Session G30: Focus Session: Graphene Devices: Fabrication, Characterization and Modeling: Solitons in Few Layer Graphene

Interacting wrinkles in graphene on patterned substrates

The wrinkling of graphene on patterned substrates is interesting both because graphene is an exemplary thin sheet with effective mechanical thickness less than 1 angstrom, and because of the importance of strain for graphene's electronic properties. We present a combination of atomistic and large-scale coarse-grained numerical simulations of graphene on top of a substrate of size $\sim 1 \mu$m$^2$ decorated with nanoparticles of diameter $\sim 10$nm. We are able to reproduce previous experimental results in which substrate protrusions are connected by a network of long narrow wrinkles [1], and we clarify the role of substrate-graphene interactions in determining the morphology of these. Our simulations also allow us to explore in further detail a previously-overlooked feature, namely the possibility for interacting wrinkles to form stable ``avoiding'' configurations, in a manner reminiscent of interacting cracks [2]. By nucleating and growing wrinkles in a controlled way, we are able to characterize the role of long-range stress fields in determining whether two wrinkles will avoid or merge. \\[4pt] [1] M. Yamamoto et al, Phys. Rev. X 2, 041018 (2012).\\[0pt] [2] M. L. Fender, F. Lechenault, and K. E. Daniels, Phys. Rev. Lett. 105, 125505 (2010).   

Ripple domains on graphene on a SiO$_2$ substrate

Out-of-plane lattice distortions in two-dimensional materials are prevalent among structural movements at finite temperature. Graphene's negative thermal expansion coefficient is a direct consequence of such an intrinsic property. In our recent work, we have shown that friction measurements on graphene exfoliated on a silicon oxide substrate exhibit an anomalous anisotropy whose origin is attributed to the formation of ripple domains. We further uncover the atomistic origin of the observed friction domains using a newly developed method called cantilever torsion microscopy (CTM) together with angle-resolved photoemission spectroscopy (ARPES) measurements. We experimentally demonstrate that ripples on graphene are formed along the zigzag direction of the hexagonal lattice. We have also calculated theoretically the bending stiffness of carbon-carbon bonds and adhesive interactions between graphene and the surface underneath it that are consistent with our experimental results.   

Transport in Strained Graphene with Applied Magnetic Fields

Strain in graphene layers produces synthetic gauge fields that may be used to modify the properties of its electron system [1,2]. We study single layers of graphene transferred over Ti/Au electrical contacts on oxidized Si wafers with etched triangular holes in the oxide. The layers are strained by applying pressure either electrostatically from a gate voltage or hydrostatically from an external inert gas. We investigate electronic transport in this suspended variable-strain graphene system under applied magnetic fields and find that the device conductance is modulated by the external pressure [3] as well as by the Hall effect. We will discuss our latest results.\\[4pt] [1] Guinea, F., Katsnelson, M. I., Geim, A. K. Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering. Nat. Phys. 6, 30-33 (2009).\\[0pt] [2] Levy, N., et al. Strain-induced pseudo--magnetic fields greater than 300 tesla in graphene nanobubbles. Science, 329 544-547 (2010).\\[0pt] [3] Smith, A. D., et al., Pressure sensors based on suspended graphene membranes. Solid-State Electron. 88, 89-94 (2013).   

Interlayer strain solitons in bilayer graphene

The interlayer registry between graphene layers can have dramatic effects on the physical and electronic properties of few-layer graphene. For example, in the presence of a perpendicular electric field, a band gap appears in the electronic spectrum of so-called Bernal-stacked graphene. This band gap is intimately tied to a structural spontaneous symmetry-breaking, where one of the graphene layers shifts by an atomic spacing with respect to the other. This shift can happen in multiple directions, resulting in stacking domains with soliton-like structural boundaries between them. Theorists have recently proposed that novel electronic states exist at these boundaries, but very little is known about their structural properties. Here we use electron microscopy to measure with nanoscale and atomic resolution the widths, motion, and topological structure of soliton boundaries and related topological defects in bilayer graphene [1]. We find that each soliton consists of an atomic-scale registry shift between the two graphene layers occurring over 6-11 nm. We infer the minimal energy barrier to interlayer translation and observe soliton motion during in-situ heating. The abundance of these structures across a variety samples, as well as their unusual properties, suggests that they will have substantial effects on the electronic and mechanical properties of bilayer graphene. \\[4pt] [1] Jonathan S. Alden, Adam W. Tsen, Pinshane Y. Huang, Robert Hovden, Lola Brown, Jiwoong Park, David A. Muller, and Paul L. McEuen, PNAS 110, 11256-11260 (2013)   

