Programmable Extreme Pseudomagnetic Fields in Graphene by a Uniaxial Stretch

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.

Imaging quantum oscillations and millitesla pseudomagnetic fields in graphene

The exceptional control of the electronic energy bands in atomically thin quantum materials has led to the discovery of several emergent phenomena1. However, at present there is no versatile method for mapping the local band structure in advanced two-dimensional materials devices in which the active layer is commonly embedded in the insulating layers and metallic gates. Using a scanning superconducting quantum interference device, here we image the de Haas-van Alphen quantum oscillations in a model system, the Bernal-stacked trilayer graphene with dual gates, which shows several highly tunable bands2-4. By resolving thermodynamic quantum oscillations spanning more than 100 Landau levels in low magnetic fields, we reconstruct the band structure and its evolution with the displacement field with excellent precision and nanoscale spatial resolution. Moreover, by developing Landau-level interferometry, we show shear-strain-induced pseudomagnetic fields and map their spatial dependence. In contrast to artificially induced large strain, which leads to pseudomagnetic fields of hundreds of tesla5-7, we detect naturally occurring pseudomagnetic fields as low as 1 mT corresponding to graphene twisting by 1 millidegree, two orders of magnitude lower than the typical angle disorder in twisted bilayer graphene8-11. This ability to resolve the local band structure and strain at the nanoscale level enables the characterization and use of tunable band engineering in practical van der Waals devices.

Strain-Induced Plasmon Confinement in Polycrystalline Graphene

Terahertz spectroscopy is a perfect tool to investigate the electronic intraband conductivity of graphene, but a phenomenological model (Drude-Smith) is often needed to describe disorder. By studying the THz response of isotropically strained polycrystalline graphene and using a fully atomistic computational approach to fit the results, we demonstrate here the connection between the Drude-Smith parameters and the microscopic behavior. Importantly, we clearly show that the strain-induced changes in the conductivity originate mainly from the increased separation between the single-crystal grains, leading to enchanced localization of the plasmon excitations. Only at the lowest strain values explored, a behavior consistent with the deformation of the individual grains can instead be observed.

Realizing One-Dimensional Electronic States in Graphene via Coupled Zeroth Pseudo-Landau Levels

Strain-induced pseudomagnetic fields can mimic real magnetic fields to generate a zero-magnetic-field analog of the Landau levels (LLs), i.e., the pseudo-Landau levels (PLLs), in graphene. The distinct nature of the PLLs enables one to realize novel electronic states beyond what is feasible with real LLs. Here, we show that it is possible to realize exotic electronic states through the coupling of zeroth PLLs in strained graphene. In our experiment, nanoscale strained structures embedded with PLLs are generated along a one-dimensional (1D) channel of suspended graphene monolayer. Our results demonstrate that the zeroth PLLs of the strained structures are coupled together, exhibiting a serpentine pattern that snakes back and forth along the 1D suspended graphene monolayer. These results are verified theoretically by large-scale tight-binding calculations of the strained samples. Our result provides a new approach to realizing novel quantum states and to engineering the electronic properties of graphene by using localized PLLs as building blocks.

Acoustically Induced Giant Synthetic Hall Voltages in Graphene

Any departure from graphene's flatness leads to the emergence of artificial gauge fields that act on the motion of the Dirac fermions through an associated pseudomagnetic field. Here, we demonstrate the tunability of strong gauge fields in nonlocal experiments using a large planar graphene sheet that conforms to the deformation of a piezoelectric layer by a surface acoustic wave. The acoustic wave induces a longitudinal and a giant synthetic Hall voltage in the absence of external magnetic fields. The superposition of a synthetic Hall potential and a conventional Hall voltage can annihilate the sample's transverse potential at large external magnetic fields. Surface acoustic waves thus provide a promising and facile avenue for the exploitation of gauge fields in large planar graphene systems.

Triaxially strained suspended graphene for large-area pseudo-magnetic fields

Strain-engineered graphene has garnered much attention recently owing to the possibilities of creating substantial energy gaps enabled by pseudo-magnetic fields (PMFs). While theoretical works proposed the possibility of creating large-area PMFs by straining monolayer graphene along three crystallographic directions, clear experimental demonstration of such promising devices remains elusive. Herein, we experimentally demonstrate a triaxially strained suspended graphene structure that has the potential to possess large-scale and quasi-uniform PMFs. Our structure employs uniquely designed metal electrodes that function both as stressors and metal contacts for current injection. Raman characterization and tight-binding simulations suggest the possibility of achieving PMFs over a micrometer-scale area. Current-voltage measurements confirm an efficient current injection into graphene, showing the potential of our devices for a new class of optoelectronic applications. We also theoretically propose a photonic crystal-based laser structure that obtains strongly localized optical fields overlapping with the spatial area under uniform PMFs, thus presenting a practical route toward the realization of graphene lasers.

