Pseudomagnetic fields and ballistic transport in a suspended graphene sheet

Mechanical Control of Quantum Transport in Graphene

2D materials (2DMs) are fundamentally electro-mechanical systems. Their environment unavoidably strains them and modifies their quantum transport properties. For instance, a simple uniaxial strain can completely turn off the conductance of ballistic graphene or switch on/off the superconducting phase of magic-angle bilayer graphene. This article reports measurements of quantum transport in strained graphene transistors which agree quantitatively with models based on mechanically-induced gauge potentials. A scalar potential is mechanically induced in situ to modify graphene's work function by up to 25 meV. Mechanically generated vector potentials suppress the ballistic conductance of graphene by up to 30% and control its quantum interferences. The data are measured with a custom experimental platform able to precisely tune both the mechanics and electrostatics of suspended graphene transistors at low-temperature over a broad range of strain (up to 2.6%). This work opens many opportunities to harness quantitative strain effects in 2DM quantum transport and technologies.

Valley-polarized and enhanced transmission in graphene with a smooth strain profile

We explore the influence of strain on the valley-polarized transmission of graphene by employing the wave-function matching and the non-equilibrium Green's function technique. When the transmission is along the armchair direction, we show that the valley polarization and transmission can be improved by increasing the width of the strained region and increasing (decreasing) the extensional strain in the armchair (zigzag) direction. It is noted that the shear strain does not affect transmission and valley polarization. Furthermore, when we consider the smooth strain barrier, the valley-polarized transmission can be enhanced by increasing the smoothness of the strain barrier. We hope that our finding can shed new light on constructing graphene-based valleytronic and quantum computing devices by solely employing strain.

Eddy Current Measurement of Chemiresistive Sensing Transients in Graphene-hBN Heterostructures

The development of graphene-based electronic and gas sensing devices has motivated considerable research interest in the properties of graphene-hBN heterostructures. Eddy current measurements of the sheet conductance of graphene-hBN heterostructures show a relatively low conductance, as compared to results previously reported in the literature, all of which were obtained using contact-based measurement methods. Chemiresistive measurements of the graphene-hBN heterostructure response to oxygen adsorption, including hysteric effects under transient multicycle loading, show that the incremental sheet conductance responses of graphene and graphene-hBN sensors differ in sign. A transient, nonlinear, history dependent constitutive model of graphene-hBN response to oxygen adsorption distinguishes stochastic variations in material properties from deterministic variations in sensor performance. The deterministic variations are due to sensing process hysteresis, a phenomenon of central interest in the development of graphene-based sensor systems.

Magnon Landau Levels and Emergent Supersymmetry in Strained Antiferromagnets

Inhomogeneous strain applied to lattice systems can induce artificial gauge fields for particles moving on this lattice. Here we demonstrate how to engineer a novel state of matter, namely an antiferromagnet with a Landau-level excitation spectrum of magnons. We consider a honeycomb-lattice Heisenberg model and show that triaxial strain leads to equally spaced pseudo-Landau levels at the upper end of the magnon spectrum, with degeneracies characteristic of emergent supersymmetry. We also present a particular strain protocol which induces perfectly quantized magnon Landau levels over the whole bandwidth. We discuss experimental realizations and generalizations.

Bandgap and pseudohelicity effects over conductance in gapped graphene junctures

We study the conductance in gapped single-layer graphene junctures as a function of bangap, pseudohelicity and charge carriers density. To do it, we first calculate the transmission coefficients of massive charge carries for p-n and n-p-n junctures of gapped single-layer graphene. Next, we calculate the conductance for these two systems using the Landauer formula. Only for the p-n juncture case and non-zero bandgap values, we find the existence of a contribution to the conductance from pseudohelicity inversion states, which is small compared to the contribution from pseudohelicity conservation states. Also, we find for both type of junctures that there exists a window of charge carriers densities values where the conductance is zero (conductance gap), in such a way that the size of this window depends on the squared of the bandgap. We observe that the existence of a bandgap in the system leads to valley mixing and this fact could be useful for the future design of devices based on single-layer graphene.

