Evolution of superconductivity in twisted graphene multilayers.

The group of moiré graphene superconductors keeps growing, and by now it contains twisted graphene multilayers as well as untwisted stacks. We analyze here the contribution of long-range charge fluctuations in the superconductivity of twisted double bilayers and helical trilayers, and compare the results to twisted bilayer graphene. A diagrammatic approach which depends on a few, well-known parameters is used. We find that the critical temperature and the order parameter differ significantly between twisted double bilayers and helical trilayers on one hand, and twisted bilayer graphene on the other. This trend, consistent with experiments, can be associated with the role played by moiré Umklapp processes in the different systems.

Topological Flat Bands in Graphene Super-Moiré Lattices.

Moiré-pattern-based potential engineering has become an important way to explore exotic physics in a variety of two-dimensional condensed matter systems. While these potentials have induced correlated phenomena in almost all commonly studied 2D materials, monolayer graphene has remained an exception. We demonstrate theoretically that a single layer of graphene, when placed between two bulk boron nitride crystal substrates with the appropriate twist angles, can support a robust topological ultraflat band emerging as the second hole band. This is one of the simplest platforms to design and exploit topological flat bands.

Dispersion-Selective Band Engineering in an Artificial Kagome Superlattice.

The relentless pursuit of band structure engineering continues to be a fundamental aspect in solid-state research. Here, we meticulously construct an artificial kagome potential to generate and control multiple Dirac bands of graphene. This unique high-order potential harbors natural multiperiodic components, enabling the reconstruction of band structures through different potential contributions. As a result, the band components, each characterized by distinct dispersions, shift in energy at different velocities in response to the variation of artificial potential. Thereby, we observe a significant spectral weight redistribution of the multiple Dirac peaks. Furthermore, the magnetic field can effectively weaken the superlattice effect and reactivate the intrinsic Dirac band. Overall, we achieve actively dispersion-selective band engineering, a functionality that would substantially increase the freedom in band design.

Coulomb interaction, phonons, and superconductivity in twisted bilayer graphene.

The polarizability of twisted bilayer graphene, due to the combined effect of electron-hole pairs, plasmons, and acoustic phonons, is analyzed. The screened Coulomb interaction allows for the formation of Cooper pairs and superconductivity in a significant range of twist angles and fillings. The tendency toward superconductivity is enhanced by the coupling between longitudinal phonons and electron-hole pairs. Scattering processes involving large momentum transfers, Umklapp processes, play a crucial role in the formation of Cooper pairs. The magnitude of the superconducting gap changes among the different pockets of the Fermi surface.

Van der Waals interaction affects wrinkle formation in two-dimensional materials.

Nonlinear mechanics of solids is an exciting field that encompasses both beautiful mathematics, such as the emergence of instabilities and the formation of complex patterns, as well as multiple applications. Two-dimensional crystals and van der Waals (vdW) heterostructures allow revisiting this field on the atomic level, allowing much finer control over the parameters and offering atomistic interpretation of experimental observations. In this work, we consider the formation of instabilities consisting of radially oriented wrinkles around mono- and few-layer "bubbles" in two-dimensional vdW heterostructures. Interestingly, the shape and wavelength of the wrinkles depend not only on the thickness of the two-dimensional crystal forming the bubble, but also on the atomistic structure of the interface between the bubble and the substrate, which can be controlled by their relative orientation. We argue that the periodic nature of these patterns emanates from an energetic balance between the resistance of the top membrane to bending, which favors large wavelength of wrinkles, and the membrane-substrate vdW attraction, which favors small wrinkle amplitude. Employing the classical "Winkler foundation" model of elasticity theory, we show that the number of radial wrinkles conveys a valuable relationship between the bending rigidity of the top membrane and the strength of the vdW interaction. Armed with this relationship, we use our data to demonstrate a nontrivial dependence of the bending rigidity on the number of layers in the top membrane, which shows two different regimes driven by slippage between the layers, and a high sensitivity of the vdW force to the alignment between the substrate and the membrane.

Experimental Demonstration of a Magnetically Induced Warping Transition in a Topological Insulator Mediated by Rare-Earth Surface Dopants.

