High-Mobility Compensated Semimetals, Orbital Magnetization, and Umklapp Scattering in Bilayer Graphene Moiré Superlattices.

Twist-controlled moiré superlattices (MSs) have emerged as a versatile platform for realizing artificial systems with complex electronic spectra. The combination of Bernal-stacked bilayer graphene (BLG) and hexagonal boron nitride (hBN) can give rise to an interesting MS, which has recently featured a set of unexpected behaviors, such as unconventional ferroelectricity and the electronic ratchet effect. Yet, the understanding of the electronic properties of BLG/hBN MS has, at present, remained fairly limited. Here, we combine magneto-transport and low-energy sub-THz excitation to gain insights into the properties of this MS. We demonstrate that the alignment between BLG and hBN crystal lattices results in the emergence of compensated semimetals at some integer fillings of the moiré bands, separated by van Hove singularities where the Lifshitz transition occurs. A particularly pronounced semimetal develops when eight holes reside in the moiré unit cell, where coexisting high-mobility electron and hole systems feature strong magnetoresistance reaching 2350% already at B = 0.25 T. Next, by measuring the THz-driven Nernst effect in remote bands, we observe valley splitting, indicating an orbital magnetization characterized by a strongly enhanced effective gv-factor of 340. Finally, using THz photoresistance measurements, we show that the high-temperature conductivity of the BLG/hBN MS is limited by electron-electron umklapp processes. Our multifaceted analysis introduces THz-driven magnetotransport as a convenient tool to probe the band structure and interaction effects in van der Waals materials and provides a comprehensive understanding of the BLG/hBN MS.

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.

Optical properties and plasmons in moiré structures.

The discoveries of numerous exciting phenomena in twisted bilayer graphene (TBG) are stimulating significant investigations on moiré structures that possess a tunable moiré potential. Optical response can provide insights into the electronic structures and transport phenomena of non-twisted and twisted moiré structures. In this article, we review both experimental and theoretical studies of optical properties such as optical conductivity, dielectric function, non-linear optical response, and plasmons in moiré structures composed of graphene, hexagonal boron nitride (hBN), and/or transition metal dichalcogenides. Firstly, a comprehensive introduction to the widely employed methodology on optical properties is presented. After, moiré potential induced optical conductivity and plasmons in non-twisted structures are reviewed, such as single layer graphene-hBN, bilayer graphene-hBN and graphene-metal moiré heterostructures. Next, recent investigations of twist-angle dependent optical response and plasmons are addressed in twisted moiré structures. Additionally, we discuss how optical properties and plasmons could contribute to the understanding of the many-body effects and superconductivity observed in moiré structures.

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.

Giant Atomic Swirl in Graphene Bilayers with Biaxial Heterostrain.

The study of moiré engineering started with the advent of van der Waals heterostructures, in which stacking 2D layers with different lattice constants leads to a moiré pattern controlling their electronic properties. The field entered a new era when it was found that adjusting the twist between two graphene layers led to strongly-correlated-electron physics and topological effects associated with atomic relaxation. A twist is now routinely used to adjust the properties of 2D materials. This study investigates a new type of moiré superlattice in bilayer graphene when one layer is biaxially strained with respect to the other-so-called biaxial heterostrain. Scanning tunneling microscopy measurements uncover spiraling electronic states associated with a novel symmetry-breaking atomic reconstruction at small biaxial heterostrain. Atomistic calculations using experimental parameters as inputs reveal that a giant atomic swirl forms around regions of aligned stacking to reduce the mechanical energy of the bilayer. Tight-binding calculations performed on the relaxed structure show that the observed electronic states decorate spiraling domain wall solitons as required by topology. This study establishes biaxial heterostrain as an important parameter to be harnessed for the next step of moiré engineering in van der Waals multilayers.

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.

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.

Observation of Superconducting Collective Modes from Competing Pairing Instabilities in Single-Layer NbSe2.

In certain unconventional superconductors with sizable electronic correlations, the availability of closely competing pairing channels leads to characteristic soft collective fluctuations of the order parameters, which leave fingerprints in many observables and allow the phase competition to be scrutinized. Superconducting layered materials, where electron-electron interactions are enhanced with decreasing thickness, are promising candidates to display these correlation effects. In this work, the existence of a soft collective mode in single-layer NbSe2 , observed as a characteristic resonance excitation in high-resolution tunneling spectra is reported. This resonance is observed along with higher harmonics, its frequency Ω/2Δ is anticorrelated with the local superconducting gap Δ, and its amplitude gradually vanishes by increasing the temperature and upon applying a magnetic field up to the critical values (TC and HC2 ), which sets an unambiguous link to the superconducting state. Aided by a microscopic model that captures the main experimental observations, this resonance is interpreted as a collective Leggett mode that represents the fluctuation toward a proximate f-wave triplet state, due to subleading attraction in the triplet channel. These findings demonstrate the fundamental role of correlations in superconducting 2D transition metal dichalcogenides, opening a path toward unconventional superconductivity in simple, scalable, and transferable 2D superconductors.

