Charge-polarized interfacial superlattices in marginally twisted hexagonal boron nitride.

When two-dimensional crystals are brought into close proximity, their interaction results in reconstruction of electronic spectrum and crystal structure. Such reconstruction strongly depends on the twist angle between the crystals, which has received growing attention due to interesting electronic and optical properties that arise in graphene and transitional metal dichalcogenides. Here we study two insulating crystals of hexagonal boron nitride stacked at small twist angle. Using electrostatic force microscopy, we observe ferroelectric-like domains arranged in triangular superlattices with a large surface potential. The observation is attributed to interfacial elastic deformations that result in out-of-plane dipoles formed by pairs of boron and nitrogen atoms belonging to opposite interfacial surfaces. This creates a bilayer-thick ferroelectric with oppositely polarized (BN and NB) dipoles in neighbouring domains, in agreement with our modeling. These findings open up possibilities for designing van der Waals heterostructures and offer an alternative probe to study moiré-superlattice electrostatic potentials.

Giant oscillations in a triangular network of one-dimensional states in marginally twisted graphene.

At very small twist angles of ∼0.1°, bilayer graphene exhibits a strain-accompanied lattice reconstruction that results in submicron-size triangular domains with the standard, Bernal stacking. If the interlayer bias is applied to open an energy gap inside the domain regions making them insulating, such marginally twisted bilayer graphene is expected to remain conductive due to a triangular network of chiral one-dimensional states hosted by domain boundaries. Here we study electron transport through this helical network and report giant Aharonov-Bohm oscillations that reach in amplitude up to 50% of resistivity and persist to temperatures above 100 K. At liquid helium temperatures, the network exhibits another kind of oscillations that appear as a function of carrier density and are accompanied by a sign-changing Hall effect. The latter are attributed to consecutive population of the narrow minibands formed by the network of one-dimensional states inside the gap.

Polariton Anomalous Hall Effect in Transition-Metal Dichalcogenides.

We analyze the properties of strongly coupled excitons and photons in systems made of semiconducting two-dimensional transition-metal dichalcogenides embedded in optical cavities. Through a detailed microscopic analysis of the coupling, we unveil novel, highly tunable features of the spectrum that result in polariton splitting and a breaking of light-matter selection rules. The dynamics of the composite polaritons is influenced by the Berry phase arising both from their constituents and from the confinement-enhanced coupling. We find that light-matter coupling emerges as a mechanism that enhances the Berry phase of polaritons well beyond that of its elementary constituents, paving the way to achieve a polariton anomalous Hall effect.

Topological π Junctions from Crossed Andreev Reflection in the Quantum Hall Regime.

We consider a two-dimensional electron gas (2DEG) in the quantum Hall regime in the presence of a Zeeman field, with the Fermi level tuned to a filling factor of ν=1. We show that, in the presence of spin-orbit coupling, contacting the 2DEG with a narrow strip of an s-wave superconductor produces a topological superconducting gap along the contact as a result of crossed Andreev reflection (CAR) processes across the strip. The sign of the topological gap, controlled by the CAR amplitude, depends periodically on the Fermi wavelength and strip width and can be externally tuned. An interface between two halves of a long strip with topological gaps of opposite sign implements a robust π junction, hosting a pair of Majorana zero modes that do not split despite their overlap. We show that such a configuration can be exploited to perform protected non-Abelian tunnel-braid operations without any fine tuning.

Ultrathin graphene-based membrane with precise molecular sieving and ultrafast solvent permeation.

