in the microfluidic device. The device was used to sort polymer particles and HeLa cells, demonstrating that this unique combination provides improved capability for continuous DEP sorting of particles in a microfluidic device. V C 2014 AIP Publishing LLC.