Deep Elastic Strain Engineering of 2D Materials and Their Twisted Bilayers

Conventionally, tuning materials' properties can be done through strategies such as alloying, doping, defect engineering, and phase engineering, while in fact mechanical straining can be another effective approach. In particular, elastic strain engineering (ESE), unlike conventional strain engineering mainly based on epitaxial growth, allows for continuous and reversible modulation of material properties by mechanical loading/unloading. The exceptional intrinsic mechanical properties (including elasticity and strength) of two-dimensional (2D) materials make them naturally attractive candidates for potential ESE applications. Here, we demonstrated that using the strain effect to modulate the physical and chemical properties toward novel functional device applications, which could be a general strategy for various 2D materials and their heterostructures. We then show how ultralarge, uniform elastic strain in free-standing 2D monolayers can permit deep elastic strain engineering (DESE), which can result in fundamentally changed electronic and optoelectronic properties for unconventional device applications. In addition to monolayers and van der Waals (vdW) heterostructures, we propose that DESE can be also applied to twisted bilayer graphene and other emerging twisted vdW structures, allowing for unprecedented functional 2D material applications.

Pseudomagnetic Fields Enabled Manipulation of On-Chip Elastic Waves

The physical realization of pseudomagnetic fields (PMFs) is an engaging frontier of research. As in graphene, elastic PMF can be realized by the structural modulations of Dirac materials. We show that, in the presence of PMFs, the conical dispersions split into elastic Landau levels, and the elastic modes robustly propagate along the edges, similar to the quantum Hall edge transports. In particular, we reveal unique elastic snake states in an on-chip heterostructure with two opposite PMFs. The flexibility in the micromanufacture of silicon chips and the low loss of elastic waves provide an unprecedented opportunity to demonstrate various fascinating topological transports of the edge states under PMFs. These properties open new possibilities for designing functional elastic wave devices in miniature and compact scales.

Pseudo-magnetic field-induced slow carrier dynamics in periodically strained graphene

The creation of pseudo-magnetic fields in strained graphene has emerged as a promising route to investigate intriguing physical phenomena that would be unattainable with laboratory superconducting magnets. The giant pseudo-magnetic fields observed in highly deformed graphene can substantially alter the optical properties of graphene beyond a level that can be feasible with an external magnetic field, but the experimental signatures of the influence of such pseudo-magnetic fields have yet to be unveiled. Here, using time-resolved infrared pump-probe spectroscopy, we provide unambiguous evidence for slow carrier dynamics enabled by the pseudo-magnetic fields in periodically strained graphene. Strong pseudo-magnetic fields of ~100 T created by non-uniform strain in  graphene on nanopillars are found to significantly decelerate the relaxation processes of hot carriers by more than an order of magnitude. Our findings offer alternative opportunities to harness the properties of graphene enabled by pseudo-magnetic fields for optoelectronics and condensed matter physics.

The effect of strain-induced pseudo-magnetic fields on the optical properties of graphene has not been experimentally explored yet. Here, pseudo-magnetic fields reaching values of 100 T are shown to increase by more than an order of magnitude the relaxation lifetime of hot carriers in periodically strained graphene.

Valley Polarization and Inversion in Strained Graphene via Pseudo-Landau Levels, Valley Splitting of Real Landau Levels, and Confined States

It is quite easy to control spin polarization and the spin direction of a system via magnetic fields. However, there is no such direct and efficient way to manipulate the valley pseudospin degree of freedom. Here, we demonstrate experimentally that it is possible to realize valley polarization and valley inversion in graphene by using both strain-induced pseudomagnetic fields and real magnetic fields. Pseudomagnetic fields, which are quite different from real magnetic fields, point in opposite directions at the two distinct valleys of graphene. Therefore, the coexistence of pseudomagnetic fields and real magnetic fields leads to imbalanced effective magnetic fields at two distinct valleys of graphene. This allows us to control the valley in graphene as conveniently as the electron spin. In this work, we report a consistent observation of valley polarization and inversion in strained graphene via pseudo-Landau levels, splitting of real Landau levels, and valley splitting of confined states using scanning tunneling spectroscopy. Our results highlight a pathway to valleytronics in strained graphene-based platforms.