Interfacial engineering in graphene bandgap

Graphene exhibits superior mechanical strength, high thermal conductivity, strong light-matter interactions, and, in particular, exceptional electronic properties. These merits make graphene an outstanding material for numerous potential applications. However, a graphene-based high-performance transistor, which is the most appealing application, has not yet been produced, which is mainly due to the absence of an intrinsic electronic bandgap in this material. Therefore, bandgap opening in graphene is urgently needed, and great efforts have been made regarding this topic over the past decade. In this review article, we summarise recent theoretical and experimental advances in interfacial engineering to achieve bandgap opening. These developments are divided into two categories: chemical engineering and physical engineering. Chemical engineering is usually destructive to the pristine graphene lattice via chemical functionalization, the introduction of defects, doping, chemical bonds with substrates, and quantum confinement; the latter largely maintains the atomic structure of graphene intact and includes the application of an external field, interactions with substrates, physical adsorption, strain, electron many-body effects and spin-orbit coupling. Although these pioneering works have not met all the requirements for electronic applications of graphene at once, they hold great promise in this direction and may eventually lead to future applications of graphene in semiconductor electronics and beyond.

Strain-Induced Landau Levels in Arbitrary Dimensions with an Exact Spectrum

Certain nonuniform strain applied to graphene flakes has been shown to induce pseudo-Landau levels in the single-particle spectrum, which can be rationalized in terms of a pseudomagnetic field for electrons near the Dirac points. However, this Landau level structure is, in general, approximate and restricted to low energies. Here, we introduce a family of strained bipartite tight-binding models in arbitrary spatial dimension d and analytically prove that their entire spectrum consists of perfectly degenerate pseudo-Landau levels. This construction generalizes the case of triaxial strain on graphene's honeycomb lattice to arbitrary d; in d=3, our model corresponds to tetraxial strain on the diamond lattice. We discuss general aspects of pseudo-Landau levels in arbitrary d.

Strain-induced effects in the electronic and spin properties of a monolayer of ferromagnetic GdAg2

We report on the structural, electronic and magnetic properties of a monolayer of GdAg₂, forming a moiré pattern on Ag(111). Combining scanning tunneling microscopy and ab initio spin-polarized calculations, we show that the electronic band structure can be shifted linearly via thermal controlled strain of the intra-layer atomic distance in the range of 1-7%, leading to lateral hetero-structuring. Furthermore, the coupling of the incommensurable GdAg₂ alloy layer to the Ag(111) substrate leads to spatially varying atomic relaxation causing subsurface layer buckling, texturing of the electronic and spin properties, and inhomogeneity of the magnetic anisotropy energy across the layer. These results provide perspectives for control of electronic properties and magnetic ordering in atomically-thin layers.

Field Emission of Wet Transferred Suspended Graphene Fabricated on Interdigitated Electrodes

Suspended graphene (SG) membranes could enable strain-engineering of ballistic Dirac fermion transport and eliminate the extrinsic bulk disorder by annealing. When freely suspended without contact to any substrates, graphene could be considered as the ultimate two-dimensional (2D) morphology, leading to special field characteristics with the 2D geometrical effect and effectively utilized as an outstanding structure to explore the fundamental electronic or optoelectronic mechanism. In this paper, we report field emission characterization on an individual suspended few-layer graphene. A controllable wet transfer method is used to obtain the continuous and suspended graphene membrane on interdigitated gold electrodes. This suspended structure displays an overall field emission from the entirely surface, except for the variation in the emitting positions, acquiring a better enhancement than the exfoliated graphene on the conventional flat substrate. We also observe the transition process from space charge flow at low bias to the Fowler-Nordheim theory at high current emission regime. It could enable theoretical and experimental investigation of the typical electron emission properties of the 2D regime. Numerical simulations are also carried out to study the electrical properties of the suspended structure. Further improvement on the fabrication would realize low disorder, high quality, and large-scale suspended graphene devices.

