Exceptional electronic transport and quantum oscillations in thin bismuth crystals grown inside van der Waals materials.

Confining materials to two-dimensional forms changes the behaviour of the electrons and enables the creation of new devices. However, most materials are challenging to produce as uniform, thin crystals. Here we present a synthesis approach where thin crystals are grown in a nanoscale mould defined by atomically flat van der Waals (vdW) materials. By heating and compressing bismuth in a vdW mould made of hexagonal boron nitride, we grow ultraflat bismuth crystals less than 10 nm thick. Due to quantum confinement, the bismuth bulk states are gapped, isolating intrinsic Rashba surface states for transport studies. The vdW-moulded bismuth shows exceptional electronic transport, enabling the observation of Shubnikov-de Haas quantum oscillations originating from the (111) surface state Landau levels. By measuring the gate-dependent magnetoresistance, we observe multi-carrier quantum oscillations and Landau level splitting, with features originating from both the top and bottom surfaces. Our vdW mould growth technique establishes a platform for electronic studies and control of bismuth's Rashba surface states and topological boundary modes1-3. Beyond bismuth, the vdW-moulding approach provides a low-cost way to synthesize ultrathin crystals and directly integrate them into a vdW heterostructure.

Correlated insulator behaviour at half-filling in magic-angle graphene superlattices.

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.

Electrically driven amplification of terahertz acoustic waves in graphene.

In graphene devices, the electronic drift velocity can easily exceed the speed of sound in the material at moderate current biases. Under these conditions, the electronic system can efficiently amplify acoustic phonons, leading to an exponential growth of sound waves in the direction of the carrier flow. Here, we show that such phonon amplification can significantly modify the electrical properties of graphene devices. We observe a superlinear growth of the resistivity in the direction of the carrier flow when the drift velocity exceeds the speed of sound - resulting in a sevenfold increase over a distance of 8 µm. The resistivity growth is observed at carrier densities away from the Dirac point and is enhanced at cryogenic temperatures. We develop a theoretical model for the resistivity growth due to the electrical amplification of acoustic phonons - reaching frequencies up to 2.2 THz - where the wavelength is controlled by gate-tunable transitions across the Fermi surface. These findings provide a route to on-chip high-frequency sound generation and detection in the THz frequency range.

Controllable strain-driven topological phase transition and dominant surface-state transport in HfTe5.

The fine-tuning of topologically protected states in quantum materials holds great promise for novel electronic devices. However, there are limited methods that allow for the controlled and efficient modulation of the crystal lattice while simultaneously monitoring the changes in the electronic structure within a single sample. Here, we apply significant and controllable strain to high-quality HfTe5 samples and perform electrical transport measurements to reveal the topological phase transition from a weak topological insulator phase to a strong topological insulator phase. After applying high strain to HfTe5 and converting it into a strong topological insulator, we found that the resistivity of the sample increased by 190,500% and that the electronic transport was dominated by the topological surface states at cryogenic temperatures. Our results demonstrate the suitability of HfTe5 as a material for engineering topological properties, with the potential to generalize this approach to study topological phase transitions in van der Waals materials and heterostructures.

Mechanically reconfigurable van der Waals devices via low-friction gold sliding.

Interfaces of van der Waals (vdW) materials, such as graphite and hexagonal boron nitride (hBN), exhibit low-friction sliding due to their atomically flat surfaces and weak vdW bonding. We demonstrate that microfabricated gold also slides with low friction on hBN. This enables the arbitrary post-fabrication repositioning of device features both at ambient conditions and in situ to a measurement cryostat. We demonstrate mechanically reconfigurable vdW devices where device geometry and position are continuously tunable parameters. By fabricating slidable top gates on a graphene-hBN device, we produce a mechanically tunable quantum point contact where electron confinement and edge-state coupling can be continuously modified. Moreover, we combine in situ sliding with simultaneous electronic measurements to create new types of scanning probe experiments, where gate electrodes and even entire vdW heterostructure devices can be spatially scanned by sliding across a target.

Quantum Hall effect, screening, and layer-polarized insulating states in twisted bilayer graphene.

We investigate electronic transport in dual-gated twisted-bilayer graphene. Despite the subnanometer proximity between the layers, we identify independent contributions to the magnetoresistance from the graphene Landau level spectrum of each layer. We demonstrate that the filling factor of each layer can be independently controlled via the dual gates, which we use to induce Landau level crossings between the layers. By analyzing the gate dependence of the Landau level crossings, we characterize the finite interlayer screening and extract the capacitance between the atomically spaced layers. At zero filling factor, we observe an insulating state at large displacement fields, which can be explained by the presence of counterpropagating edge states with interlayer coupling.