Quantum Hall Response to Time-Dependent Strain Gradients in Graphene

Mechanical deformations of graphene induce a term in the Dirac Hamiltonian that is reminiscent of an electromagnetic vector potential. Strain gradients along particular lattice directions induce local pseudomagnetic fields and substantial energy gaps as indeed observed experimentally. Expanding this analogy, we propose to complement the pseudomagnetic field by a pseudoelectric field, generated by a time-dependent oscillating stress applied to a graphene ribbon. The joint Hall-like response to these crossed fields results in a strain-induced charge current along the ribbon. We analyze in detail a particular experimental implementation in the (pseudo)quantum Hall regime with weak intervalley scattering. This allows us to predict an (approximately) quantized Hall current that is unaffected by screening due to diffusion currents.

Strain Engineering of 2D Materials: Issues and Opportunities at the Interface

Triggered by the growing needs of developing semiconductor devices at ever-decreasing scales, strain engineering of 2D materials has recently seen a surge of interest. The goal of this principle is to exploit mechanical strain to tune the electronic and photonic performance of 2D materials and to ultimately achieve high-performance 2D-material-based devices. Although strain engineering has been well studied for traditional semiconductor materials and is now routinely used in their manufacturing, recent experiments on strain engineering of 2D materials have shown new opportunities for fundamental physics and exciting applications, along with new challenges, due to the atomic nature of 2D materials. Here, recent advances in the application of mechanical strain into 2D materials are reviewed. These developments are categorized by the deformation modes of the 2D material-substrate system: in-plane mode and out-of-plane mode. Recent state-of-the-art characterization of the interface mechanics for these 2D material-substrate systems is also summarized. These advances highlight how the strain or strain-coupled applications of 2D materials rely on the interfacial properties, essentially shear and adhesion, and finally offer direct guidelines for deterministic design of mechanical strains into 2D materials for ultrathin semiconductor applications.

Controlling Rotation of Two-Dimensional Material Flakes

Interlayer rotational alignment in van der Waals (vdW) structures of two-dimensional (2D) materials couples strongly to electronic properties and, therefore, has significant technological implications. Nevertheless, controlling the rotation of an arbitrary 2D material flake remains a challenge in the development of rotation-tunable electronics, for the emerging field of twistronics. In this article, we reveal a general moiré-driven mechanism that governs the interlayer rotation. Controlling the moiré can therefore hold promise for controlling the interlayer rotation. We further demonstrate mismatch strain engineering as a useful tool to design the interlayer rotation via changing the energy landscape of moiré within a finite-sized region. The robustness and programmable nature of our approach arise from moiré symmetry, energetics, and mechanics. Our approach provides another possibility to the on-demand design of rotation-tunable electronics.

In Situ Strain Tuning in hBN-Encapsulated Graphene Electronic Devices

Using a simple setup to bend a flexible substrate, we demonstrate deterministic and reproducible in situ strain tuning of graphene electronic devices. Central to this method is the full hBN encapsulation of graphene, which preserves the exceptional quality of pristine graphene for transport experiments. In addition, the on-substrate approach allows one to exploit strain effects in the full range of possible sample geometries and at the same time guarantees that changes in the gate capacitance remain negligible during the deformation process. We use Raman spectroscopy to spatially map the strain magnitude in devices with two different geometries and demonstrate the possibility to engineer a strain gradient, which is relevant for accessing the valley degree of freedom with pseudomagnetic fields. Comparing the transport characteristics of a suspended device with those of an on-substrate device, we demonstrate that our new approach does not suffer from the ambiguities encountered in suspended devices.

