Novel effects of strains in graphene and other two dimensional materials

The analysis of the electronic properties of strained or lattice deformed graphene combines ideas from classical condensed matter physics, soft matter, and geometrical aspects of quantum field theory (QFT) in curved spaces. Recent theoretical and experimental work shows the influence of strains in many properties of graphene not considered before, such as electronic transport, spin-orbit coupling, the formation of Moir\'e patterns, optics, ... There is also significant evidence of anharmonic effects, which can modify the structural properties of graphene. These phenomena are not restricted to graphene, and they are being intensively studied in other two dimensional materials, such as the metallic dichalcogenides. We review here recent developments related to the role of strains in the structural and electronic properties of graphene and other two dimensional compounds.Comment: 75 pages, 15 figures, review articl

Energy spectrum for charge carriers in graphene with folded deformations or with flexural modes with Gaussian and L\'evy distributed random pseudo-magnetic fields

The electronic behaviour in graphene under a flexural field with random height displacements, considered as pseudo-magnetic fields, is studied. General folded deformations (not necessarily random) were first studied, giving an expression for the zero energy modes. For Gaussian folded deformations, it is possible to use a Coulomb gauge norm for the fields allowing contact with previous work on the quantum Hall effect with random fields, showing that the density of states has a power law behaviour and that the zero energy modes wavefunctions are multifractal. This hints of an unusual electron velocity distribution. Also, an Aharonov-Bohm pseudo-effect is produced. For more general non-folded general flexural strain, is not possible to use a Coulomb gauge. However, a Random Phase Approximation (RPA) and the scheme of random matrix theory allows to tackle the problem. For Gaussian distributed fields, the spectrum presents an average gap and for some cases, a breaking of the particle-hole symmetry. Finally, for the case of L\'evy distributed fields, nearly flat bands are seen due to strong electron localization

A Review on Mechanics and Mechanical Properties of 2D Materials - Graphene and Beyond

Since the first successful synthesis of graphene just over a decade ago, a variety of two-dimensional (2D) materials (e.g., transition metal-dichalcogenides, hexagonal boron-nitride, etc.) have been discovered. Among the many unique and attractive properties of 2D materials, mechanical properties play important roles in manufacturing, integration and performance for their potential applications. Mechanics is indispensable in the study of mechanical properties, both experimentally and theoretically. The coupling between the mechanical and other physical properties (thermal, electronic, optical) is also of great interest in exploring novel applications, where mechanics has to be combined with condensed matter physics to establish a scalable theoretical framework. Moreover, mechanical interactions between 2D materials and various substrate materials are essential for integrated device applications of 2D materials, for which the mechanics of interfaces (adhesion and friction) has to be developed for the 2D materials. Here we review recent theoretical and experimental works related to mechanics and mechanical properties of 2D materials. While graphene is the most studied 2D material to date, we expect continual growth of interest in the mechanics of other 2D materials beyond graphene

Designing electronic properties of two-dimensional crystals through optimization of deformations

One of the enticing features common to most of the two-dimensional electronic systems that are currently at the forefront of materials science research is the ability to easily introduce a combination of planar deformations and bending in the system. Since the electronic properties are ultimately determined by the details of atomic orbital overlap, such mechanical manipulations translate into modified electronic properties. Here, we present a general-purpose optimization framework for tailoring physical properties of two-dimensional electronic systems by manipulating the state of local strain, allowing a one-step route from their design to experimental implementation. A definite example, chosen for its relevance in light of current experiments in graphene nanostructures, is the optimization of the experimental parameters that generate a prescribed spatial profile of pseudomagnetic fields in graphene. But the method is general enough to accommodate a multitude of possible experimental parameters and conditions whereby deformations can be imparted to the graphene lattice, and complies, by design, with graphene's elastic equilibrium and elastic compatibility constraints. As a result, it efficiently answers the inverse problem of determining the optimal values of a set of external or control parameters that result in a graphene deformation whose associated pseudomagnetic field profile best matches a prescribed target. The ability to address this inverse problem in an expedited way is one key step for practical implementations of the concept of two-dimensional systems with electronic properties strain-engineered to order. The general-purpose nature of this calculation strategy means that it can be easily applied to the optimization of other relevant physical quantities which directly depend on the local strain field, not just in graphene but in other two-dimensional electronic membranes.Comment: 37 pages, 9 figures. This submission contains low-resolution bitmap images; high-resolution images can be found in version 1, which is ~13.5 M