Graphene oxide (GO) membranes continue to attract intense interest due to their unique molecular sieving properties combined with fast permeation. However, their use is limited to aqueous solutions because GO membranes appear impermeable to organic solvents, a phenomenon not yet fully understood. Here, we report efficient and fast filtration of organic solutions through GO laminates containing smooth two-dimensional (2D) capillaries made from large (10-20 µm) flakes. Without modification of sieving characteristics, these membranes can be made exceptionally thin, down to ∼10 nm, which translates into fast water and organic solvent permeation. We attribute organic solvent permeation and sieving properties to randomly distributed pinholes interconnected by short graphene channels with a width of 1 nm. With increasing membrane thickness, organic solvent permeation rates decay exponentially but water continues to permeate quickly, in agreement with previous reports. The potential of ultrathin GO laminates for organic solvent nanofiltration is demonstrated by showing >99.9% rejection of small molecular weight organic dyes dissolved in methanol. Our work significantly expands possibilities for the use of GO membranes in purification and filtration technologies.

The electron-phonon interaction at deep Bi 2 Te3-semiconductor interfaces from Brillouin light scattering.

It is shown that the electron-phonon interaction at a conducting interface between a topological insulator thin film and a semiconductor substrate can be directly probed by means of high-resolution Brillouin light scattering (BLS). The observation of Kohn anomalies in the surface phonon dispersion curves of a 50 nm thick Bi2Te3 film on GaAs, besides demonstrating important electron-phonon coupling effects in the GHz frequency domain, shows that information on deep interface electrons can be obtained by tuning the penetration depth of optically-generated surface phonons so as to selectively probe the interface region, as in a sort of quantum sonar.

Universal shape and pressure inside bubbles appearing in van der Waals heterostructures.

Trapped substances between a two-dimensional (2D) crystal and an atomically flat substrate lead to the formation of bubbles. Their size, shape and internal pressure are determined by the competition between van der Waals attraction of the crystal to the substrate and the elastic energy needed to deform it, allowing to use bubbles to study elastic properties of 2D crystals and conditions of confinement. Using atomic force microscopy, we analysed a variety of bubbles formed by monolayers of graphene, boron nitride and MoS2. Their shapes are found to exhibit universal scaling, in agreement with our analysis based on the theory of elasticity of membranes. We also measured the hydrostatic pressure induced by the confinement, which was found to reach tens of MPa inside submicron bubbles. This agrees with our theory estimates and suggests that for even smaller, sub-10 nm bubbles the pressure can be close to 1 GPa and may modify properties of a trapped material.

Superconductivity in Ca-doped graphene laminates.

Despite graphene's long list of exceptional electronic properties and many theoretical predictions regarding the possibility of superconductivity in graphene, its direct and unambiguous experimental observation has not been achieved. We searched for superconductivity in weakly interacting, metal decorated graphene crystals assembled into so-called graphene laminates, consisting of well separated and electronically decoupled graphene crystallites. We report robust superconductivity in all Ca-doped graphene laminates. They become superconducting at temperatures (Tc) between ≈4 and ≈6 K, with Tc's strongly dependent on the confinement of the Ca layer and the induced charge carrier concentration in graphene. We find that Ca is the only dopant that induces superconductivity in graphene laminates above 1.8 K among several dopants used in our experiments, such as potassium, caesium and lithium. By revealing the tunability of the superconducting response through doping and confinement of the metal layer, our work shows that achieving superconductivity in free-standing, metal decorated monolayer graphene is conditional on an optimum confinement of the metal layer and sufficient doping, thereby bringing its experimental realization within grasp.

Competition between spontaneous symmetry breaking and single-particle gaps in trilayer graphene.

Many physical phenomena can be understood by single-particle physics; that is, treating particles as non-interacting entities. When this fails, many-body interactions lead to spontaneous symmetry breaking and phenomena such as fundamental particles' mass generation, superconductivity and magnetism. Competition between single-particle and many-body physics leads to rich phase diagrams. Here we show that rhombohedral-stacked trilayer graphene offers an exciting platform for studying such interplay, in which we observe a giant intrinsic gap ~42 meV that can be partially suppressed by an interlayer potential, a parallel magnetic field or a critical temperature ~36 K. Among the proposed correlated phases with spatial uniformity, our results are most consistent with a layer antiferromagnetic state with broken time reversal symmetry. These results reflect the interplay between externally induced and spontaneous symmetry breaking whose relative strengths are tunable by external fields, and provide insight into other low-dimensional systems.