Landau Quantization of a Narrow Doubly-Folded Wrinkle in Monolayer Graphene

Folding can be an effective way to tailor the electronic properties of graphene and has attracted wide study interest in finding its novel properties. Here we present the experimental characterizations of the structural and electronic properties of a narrow graphene wrinkle on a SiO₂/Si substrate using scanning tunneling microscopy/spectroscopy. Pronounced and nearly equally separated conductance peaks are observed in the d I/d V spectra of the wrinkle. We attribute these peaks to pseudo-Landau levels (PLLs) that are caused by a gradient-strain-induced pseudomagnetic field up to about 42 T in the narrow wrinkle. The introduction of the gradient strain and thus the pseudomagnetic field can be ascribed to the lattice deformation. A doubly-folded structure of the wrinkle is suggested. Our density functional theory calculations show that the band structure of the doubly folded graphene wrinkle has a parabolic dispersion, which can well explain the equally separated PLLs. The effective mass of carriers is obtained to be about 0.02 m_e ( m_e: the rest mass of electron), and interestingly, it is revealed that there exists valley polarization in the wrinkle. Such properties of the strained doubly folded wrinkle may provide a platform to explore some exciting phenomena in graphene, like zero-field quantum valley Hall effect.

Atomic-scale strain manipulation of a charge density wave

Charge density waves (CDWs) are simple periodic reorganizations of charge in a crystal, and yet they are still poorly understood and continue to bear surprises. External perturbations, such as strain or pressure, can in principle push a CDW phase into a different ordering geometry. However, engineering this type of quantum criticality has been experimentally challenging. Here, we implement a simple method for straining bulk materials. By applying it to 2H-NbSe₂, a prototypical CDW system studied for decades, we discover two dramatic strain-induced CDW phase transitions. Our atomic-scale spectroscopic imaging measurements, combined with theory, reveal the distinct roles of electrons and phonons in forming these emergent states, thus opening a window into the rich phenomenology of CDWs.

A charge density wave (CDW) is one of the fundamental instabilities of the Fermi surface occurring in a wide range of quantum materials. In dimensions higher than one, where Fermi surface nesting can play only a limited role, the selection of the particular wavevector and geometry of an emerging CDW should in principle be susceptible to controllable manipulation. In this work, we implement a simple method for straining materials compatible with low-temperature scanning tunneling microscopy/spectroscopy (STM/S), and use it to strain-engineer CDWs in 2H-NbSe₂. Our STM/S measurements, combined with theory, reveal how small strain-induced changes in the electronic band structure and phonon dispersion lead to dramatic changes in the CDW ordering wavevector and geometry. Our work unveils the microscopic mechanism of a CDW formation in this system, and can serve as a general tool compatible with a range of spectroscopic techniques to engineer electronic states in any material where local strain or lattice symmetry breaking plays a role.

Observation of elastic topological states in soft materials

Topological elastic metamaterials offer insight into classic motion law and open up opportunities in quantum and classic information processing. Theoretical modeling and numerical simulation of elastic topological states have been reported, whereas the experimental observation remains relatively unexplored. Here we present an experimental observation and numerical simulation of tunable topological states in soft elastic metamaterials. The on-demand reversible switch in topological phase has been achieved by changing filling ratio, tension, and/or compression of the elastic metamaterials. By combining two elastic metamaterials with distinct topological invariants, we further demonstrate the formation and dynamic tunability of topological interface states by mechanical deformation, and the manipulation of elastic wave propagation. Moreover, we provide a topological phase diagram of elastic metamaterials under deformation. Our approach to dynamically control interface states in soft materials paves the way to various phononic systems involving thermal management and soft robotics requiring better use of energy.

Here the authors present an experimental observation of topological states in soft elastic metamaterials. They show reversibility in topological phases by changing filling ratio, tension and/or compression, while also demonstrating tunability of topological interface states by mechanical deformation.

Strain-induced bi-thermoelectricity in tapered carbon nanotubes

We show that carbon-based nanostructured materials are a novel testbed for controlling thermoelectricity and have the potential to underpin the development of new cost-effective environmentally-friendly thermoelectric materials. In single-molecule junctions, it is known that transport resonances associated with the discrete molecular levels play a key role in the thermoelectric performance, but such resonances have not been exploited in carbon nanotubes (CNTs). Here we study junctions formed from tapered CNTs and demonstrate that such structures possess transport resonances near the Fermi level, whose energetic location can be varied by applying strain, resulting in an ability to tune the sign of their Seebeck coefficient. These results reveal that tapered CNTs form a new class of bi-thermoelectric materials, exhibiting both positive and negative thermopower. This ability to change the sign of the Seebeck coefficient allows the thermovoltage in carbon-based thermoelectric devices to be boosted by placing CNTs with alternating-sign Seebeck coefficients in tandem.