Suspended graphene devices with local gate control on an insulating substrate

We present a fabrication process for graphene-based devices where a graphene monolayer is suspended above a local metallic gate placed in a trench. As an example we detail the fabrication steps of a graphene field-effect transistor. The devices are built on a bare high-resistivity silicon substrate. At temperatures of 77 K and below, we observe the field-effect modulation of the graphene resistivity by a voltage applied to the gate. This fabrication approach enables new experiments involving graphene-based superconducting qubits and nano-electromechanical resonators. The method is applicable to other two-dimensional materials.

Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

Tailoring 10 nm scale suspended graphene junctions and quantum dots

The possibility to make 10 nm scale, and low-disorder, suspended graphene devices would open up many possibilities to study and make use of strongly coupled quantum electronics, quantum mechanics, and optics. We present a versatile method, based on the electromigration of gold-on-graphene bow-tie bridges, to fabricate low-disorder suspended graphene junctions and quantum dots with lengths ranging from 6 nm up to 55 nm. We control the length of the junctions, and shape of their gold contacts by adjusting the power at which the electromigration process is allowed to avalanche. Using carefully engineered gold contacts and a nonuniform downward electrostatic force, we can controllably tear the width of suspended graphene channels from over 100 nm down to 27 nm. We demonstrate that this lateral confinement creates high-quality suspended quantum dots. This fabrication method could be extended to other two-dimensional materials.

Strain-induced pseudomagnetic fields in twisted graphene nanoribbons

We present, for the first time, an atomic-level and quantitative study of a strain-induced pseudomagnetic field in graphene nanoribbons with widths of hundreds of nanometers. We show that twisting strongly affects the band structures of graphene nanoribbons with arbitrary chirality and generates well-defined pseudo-Landau levels, which mimics the quantization of massive Dirac fermions in a magnetic field up to 160 T. Electrons are localized either at ribbon edges forming the edge current or at the ribbon center forming the snake orbit current, both being valley polarized. Our result paves the way for the design of new graphene-based nanoelectronics.

Topological Defects in Topological Insulators and Bound States at Topological Superconductor Vortices

The scattering of Dirac electrons by topological defects could be one of the most relevant sources of resistance in graphene and at the boundary surfaces of a three-dimensional topological insulator (3D TI). In the long wavelength, continuous limit of the Dirac equation, the topological defect can be described as a distortion of the metric in curved space, which can be accounted for by a rotation of the Gamma matrices and by a spin connection inherited with the curvature. These features modify the scattering properties of the carriers. We discuss the self-energy of defect formation with this approach and the electron cross-section for intra-valley scattering at an edge dislocation in graphene, including corrections coming from the local stress. The cross-section contribution to the resistivity, ρ, is derived within the Boltzmann theory of transport. On the same lines, we discuss the scattering of a screw dislocation in a two-band 3D TI, like Bi_1-xSb_x, and we present the analytical simplified form of the wavefunction for gapless helical states bound at the defect. When a 3D TI is sandwiched between two even-parity superconductors, Dirac boundary states acquire superconductive correlations by proximity. In the presence of a magnetic vortex piercing the heterostructure, two Majorana states are localized at the two interfaces and bound to the vortex core. They have a half integer total angular momentum each, to match with the unitary orbital angular momentum of the vortex charge.

Transport signatures of pseudomagnetic Landau levels in strained graphene ribbons

In inhomogeneously strained graphene, low-energy electrons experience a valley-antisymmetric pseudomagnetic field which leads to the formation of localized states at the edge between the valence and conduction bands, understood in terms of peculiar n=0 pseudomagnetic Landau levels. Here we show that such states can manifest themselves as an isolated quadruplet of low-energy conductance resonances in a suspended stretched graphene ribbon, where clamping by the metallic contacts results in a strong inhomogeneity of strain near the ribbon ends.

Poly(methyl methacrylate)/graphene oxide layered films as generators for mechanical energy harvesting

In this work we introduce a simple practical way to transfer large flakes of partially reduced graphene oxide (rGO) as well as poly(methyl methacrylate)/rGO films onto arbitrary substrates where the electrode geometry is defined before the film deposition to fabricate devices. It was reported how such films when stimulated by an ultrasound transducer convert mechanical energy to electricity. The possibility to utilize polymer nanocomposites as nanogenerators is of current interest to enhance mechanical energy harvesting and to add new functionalities to polymer nanocomposites.