Electronic properties of strained graphene: A new Dirac Hamiltonian that solves several issues in previous ones

In the literature, strained graphene is usually described using a combination of tight-binding model and linear elasticity theory. This leads to the appearance of pseudomagnetic fields. However, as we will discuss, the resulting equations contains some problems. The most important is that the Fermi energy does not appears in the high-symmetry points of the reciprocal lattice as assumed in previous theories. In this work we consider the particular case of a uniform strain, which can be solved in some cases without any approximation. Then the dispersion relation is simply shifted and deformed. Among our results highlights [1], we present analytical expressions for the shift of the Dirac points and the corresponding Dirac-like equation, which cannot be derived from the usual theory of the strain-induced pseudomagnetic field. The obtained Dirac-like equation is tested against tight-binding computer simulations showing a good agreement. As an application, we generalize the frequency-dependent conductivity expression of graphene under uniform strain, which is calculated by using the Kubo formula. Finally, we discuss a generalization of our results, for the case of nonuniform strain. \\[4pt] [1] M. Oliva-Leyva, and G.G.Naumis, PRB 88, 08543 (2013).   

Strain Effects in Graphene Transport Measurements on Micropatterned Substrates

Since its initial isolation in 2004, graphene has been the subject of intense study due to its extraordinary electrical and mechanical properties. However, the interplay between these properties remains comparatively unexplored. Here we present transport and scanning probe microscopy measurements of graphene devices on micropatterned substrates, where the interactions between surface adhesion, mechanical strain, and electrical conductivity can be observed. We find a positive correlation between strain applied via the substrate and electrical resistivity, and explore the mechanisms responsible for this increase, including surface delamination, microcrack formation, and mechanical strain in the graphene lattice structure, using atomic force microscopy measurements.   

Effect of homogeneous strain on the Landau levels and the Klein tunneling in graphene

We analyze the effect of homogeneous strain on the Landau levels (LLs) spectra and Klein tunneling of graphene. Using the tight-binding approach to first nearest neighbors, we study the electron dynamics in graphene under homogeneous strained and uniform perpendicular magnetic field. We obtain an analytical expression for the energy of the LLs in function of strain for low magnetic fields. For Klein tunneling, we study how can change the tunneling transmission when the graphene layer is under a homogeneous strain. In particular, we analyze the effects of uniaxial, shear, and isotropic strain and combinations of these deformations. Our results show that homogeneous deformations in graphene induce changes in the LLs spectra or Klein tunneling, due to the linear dependence of the effective Fermi velocity with the tensile strain. The effects of homogeneous strain on conductivity, Hall resistance, and others electronic properties of graphene, are discussed.   

Controlling thermal and electrical properties of graphene by strain-engineering its flexural phonons

We explore the effects of flexural phonons on the thermal and electrical properties of graphene. To control the amplitude of flexural phonons, we developed a technique to engineer uniform mechanical strain between 0 and 1{\%} in suspended graphene. We determine the level of strain, thermal conductivity and carrier mobility of graphene through a combination of mechanical resonance and electrical transport measurements. Depending on strain, we find significant changes in the thermal expansion coefficient, thermal conductivity, and carrier mobility of suspended graphene. These changes are consistent with the expected contribution of flexural phonons.   

Excitonic Pairing between Strained Graphene Layers

It is well known that inter-layer electron-hole (excitonic) pairing, caused by the inter-layer Coulomb interaction, can occur between graphene sheets appropriately doped with electrons and holes. However in such a system the energy of the excitonic condensate, as well the corresponding critical temperature, are very small due to the effective screening of the inter-layer interaction potential. We study pairing between two uniaxially- strained graphene layers, focusing particularly on the dependence of the pairing gap on the applied strain. The graphene layers are modeled as anisotropic Dirac fermion systems. We find a strong dependence on the strain, particularly in the weak-coupling regime where screening is not very relevant. In this case the condensate energy is enhanced due to the increase of the density of states as a function of anisotropy. At moderate and strong coupling the pairing becomes less sensitive to strain because of the subtle interplay between density of states effects and the strain-modified screening of the inter-layer Coulomb potential. We also analyze the possibility of higher angular momentum pairing (beyond the conventional s-wave) for the strained graphene layers. In addition, we propose that pairing can be further enhanced at the Lifshitz transition point when a relatively large strain is applied in the zig-zag direction. At such topological transition the electronic dispersion deviates strongly from the simplest anisotropic (elliptical) Dirac cone and becomes quadratic in one of the lattice directions while remaining Dirac-like along the other.   