Magnetic topological insulators constitute a novel class of materials whose topological surface states (TSSs) coexist with long-range ferromagnetic order, eventually breaking time-reversal symmetry. The subsequent bandgap opening is predicted to co-occur with a distortion of the TSS warped shape from hexagonal to trigonal. We demonstrate such a transition by means of angle-resolved photoemission spectroscopy on the magnetically rare-earth (Er and Dy) surface-doped topological insulator Bi2Se2Te. Signatures of the gap opening are also observed. Moreover, increasing the dopant coverage results in a tunable p-type doping of the TSS, thereby allowing for a gradual tuning of the Fermi level toward the magnetically induced bandgap. A theoretical model where a magnetic Zeeman out-of-plane term is introduced in the Hamiltonian governing the TSS rationalizes these experimental results. Our findings offer new strategies to control magnetic interactions with TSSs and open up viable routes for the realization of the quantum anomalous Hall effect.

Strain-Induced Quasi-1D Channels in Twisted Moiré Lattices.

We study the effects of strain in moiré systems composed of honeycomb lattices. We elucidate the formation of almost perfect one-dimensional moiré patterns in twisted bilayer systems. The formation of such patterns is a consequence of an interplay between twist and strain which gives rise to a collapse of the reciprocal space unit cell. As a criterion for such collapse we find a simple relation between the two quantities and the material specific Poisson ratio. The induced one-dimensional behavior is characterized by two, usually incommensurate, periodicities. Our results offer explanations for the complex patterns of one-dimensional channels observed in low angle twisted bilayer graphene systems and twisted bilayer dicalcogenides. Our findings can be applied to any hexagonal twisted moiré pattern and can be easily extended to other geometries.

Junctions and Superconducting Symmetry in Twisted Bilayer Graphene.

Junctions provide a wealth of information on the symmetry of the order parameter of superconductors. We analyze junctions between a scanning tunneling microscope (STM) tip and superconducting twisted bilayer graphene (TBG) and TBG Josephson junctions (JJs). We compare superconducting phases that are even or odd under valley exchange (s- or f-wave). The critical current in mixed (s and f) JJs strongly depends on the angle between the junction and the lattice. In STM-TBG junctions, due to Andreev reflection, the f-wave leads to a prominent peak in subgap conductance, as seen in experiments.

Purcell-like Enhancement of Electron-Phonon Interactions in Long-Period Superlattices: Linear-Temperature Resistivity and Cooling Power.

In the Purcell effect, the efficiency of optical emitters is enhanced by reducing the optical mode volume. Here we predict an analogous enhancement for electron-phonon (el-ph) scattering, achieved by compressing the electronic Wannier orbitals. Reshaped Wannier orbitals are a prominent attribute of graphene moiré superlattices, where the orbital size is tunable by the twist angle. A reduction in the orbital size leads to an enhancement in the el-ph interaction strength, yielding the values considerably larger than those in pristine monolayer graphene. The enhanced coupling boosts the el-ph scattering rates, pushing them above the values expected for the flat-band-enhanced density of electronic states. The enhanced phonon emission and scattering rates are manifested through the observables such as the electron-lattice cooling and the linear-temperature (T) resistivity, both of which are directly tunable by the moiré twist angle.

Heterostrain Determines Flat Bands in Magic-Angle Twisted Graphene Layers.

The moiré of twisted graphene bilayers can generate flat bands in which charge carriers do not possess enough kinetic energy to escape Coulomb interactions with each other, leading to the formation of novel strongly correlated electronic states. This exceptionally rich physics relies on the precise arrangement between the layers. Here, we survey published scanning tunneling microscope measurements to prove that near the magic-angle, native heterostrain, the relative deformations between the layers, dominates twist in determining the flat bands as opposed to the common belief. This is demonstrated at full filling where electronic correlations have a weak effect and where we also show that tip-induced strain can have a strong influence. In the opposite situation of zero doping, we find that electronic correlation further renormalizes the flat bands in a way that strongly depends on experimental details.

Electrostatic effects, band distortions, and superconductivity in twisted graphene bilayers.

Bilayer graphene twisted by a small angle shows a significant charge modulation away from neutrality, as the charge in the narrow bands near the Dirac point is mostly localized in a fraction of the Moiré unit cell. The resulting electrostatic potential leads to a filling-dependent change in the low-energy bands, of a magnitude comparable to or larger than the bandwidth. These modifications can be expressed in terms of new electron-electron interactions, which, when expressed in a local basis, describe electron-assisted hopping terms. These interactions favor superconductivity at certain fillings.