Ultra-large polymer-free suspended graphene films

Due to its extraordinary properties, suspended graphene is a critical element in a wide range of applications. Preparation methods that preserve the unique properties of graphene are therefore in high demand. To date, all protocols for the production of large graphene films have relied on the application of a polymer film to stabilize graphene during the transfer process. However, this inevitably introduces contaminations that have proven to be extremely difficult, if not impossible, to remove entirely. Here we report the polymer-free fabrication of suspended films consisting of three graphene layers spanning circular holes of 150 $\mu$m diameter. We find a high fabrication yield, very uniform properties of the freestanding graphene across all holes as well across individual holes. A detailed analysis by confocal Raman and THz spectroscopy reveals that the triple-layer samples exhibit structural and electronic properties similar to those of monolayer graphene. We demonstrate their usability as ion-electron converters in time-of-flight mass spectrometry and related applications. They are two orders of magnitude thinner than previous carbon foils typically used in these types of experiments, while still being robust and exhibiting a sufficiently high electron yield. These results are an important step towards replacing free-standing ultra-thin carbon films or graphene from polymer-based transfers with much better defined and clean graphene.Comment: 9 pagers, 5 figure

Towards a microscopic understanding of phonon heat conduction

Heat conduction by phonons is a ubiquitous process that incorporates a wide range of physics and plays an essential role in applications ranging from space power generation to LED lighting. Heat conduction has been studied for over two hundred years, yet many microscopic aspects of heat conduction have remained unclear in most crystalline solids, including which phonons carry heat and how natural and artificial structures scatter specific phonons. Fortunately, recent advances in both computation and experiment are enabling an unprecedented microscopic view of thermal transport by phonons. In this topical review, we provide an overview of these methods, the insights they are providing, and their impact on the science and engineering of heat conduction

Mirror Buckling Transitions in Freestanding Graphene Membranes induced through Scanning Tunneling Microscopy

Graphene has the ability to provide for a technological revolution. First isolated and characterized in 2004, this material shows promise in the field of flexible electronics. The electronic properties of graphene can be tuned by controlling the shape of the membrane. Of particular interest in this endeavor are the thermal ripples in graphene membranes. Years of theoretical work by such luminaries as Lev Landau, Rudolf Peierls, David Mermin and Herbert Wagner have established that 2D crystals should not be thermodynamically stable. Experimental research on thin films has supported this finding. Yet graphene exists, and freestanding graphene films have been grown on large scales. It turns out that coupling between the bending and stretching phonons can stabilize the graphene in a flat, albeit rippled phase. These ripples have attracted much attention, and recent work has shown how to arrange these ripples in a variety of configurations. In this thesis, I will present work done using a scanning tunneling microscope (STM) to interact with freestanding graphene membranes. First I will present STM images of freestanding graphene and show how these images show signs of distortion under the electrostatic influence of the STM tip. This electrostatic attraction between the STM tip and the graphene sample can be used to pull on the graphene sample. At the same time, by employing Joule heating in order to heat graphene using the tunneling current, and exploiting the negative coefficient of thermal expansion, a repulsive thermal load can be generated. By repeatedly pulling on the graphene using the electrostatic potential, while sequentially increasing the setpoint current we can generate a thermal mirror buckling event. Slowly heating the graphene using the tunneling current, prepares a small convex region of graphene under the tip. By increasing thermal stress, as well as pulling using the out of plane electrostatic force, the graphene suddenly and irreversibly switches the sign of its curvature. This event is discovered using STM measurements and supplemented by molecular dynamics simulations. Finally, I will show how to characterize this transition using the famed Ising model. The ripples are modeled as individual Ising spins, which at low temperature exhibit antiferromagnetic coupling. By heating the graphene membrane, the strain increases, changing the antiferromagnetic coupling to ferromagnetic coupling, which characterizes the irreversible transition from a soft, flexible state to a rigid configuration

Moire structures in twisted bilayer graphene studied by transmission electron microscopy

We investigate imaging of moire structures in free-standing twisted bilayer graphene (TBG) carried out by transmission electron microscopy (TEM) in diffraction and in-line Gabor holography modes. Electron diffraction patterns of TBG acquired at typical TEM electron energies of 80 - 300 keV exhibit the diffraction peaks caused by diffraction on individual layers. However, diffraction peaks at the scattering angles related to the periodicity of the moire structure have not been observed in such diffraction patterns. We show that diffraction on moire structure can create intense diffraction peaks if the energy of the probing electrons is very low, in the range of a few tens of eV. Experimental diffraction patterns of TBG acquired with low-energy electrons of 236 eV exhibiting peaks attributed to the moire structure periodicity are shown. In holography mode, the intensity of the wave transmitted through the sample and measured in the far-field can be enhanced or decreased depending on the atomic arrangement, as for example AA or AB stacking. Thus, a decrease of intensity in the far-field must not necessarily be associated with some absorption inside the sample but can simply be a result of a particular atomic arrangement. We believe that our findings can be important for exploiting graphene as a support in electron imaging