Quantum spin Hall effect in two-dimensional crystals of transition-metal dichalcogenides.

We propose to engineer time-reversal-invariant topological insulators in two-dimensional crystals of transition-metal dichalcogenides (TMDCs). We note that, at low doping, semiconducting TMDCs under shear strain will develop spin-polarized Landau levels residing in different valleys. We argue that gaps between Landau levels in the range of 10-100 K are within experimental reach. In addition, we point out that a superlattice arising from a moiré pattern can lead to topologically nontrivial subbands. As a result, the edge transport becomes quantized, which can be probed in multiterminal devices made using strained 2D crystals and/or heterostructures. The strong d character of valence and conduction bands may also allow for the investigation of the effects of electron correlations on the topological phases.

Many-body renormalization of the minimal conductivity in graphene.

The conductance of ballistic graphene at the neutrality point is due to coherent electron tunneling between the leads, the so called pseudodiffusive regime. The conductance scales as a function of the sample dimensions in the same way as in a diffusive metal, despite the difference in the physical mechanisms involved. The electron-electron interaction modifies this regime, and plays a role similar to that of the environment in macroscopic quantum phenomena. We show that interactions can change substantially the transport properties. In the presence of nearby metallic layers, the conductance near the neutrality point can decrease with decreasing temperature, and reach values well below the quantum unit of conductance, as in an insulator.

Stacking boundaries and transport in bilayer graphene.

Pristine bilayer graphene behaves in some instances as an insulator with a transport gap of a few millielectronvolts. This behavior has been interpreted as the result of an intrinsic electronic instability induced by many-body correlations. Intriguingly, however, some samples of similar mobility exhibit good metallic properties with a minimal conductivity of the order of 2e(2)/h. Here, we propose an explanation for this dichotomy, which is unrelated to electron interactions and based instead on the reversible formation of boundaries between stacking domains ("solitons"). We argue, using a numerical analysis, that the hallmark features of the previously inferred many-body insulating state can be explained by scattering on boundaries between domains with different stacking order (AB and BA). We furthermore present experimental evidence, reinforcing our interpretation, of reversible switching between a metallic and an insulating regime in suspended bilayers when subjected to thermal cycling or high current annealing.

Cloning of Dirac fermions in graphene superlattices.

Superlattices have attracted great interest because their use may make it possible to modify the spectra of two-dimensional electron systems and, ultimately, create materials with tailored electronic properties. In previous studies (see, for example, refs 1-8), it proved difficult to realize superlattices with short periodicities and weak disorder, and most of their observed features could be explained in terms of cyclotron orbits commensurate with the superlattice. Evidence for the formation of superlattice minibands (forming a fractal spectrum known as Hofstadter's butterfly) has been limited to the observation of new low-field oscillations and an internal structure within Landau levels. Here we report transport properties of graphene placed on a boron nitride substrate and accurately aligned along its crystallographic directions. The substrate's moiré potential acts as a superlattice and leads to profound changes in the graphene's electronic spectrum. Second-generation Dirac points appear as pronounced peaks in resistivity, accompanied by reversal of the Hall effect. The latter indicates that the effective sign of the charge carriers changes within graphene's conduction and valence bands. Strong magnetic fields lead to Zak-type cloning of the third generation of Dirac points, which are observed as numerous neutrality points in fields where a unit fraction of the flux quantum pierces the superlattice unit cell. Graphene superlattices such as this one provide a way of studying the rich physics expected in incommensurable quantum systems and illustrate the possibility of controllably modifying the electronic spectra of two-dimensional atomic crystals by varying their crystallographic alignment within van der Waals heterostuctures.

Elliot-Yafet mechanism in graphene.