The role of the strain induced population imbalance in Valley polarization of graphene: Berry curvature perspective

Real magnetic and lattice deformation gauge fields have been investigated in honeycomb lattice of graphene. The coexistence of these two gauges will induce a gap difference between two valley points (K and K') of system. This gap difference allows us to study the possible topological valley Hall current and valley polarization in the graphene sheet. In the absence of magnetic field, the strain alone could not generate a valley polarization when the Fermi energy coincides exactly with the Dirac points. Since in this case there is not any imbalance between the population of the valley points. In other words each of these gauges alone could not induce any topological valley-polarized current in the system at zero Fermi energy. Meanwhile at non-zero Fermi energies population imbalance can be generated as a result of the external strain even at zero magnetic field. In the context of Berry curvature within the linear response regime the valley polarization (both magnetic free polarization, Π0, and field dependent response function, χ α ) in different values of gauge fields of lattice deformation has been obtained.

Existence of multi-radical and closed-shell semiconducting states in post-graphene organic Dirac materials

Post-graphene organic Dirac (PGOD) materials are ordered two-dimensional networks of triply bonded sp 2 carbon nodes spaced by π-conjugated linkers. PGOD materials are natural chemical extensions of graphene that promise to have an enhanced range of properties and applications. Experimentally realised molecules based on two PGOD nodes exhibit a bi-stable closed-shell/multi-radical character that can be understood through competing Lewis resonance forms. Here, following the same rationale, we predict that similar states should be accessible in PGOD materials, which we confirm using accurate density functional theory calculations. Although for graphene the semimetallic state is always dominant, for PGOD materials this state becomes marginally meta-stable relative to open-shell multi-radical and/or closed-shell states that are stabilised through symmetry breaking, in line with analogous molecular systems. These latter states are semiconducting, increasing the potential use of PGOD materials as highly tuneable platforms for future organic nano-electronics and spintronics.

Analytic approach to magneto-strain tuning of electronic transport through a graphene nanobubble: perspectives for a strain sensor

We consider the scattering of Dirac particles in graphene due to the superposition of an external magnetic field and mechanical strain. As a model for a graphene nanobubble, we find exact analytical solutions for single-particle states inside and outside a circular region submitted to the fields. Finally, we obtain analytical expressions for the scattering cross-section, as well as for the Landauer current through the circular region. Our results provide a fully-analytical treatment for electronic transport through a graphene nanobubble, showing that a combination of a physical magnetic field and strain leads to valley polarization and filtering of the electronic current. Moreover, our analytical model provides an explicit metrology principle to measure strain by performing conductance experiments under a controlled magnetic field imposed over the sample.

Electronic and optical properties of strained graphene and other strained 2D materials: a review

This review presents the state of the art in strain and ripple-induced effects on the electronic and optical properties of graphene. It starts by providing the crystallographic description of mechanical deformations, as well as the diffraction pattern for different kinds of representative deformation fields. Then, the focus turns to the unique elastic properties of graphene, and to how strain is produced. Thereafter, various theoretical approaches used to study the electronic properties of strained graphene are examined, discussing the advantages of each. These approaches provide a platform to describe exotic properties, such as a fractal spectrum related with quasicrystals, a mixed Dirac-Schrödinger behavior, emergent gravity, topological insulator states, in molecular graphene and other 2D discrete lattices. The physical consequences of strain on the optical properties are reviewed next, with a focus on the Raman spectrum. At the same time, recent advances to tune the optical conductivity of graphene by strain engineering are given, which open new paths in device applications. Finally, a brief review of strain effects in multilayered graphene and other promising 2D materials like silicene and materials based on other group-IV elements, phosphorene, dichalcogenide- and monochalcogenide-monolayers is presented, with a brief discussion of interplays among strain, thermal effects, and illumination in the latter material family.

Strain Engineering a 4a×√3a Charge Density Wave Phase in Transition Metal Dichalcogenide 1T-VSe2

We report a rectangular charge density wave (CDW) phase in strained 1T-VSe2 thin films synthesized by molecular beam epitaxy on c-sapphire substrates. The observed CDW structure exhibits an unconventional rectangular 4a×√3a periodicity, as opposed to the previously reported hexagonal 4a×4a structure in bulk crystals and exfoliated thin layered samples. Tunneling spectroscopy shows a strong modulation of the local density of states of the same 4a×√3a CDW periodicity and an energy gap of 2ΔCDW = (9.1 ± 0.1) meV. The CDW energy gap evolves into a full gap at temperatures below 500 mK, indicating a transition to an insulating phase at ultra-low temperatures. First-principles calculations confirm the stability of both 4a×4a and 4a×√3a structures arising from soft modes in the phonon dispersion. The unconventional structure becomes preferred in the presence of strain, in agreement with experimental findings.