Strain Switching in van der Waals Heterostructures Triggered by a Spin-Crossover Metal-Organic Framework.

Van der Waals heterostructures (vdWHs) provide the possibility of engineering new materials with emergent functionalities that are not accessible in another way. These heterostructures are formed by assembling layers of different materials used as building blocks. Beyond inorganic 2D crystals, layered molecular materials remain still rather unexplored, with only few examples regarding their isolation as atomically thin layers. Here, the family of van der Waals heterostructures is enlarged by introducing a molecular building block able to produce strain: the so-called spin-crossover (SCO). In these metal-organic materials, a spin transition can be induced by applying external stimuli like light, temperature, pressure, or an electric field. In particular, smart vdWHs are prepared in which the electronic and optical properties of the 2D material (graphene and WSe2 ) are clearly switched by the strain concomitant to the spin transition. These molecular/inorganic vdWHs represent the deterministic incorporation of bistable molecular layers with other 2D crystals of interest in the emergent fields of straintronics and band engineering in low-dimensional materials.

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.

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.

Magnetization Signature of Topological Surface States in a Non-Symmorphic Superconductor.

Superconductors with nontrivial band structure topology represent a class of materials with unconventional and potentially useful properties. Recent years have seen much success in creating artificial hybrid structures exhibiting the main characteristics of 2D topological superconductors. Yet, bulk materials known to combine inherent superconductivity with nontrivial topology remain scarce, largely because distinguishing their central characteristic-the topological surface states-has proved challenging due to a dominant contribution from the superconducting bulk. In this work, a highly anomalous behavior of surface superconductivity in topologically nontrivial 3D superconductor In2 Bi, where the surface states result from its nontrivial band structure, itself a consequence of the non-symmorphic crystal symmetry and strong spin-orbit coupling, is reported. In contrast to smoothly decreasing diamagnetic susceptibility above the bulk critical field, Hc2 , as seen in conventional superconductors, a near-perfect, Meissner-like screening of low-frequency magnetic fields well above Hc2 is observed. The enhanced diamagnetism disappears at a new phase transition close to the critical field of surface superconductivity, Hc3 . Using theoretical modeling, the anomalous screening is shown to be consistent with modification of surface superconductivity by the topological surface states. The possibility of detecting signatures of the surface states using macroscopic magnetization provides a new tool for the discovery and identification of topological superconductors.

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.

Indentation of solid membranes on rigid substrates with van der Waals attraction.

We revisit the indentation of a thin solid sheet of size R_{sheet} suspended on a circular hole of radius R≪R_{sheet} in a smooth rigid substrate, addressing the effects of boundary conditions at the hole's edge. Introducing a basic theoretical model for the van der Waals (vdW) sheet-substrate attraction, we demonstrate the dramatic effect of replacing the clamping condition (Schwerin model) with a sliding condition, whereby the supported part of the sheet is allowed to slide towards the indenter and relax the induced hoop compression through angstrom-scale deflections from the thermodynamic equilibrium (determined by the vdW potential). We highlight the possibility that the indentation force F may not exhibit the commonly anticipated cubic dependence on the indentation depth (F∝δ^{3}), in which the proportionality constant is governed by the sheet's stretching modulus and the hole's radius R, but rather a pseduolinear response F∝δ, whereby the proportionality constant is governed by the bending modulus, the vdW attraction, and the sheet's size R_{sheet}≫R.

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.

Piezoelectricity in Monolayer Hexagonal Boron Nitride.

2D hexagonal boron nitride (hBN) is a wide-bandgap van der Waals crystal with a unique combination of properties, including exceptional strength, large oxidation resistance at high temperatures, and optical functionalities. Furthermore, in recent years hBN crystals have become the material of choice for encapsulating other 2D crystals in a variety of technological applications, from optoelectronic and tunneling devices to composites. Monolayer hBN, which has no center of symmetry, is predicted to exhibit piezoelectric properties, yet experimental evidence is lacking. Here, by using electrostatic force microscopy, this effect is observed as a strain-induced change in the local electric field around bubbles and creases, in agreement with theoretical calculations. No piezoelectricity is found in bilayer and bulk hBN, where the center of symmetry is restored. These results add piezoelectricity to the known properties of monolayer hBN, which makes it a desirable candidate for novel electromechanical and stretchable optoelectronic devices, and pave a way to control the local electric field and carrier concentration in van der Waals heterostructures via strain. The experimental approach used here also shows a way to investigate the piezoelectric properties of other materials on the nanoscale by using electrostatic scanning probe techniques.

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.

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.

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.

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.