The differences between spin relaxation in graphene and in other materials are discussed. For relaxation by scattering processes, the Elliot-Yafet mechanism, the relation between the spin and the momentum scattering times, acquires a dependence on the carrier density, which is independent of the scattering mechanism and the relation between mobility and carrier concentration. This dependence puts severe restrictions on the origin of the spin relaxation in graphene. The density dependence of the spin relaxation allows us to distinguish between ordinary impurities and defects which modify locally the spin-orbit interaction.

Non-Abelian gauge potentials in graphene bilayers.

We study the effect of spatial modulations in the interlayer hopping of graphene bilayers, such as those that arise upon shearing or twisting. We show that their single-particle physics, characterized by charge accumulation and recurrent formation of zero-energy bands as the pattern period L increases, is governed by a non-Abelian gauge potential arising in the low-energy electronic theory due to the coupling between layers. We show that such gauge-type couplings give rise to a potential that, for certain discrete values of L, spatially confines states at zero energy in particular regions of the moiré patterns. We also draw the connection between the recurrence of the flat zero-energy bands and the non-Abelian character of the potential.

Topological superconducting state of lead nanowires in an external magnetic field.

Superconductors with an odd number of bands crossing the Fermi energy have topologically protected Andreev states at interfaces, including Majorana states in one-dimensional geometries. We propose here that repeated indentation of a Pb tip on a Pb substrate can lead to nanowires such that the resulting superconducting system has novel topological properties. We have analyzed a number of conductance curves obtained in different nanowires, and observe, in a few cases, very peculiar dependence of the critical current on magnetic field. In these cases, the form of multiple Andreev reflections observed at finite voltages are compatible with topological superconductivity. The nanowires give a low number of 1D channels, large spin orbit coupling, and a sizable Zeeman energy, provided that the applied magnetic field is higher than the Pb bulk critical field.

Integer quantum Hall effect in trilayer graphene.

By using high-magnetic fields (up to 60 T), we observe compelling evidence of the integer quantum Hall effect in trilayer graphene. The magnetotransport fingerprints are similar to those of the graphene monolayer, except for the absence of a plateau at a filling factor of ν=2. At a very low filling factor, the Hall resistance vanishes due to the presence of mixed electron and hole carriers induced by disorder. The measured Hall resistivity plateaus are well reproduced theoretically, using a self-consistent Hartree calculations of the Landau levels and assuming an ABC stacking order of the three layers.

Electron-induced rippling in graphene.

We show that the interaction between flexural phonons, when corrected by the exchange of electron-hole excitations, may drive the graphene sheet into a quantum critical point characterized by the vanishing of the bending rigidity of the membrane. Ripples arise then due to spontaneous symmetry breaking, following a mechanism similar to that responsible for the condensation of the Higgs field in relativistic field theories, and leading to a zero-temperature buckling transition in which the order parameter is given by the square of the gradient of the flexural phonon field.

Band structure and gaps of triangular graphene superlattices.

The general properties of long wavelength triangular graphene superlattices are studied. It is shown that Dirac points with and without gaps can arise at a number of high-symmetry points of the Brillouin zone. The existence of gaps can lead to insulating behaviour at commensurate fillings. Strain and magnetic superlattices are also discussed.

Strain-induced pseudomagnetic field for novel graphene electronics.

Particular strain geometry in graphene could lead to a uniform pseudomagnetic field of order 10T and might open up interesting applications in graphene nanoelectronics. Through quantum transport calculations of realistic strained graphene flakes of sizes of 100 nm, we examine possible means of exploiting this effect for practical electronics and valleytronics devices. First, we found that elastic backscattering at rough edges leads to the formation of well-defined transport gaps of order 100 meV under moderate maximum strain of 10%. Second, the application of a real magnetic field induced a separation, in space and energy, of the states arising from different valleys, leading to a way of inducing bulk valley polarization which is insensitive to short-range scattering.