Twists and the Electronic Structure of Graphitic Materials.

We analyze the effect of twists on the electronic structure of configurations of infinite stacks of graphene layers. We focus on three different cases: an infinite stack where each layer is rotated with respect to the previous one by a fixed angle, two pieces of semi-infinite graphite rotated with respect to each other, and finally a single layer of graphene rotated with respect to a graphite surface. In all three cases, we find a rich structure, with sharp resonances and flat bands for small twist angles. The method used can be easily generalized to more complex arrangements and stacking sequences.

Polaritons in layered two-dimensional materials.

In recent years, enhanced light-matter interactions through a plethora of dipole-type polaritonic excitations have been observed in two-dimensional (2D) layered materials. In graphene, electrically tunable and highly confined plasmon-polaritons were predicted and observed, opening up opportunities for optoelectronics, bio-sensing and other mid-infrared applications. In hexagonal boron nitride, low-loss infrared-active phonon-polaritons exhibit hyperbolic behaviour for some frequencies, allowing for ray-like propagation exhibiting high quality factors and hyperlensing effects. In transition metal dichalcogenides, reduced screening in the 2D limit leads to optically prominent excitons with large binding energy, with these polaritonic modes having been recently observed with scanning near-field optical microscopy. Here, we review recent progress in state-of-the-art experiments, and survey the vast library of polaritonic modes in 2D materials, their optical spectral properties, figures of merit and application space. Taken together, the emerging field of 2D material polaritonics and their hybrids provide enticing avenues for manipulating light-matter interactions across the visible, infrared to terahertz spectral ranges, with new optical control beyond what can be achieved using traditional bulk materials.

Edge Modes and Nonlocal Conductance in Graphene Superlattices.

We study the existence of edge modes in gapped moiré superlattices of graphene monolayer ribbons on a hexagonal boron nitride substrate. We find that the superlattice bands acquire finite Chern numbers, which lead to a valley Hall effect. The presence of dispersive edge modes is confirmed by calculations of the band structure of realistic nanoribbons using tight binding methods. These edge states are only weakly sensitive to disorder, as short-range scattering processes lead to mean free paths of the order of microns. The results explain the existence of edge currents when the chemical potential lies within the bulk superlattice gap, and offer an explanation for existing nonlocal resistivity measurements in graphene ribbons on boron nitride.

Formation of a highly doped ultra-thin amorphous carbon layer by ion bombardment of graphene.

Ion bombardment of graphene leads to the formation of defects which may be used to tune properties of the graphene based devices. In this work, however, we present that the presence of the graphene layer on a surface of a sample has a significant impact on the ion bombardment process: broken sp2 bonds react with the incoming ions and trap them close to the surface of the sample, preventing a standard ion implantation. For an ion bombardment with a low impact energy and significant dose (in the range of 1014 atoms cm-2) an amorphization of the graphene layer is observed but at the same time, most of the incoming ions do not penetrate the sample but stop at the surface, thus forming a highly doped ultra-thin amorphous carbon layer. The effect may be used to create thin layers containing desired atoms if no other technique is available. This approach is particularly useful for secondary ion mass spectrometry where a high concentration of Cs at the surface of a sample significantly enhances the negative ionization probability, allowing it to reach better detection limits.

Designer Dirac fermions and topological phases in molecular graphene.

The observation of massless Dirac fermions in monolayer graphene has generated a new area of science and technology seeking to harness charge carriers that behave relativistically within solid-state materials. Both massless and massive Dirac fermions have been studied and proposed in a growing class of Dirac materials that includes bilayer graphene, surface states of topological insulators and iron-based high-temperature superconductors. Because the accessibility of this physics is predicated on the synthesis of new materials, the quest for Dirac quasi-particles has expanded to artificial systems such as lattices comprising ultracold atoms. Here we report the emergence of Dirac fermions in a fully tunable condensed-matter system-molecular graphene-assembled by atomic manipulation of carbon monoxide molecules over a conventional two-dimensional electron system at a copper surface. Using low-temperature scanning tunnelling microscopy and spectroscopy, we embed the symmetries underlying the two-dimensional Dirac equation into electron lattices, and then visualize and shape the resulting ground states. These experiments show the existence within the system of linearly dispersing, massless quasi-particles accompanied by a density of states characteristic of graphene. We then tune the quantum tunnelling between lattice sites locally to adjust the phase accrual of propagating electrons. Spatial texturing of lattice distortions produces atomically sharp p-n and p-n-p junction devices with two-dimensional control of Dirac fermion density and the power to endow Dirac particles with mass. Moreover, we apply scalar and vector potentials locally and globally to engender topologically distinct ground states and, ultimately, embedded gauge fields, wherein Dirac electrons react to 'pseudo' electric and magnetic fields present in their reference frame but absent from the laboratory frame. We demonstrate that Landau levels created by these gauge fields can be taken to the relativistic magnetic quantum limit, which has so far been inaccessible in natural graphene. Molecular graphene provides a versatile means of synthesizing exotic topological electronic phases in condensed matter using tailored nanostructures.