Graphene Calisthenics: Straintronics of Graphene with Light-Reactive Azobenzene Polymer

Although a promising target for next-generation electronics, graphene's lack of a band gap is a severe hindrance. There are many ways of opening a gap, and one controllable way is through application of specific non-uniform strains which can produce extremely large pseudomagnetic fields. This effect was predicted and verified experimentally, but so far there have been few methods developed that reliably control the size, location, separation and amount of strain in graphene. We have used a layer of light-reactive azobenzene polymer beneath the graphene to produce strained monolayer graphene with light exposure. Using Raman spectroscopy, we have measured a shift of up to 20 cm$^{\mathrm{-1}}$ in the 2D peak when the graphene and polymer sample was exposed to 532 nm laser illumination indicating that the graphene is undergoing a strain from deformation of the azobenzene layer below. AFM topographic measurements and COMSOL simulations were used to verify this assertion. Use of polymeric materials to reliably strain graphene in non-uniform ways could result in controllable production of large pseudomagnetic fields in graphene and more control over graphene's low-energy charge carriers.   

Strain Engineering of Graphene: Atomistic Simulation of Y-junctions and Nanobubbles

We have studied the effects of two and three-dimensional states of strain on electronic transport in monolayer graphene. Using a combined atomistic simulation approach with molecular mechanics, molecular dynamics, tight binding exact diagonalization and Landauer-B\"{u}ttiker formulism, we have explored how various deformation patterns induce tunable pseudomagnetic field (PMF) distributions and furthermore how the Landau levels arising from PMF affect the quantum transport properties. Specifically, graphene Y-junction structures are found, under triaxial strains, to behave like pseudomagnetic quantum dots that selectively guide electron movement; valley degeneracy is broken when both strain-induced PMF and external real magnetic fields are present. Furthermore, graphene nano-bubbles with different geometries obtained by gas pressure can also be controlled as functional blocks due to PMF-restricted quantum transport by manipulation of strain. The simulation results show the promising potential to utilize graphene as a tunable building block for electronic NEMS/MEMS devices by strain engineering.   

First-Principles Calculations on the Effect of Doping and Biaxial Tensile Strain on Electron-Phonon Coupling in Graphene

Graphene has exhibited a wealth of fascinating properties, but is also known not to be a superconductor. Remarkably, we show that graphene can be made a conventional Bardeen-Cooper-Schrieffer superconductor by the combined effect of charge doping and tensile strain. While the effect of doping obviously enlarges the Fermi surface, the effect of strain profoundly increases the electron-phonon coupling. At the experimental accessible doping ($\sim4\times10^{14}$ cm$^{-2}$) and strain ($\sim16$\%) levels, the superconducting critical temperature $T_{c}$ is estimated as high as $\sim30$ K, the highest for a single-element material above the liquid hydrogen temperature.   

Unconventional magnetic ground state in strained graphene: theory of global anti-ferromagnetic phase

An unconventional magnetic ground state is proposed for the Hubbard Hamiltonian in strained graphene. We show that when the chemical potential lies close to the Dirac point, strained graphene supports magnetic ordering that simultaneously gives rise to anti-ferromagnetic and ferromagnetic orders, even for weak onsite interaction. Whereas the anti-ferromagnetic order parameter is of the same sign in the entire system, the ferromagnetic order at the boundary has the opposite sign from the bulk. The spatially-integrated ferromagnetic order parameter is this way zero, and the magnetic ground state is therefore a spin-singlet. This peculiar magnetic ordering results from the nature of the strain-induced (near) zero energy states, which have support on one sublattice in the bulk, and on the other sublattice near the boundary of a finite system. We support our claim with the self-consistent numerical mean-field calculation of the magnetic order parameters, and with a Monte-Carlo simulations of the Hubbard model in a strained honeycomb lattice.