Anisotropic etching and nanoribbon formation in single-layer graphene.

We demonstrate anisotropic etching of single-layer graphene by thermally activated nickel nanoparticles. Using this technique, we obtain sub-10-nm nanoribbons and other graphene nanostructures with edges aligned along a single crystallographic direction. We observe a new catalytic channeling behavior, whereby etched cuts do not intersect, resulting in continuously connected geometries. Raman spectroscopy and electronic measurements show that the quality of the graphene is resilient under the etching conditions, indicating that this method may serve as a powerful technique to produce graphene nanocircuits with well-defined crystallographic edges.

Electron-phonon instability in graphene revealed by global and local noise probes.

Understanding and controlling nonequilibrium electronic phenomena is an outstanding challenge in science and engineering. By electrically driving ultraclean graphene devices out of equilibrium, we observe an instability that is manifested as substantially enhanced current fluctuations and suppressed conductivity at microwave frequencies. Spatial mapping of the nonequilibrium current fluctuations using nanoscale magnetic field sensors reveals that the fluctuations grow exponentially along the direction of carrier flow. Our observations, including the dependence on density and temperature, are consistently explained by the emergence of an electron-phonon Cerenkov instability at supersonic drift velocities. These results offer the opportunity for tunable terahertz generation and active phononic devices based on two-dimensional materials.

Mach-Zehnder interferometry using spin- and valley-polarized quantum Hall edge states in graphene.

Confined to a two-dimensional plane, electrons in a strong magnetic field travel along the edge in one-dimensional quantum Hall channels that are protected against backscattering. These channels can be used as solid-state analogs of monochromatic beams of light, providing a unique platform for studying electron interference. Electron interferometry is regarded as one of the most promising routes for studying fractional and non-Abelian statistics and quantum entanglement via two-particle interference. However, creating an edge-channel interferometer in which electron-electron interactions play an important role requires a clean system and long phase coherence lengths. We realize electronic Mach-Zehnder interferometers with record visibilities of up to 98% using spin- and valley-polarized edge channels that copropagate along a pn junction in graphene. We find that interchannel scattering between same-spin edge channels along the physical graphene edge can be used to form beamsplitters, whereas the absence of interchannel scattering along gate-defined interfaces can be used to form isolated interferometer arms. Surprisingly, our interferometer is robust to dephasing effects at energies an order of magnitude larger than those observed in pioneering experiments on GaAs/AlGaAs quantum wells. Our results shed light on the nature of edge-channel equilibration and open up new possibilities for studying exotic electron statistics and quantum phenomena.

Helical edge states and fractional quantum Hall effect in a graphene electron-hole bilayer.

Helical 1D electronic systems are a promising route towards realizing circuits of topological quantum states that exhibit non-Abelian statistics. Here, we demonstrate a versatile platform to realize 1D systems made by combining quantum Hall (QH) edge states of opposite chiralities in a graphene electron-hole bilayer at moderate magnetic fields. 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 non-local transport signals and suppressed backscattering due to the opposite spin polarizations of the counterpropagating modes. Unlike other approaches used for realizing helical states, the graphene electron-hole bilayer can be used to build new 1D systems incorporating fractional edge states. Indeed, we are able to tune the bilayer devices into a regime hosting fractional and integer edge states of opposite chiralities, paving the way towards 1D helical conductors with fractional quantum statistics.

Understanding and controlling the substrate effect on graphene electron-transfer chemistry via reactivity imprint lithography.

Graphene has exceptional electronic, optical, mechanical and thermal properties, which provide it with great potential for use in electronic, optoelectronic and sensing applications. The chemical functionalization of graphene has been investigated with a view to controlling its electronic properties and interactions with other materials. Covalent modification of graphene by organic diazonium salts has been used to achieve these goals, but because graphene comprises only a single atomic layer, it is strongly influenced by the underlying substrate. Here, we show a stark difference in the rate of electron-transfer reactions with organic diazonium salts for monolayer graphene supported on a variety of substrates. Reactions proceed rapidly for graphene supported on SiO(2) and Al(2)O(3) (sapphire), but negligibly on alkyl-terminated and hexagonal boron nitride (hBN) surfaces, as shown by Raman spectroscopy. We also develop a model of reactivity based on substrate-induced electron-hole puddles in graphene, and achieve spatial patterning of chemical reactions in graphene by patterning the substrate.