Highly Ordered and Multiple-Responsive Graphene Oxide/Azoimidazolium Surfactant Intercalation Hybrids: A Versatile Control Platform

To produce graphene materials with better controllability, a new graphene oxide (GO) intercalation hybrid is fabricated with the incorporation and functionalization with the azoimidazolium (AzoIm⁺) surfactant. The hybrid exhibits a highly uniform lamellar structure in which a few layers of GO are stacked with AzoIm⁺ alternatively. Simultaneous control of the mesoscopic structures, aggregation properties, and electrochemical behavior of the hybrid is achieved by inheriting the photo, thermal, and mechanical responsiveness of azoimidazolium. Ultraviolet (UV) treatment produces a well-dispersed GO/AzoIm⁺ suspension aggregate and a precipitate, whereas the specific capacitance of the final hybrid decreases. The lamellar stacking becomes anisotropic by uniaxial stretching on a soft polymer. With a liquid crystal unit inserted between the layers, the d spacing of the lamella passes through transformation, disordering, and finally recovery stages, associated with the increasing and decreasing temperature. The explosive release of heat generated by the thermal reduction of GO is reduced in the GO/AzoIm⁺ intercalation hybrid. The release of heat is tunable by varying the relative quantity and UV treatment of AzoIm⁺. The physical properties of the hybrid allow the controlled preparation of ultrasmall Au nanodots between the GO layers. This represents a major step toward multiple-responsive integrated graphene applications.

Strained graphene Hall bar

The effects of strain, induced by a Gaussian bump, on the magnetic field dependent transport properties of a graphene Hall bar are investigated. The numerical simulations are performed using both classical and quantum mechanical transport theory and we found that both approaches exhibit similar characteristic features. The effects of the Gaussian bump are manifested by a decrease of the bend resistance, R _B, around zero-magnetic field and the occurrence of side-peaks in R _B. These features are explained as a consequence of bump-assisted scattering of electrons towards different terminals of the Hall bar. Using these features we are able to give an estimate of the size of the bump. Additional oscillations in R _B are found in the quantum description that are due to the population/depopulation of Landau levels. The bump has a minor influence on the Hall resistance even for very high values of the pseudo-magnetic field. When the bump is placed outside the center of the Hall bar valley polarized electrons can be collected in the leads.

Strain-Engineered Graphene Grown on Hexagonal Boron Nitride by Molecular Beam Epitaxy

Graphene grown by high temperature molecular beam epitaxy on hexagonal boron nitride (hBN) forms continuous domains with dimensions of order 20 μm, and exhibits moiré patterns with large periodicities, up to ~30 nm, indicating that the layers are highly strained. Topological defects in the moiré patterns are observed and attributed to the relaxation of graphene islands which nucleate at different sites and subsequently coalesce. In addition, cracks are formed leading to strain relaxation, highly anisotropic strain fields, and abrupt boundaries between regions with different moiré periods. These cracks can also be formed by modification of the layers with a local probe resulting in the contraction and physical displacement of graphene layers. The Raman spectra of regions with a large moiré period reveal split and shifted G and 2D peaks confirming the presence of strain. Our work demonstrates a new approach to the growth of epitaxial graphene and a means of generating and modifying strain in graphene.

Scanning Tunneling Spectroscopy of Proximity Superconductivity in Epitaxial Multilayer Graphene

We report on spatial measurements of the superconducting proximity effect in epitaxial graphene induced by a graphene-superconductor interface. Superconducting aluminum films were grown on epitaxial multilayer graphene on SiC. The aluminum films were discontinuous with networks of trenches in the film morphology reaching down to exposed graphene terraces. Scanning tunneling spectra measured on the graphene terraces show a clear decay of the superconducting energy gap with increasing separation from the graphene-aluminum edges. The spectra were well described by Bardeen-Cooper-Schrieffer (BCS) theory. The decay length for the superconducting energy gap in graphene was determined to be greater than 400 nm. Deviations in the exponentially decaying energy gap were also observed on a much smaller length scale of tens of nanometers.