Theory of 2D crystals: graphene and beyond.

This tutorial review presents an overview of the basic theoretical aspects of two-dimensional (2D) crystals. We revise essential aspects of graphene and the new families of semiconducting 2D materials, like transition metal dichalcogenides or black phosphorus. Minimal theoretical models for various materials are presented. Some of the exciting new possibilities offered by 2D crystals are discussed, such as manipulation and control of quantum degrees of freedom (spin and pseudospin), confinement of excitons, control of the electronic and optical properties with strain engineering, or unconventional superconducting phases.

Electrically Controllable Magnetism in Twisted Bilayer Graphene.

Twisted graphene bilayers develop highly localized states around AA-stacked regions for small twist angles. We show that interaction effects may induce either an antiferromagnetic or a ferromagnetic (FM) polarization of said regions, depending on the electrical bias between layers. Remarkably, FM-polarized AA regions under bias develop spiral magnetic ordering, with a relative 120° misalignment between neighboring regions due to a frustrated antiferromagnetic exchange. This remarkable spiral magnetism emerges naturally without the need of spin-orbit coupling, and competes with the more conventional lattice-antiferromagnetic instability, which interestingly develops at smaller bias under weaker interactions than in monolayer graphene, due to Fermi velocity suppression. This rich and electrically controllable magnetism could turn twisted bilayer graphene into an ideal system to study frustrated magnetism in two dimensions.

Strong Modulation of Optical Properties in Black Phosphorus through Strain-Engineered Rippling.

Controlling the bandgap through local-strain engineering is an exciting avenue for tailoring optoelectronic materials. Two-dimensional crystals are particularly suited for this purpose because they can withstand unprecedented nonhomogeneous deformations before rupture; one can literally bend them and fold them up almost like a piece of paper. Here, we study multilayer black phosphorus sheets subjected to periodic stress to modulate their optoelectronic properties. We find a remarkable shift of the optical absorption band-edge of up to ∼0.7 eV between the regions under tensile and compressive stress, greatly exceeding the strain tunability reported for transition metal dichalcogenides. This observation is supported by theoretical models that also predict that this periodic stress modulation can yield to quantum confinement of carriers at low temperatures. The possibility of generating large strain-induced variations in the local density of charge carriers opens the door for a variety of applications including photovoltaics, quantum optics, and two-dimensional optoelectronic devices.

Tunable phonon-induced transparency in bilayer graphene nanoribbons.

In the phenomenon of plasmon-induced transparency, which is a classical analogue of electromagnetically induced transparency (EIT) in atomic gases, the coherent interference between two plasmon modes results in an optical transparency window in a broad absorption spectrum. With the requirement of contrasting lifetimes, typically one of the plasmon modes involved is a dark mode that has limited coupling to the electromagnetic radiation and possesses relatively longer lifetime. Plasmon-induced transparency not only leads to light transmission at otherwise opaque frequency regions but also results in the slowing of light group velocity and enhanced optical nonlinearity. In this article, we report an analogous behavior, denoted as phonon-induced transparency (PIT), in AB-stacked bilayer graphene nanoribbons. Here, light absorption due to the plasmon excitation is suppressed in a narrow window due to the coupling with the infrared active Γ-point optical phonon, whose function here is similar to that of the dark plasmon mode in the plasmon-induced transparency. We further show that PIT in bilayer graphene is actively tunable by electrostatic gating and estimate a maximum slow light factor of around 500 at the phonon frequency of 1580 cm(-1), based on the measured spectra. Our demonstration opens an avenue for the exploration of few-photon nonlinear optics and slow light in this novel two-dimensional material.