Manipulation of graphene's dynamic ripples by local harmonic out-of-plane excitation

With use of carefully designed molecular dynamics simulations, we demonstrate tuning of dynamic ripples in free standing, thermally fluctuating graphene by applying a local out-of-plane sinusoidal excitation. The local dynamic morphology can be controlled via varying external modulation and the boundary conditions. We fully account for the discrete atomistic structure of graphene, as well as natural energy dissipation due in part to its remarkably high thermal conductivity. In addition to stable dynamic rippling patterns, we observed an unexpected flattening of graphene well below the thermal limit. Our results provide insight into the dynamic response of atomically thin layers to an external time-varying excitation in the presence of realistic thermal fluctuations and energy loss. This suggests intriguing possibilities for modulating the electrical and optical properties of atomically thin membranes via local dynamic morphology control.

Observation of Landau levels in potassium-intercalated graphite under a zero magnetic field

The charge carriers in graphene are massless Dirac fermions and exhibit a relativistic Landau-level quantization in a magnetic field. Recently, it has been reported that, without any external magnetic field, quantized energy levels have been also observed from strained graphene nanobubbles on a platinum surface, which were attributed to the Landau levels of massless Dirac fermions in graphene formed by a strain-induced pseudomagnetic field. Here we show the generation of the Landau levels of massless Dirac fermions on a partially potassium-intercalated graphite surface without applying external magnetic field. Landau levels of massless Dirac fermions indicate the graphene character in partially potassium-intercalated graphite. The generation of the Landau levels is ascribed to a vector potential induced by the perturbation of nearest-neighbour hopping, which may originate from a strain or a gradient of on-site potentials at the perimeters of potassium-free domains.

A signature of the Dirac-like physics of charge carriers in graphene is the occurrence of an anomalous Hall effect, resulting in a quantization of the Landau levels. Guo et al. observe Landau levels of Dirac fermions in potassium-intercalated graphite arising in the absence of an applied magnetic field.

Generation of pure bulk valley current in graphene

The generation of valley current is a fundamental goal in graphene valleytronics but no practical ways of its realization are known yet. We propose a workable scheme for the generation of bulk valley current in a graphene mechanical resonator through adiabatic cyclic deformations of the strains and a chemical potential in the suspended region. The accompanied strain gauge fields can break the spatial mirror symmetry of the problem within each of the two inequivalent valleys, leading to a finite valley current due to quantum pumping. An all-electrical measurement configuration is designed to detect the novel state with pure bulk valley currents.

Strain-induced suppression of weak localization in CVD-grown graphene

We investigate the magnetic-field- and temperature-dependent transport properties of CVD-grown graphene transferred to a flexible substrate (Kapton) and subjected to externally applied strain. In zero magnetic field, a logarithmic temperature-dependent conductivity correction, resulting from strong electron-electron interaction, becomes weaker with the application of strains as large as 0.6% because of an increased rate of chiral-symmetry-breaking scattering. With the application of a perpendicular magnetic field, we also observe positive magnetoconductance at low temperature (T = 5 K) due to weak localization. This magnetoconductance is suppressed with increasing strain, concomitant with a rapid decrease of the intervalley scattering rate (τ(i)(-1)). Our results are in good agreement with theoretical expectations and are consistent with a strain-induced decoupling between graphene and its underlying Kapton substrate.

In situ observation of electrostatic and thermal manipulation of suspended graphene membranes

Graphene is nature's thinnest elastic membrane, and its morphology has important impacts on its electrical, mechanical, and electromechanical properties. Here we report manipulation of the morphology of suspended graphene via electrostatic and thermal control. By measuring the out-of-plane deflection as a function of applied gate voltage and number of layers, we show that graphene adopts a parabolic profile at large gate voltages with inhomogeneous distribution of charge density and strain. Unclamped graphene sheets slide into the trench under tension; for doubly clamped devices, the results are well-accounted for by membrane deflection with effective Young's modulus E = 1.1 TPa. Upon cooling to 100 K, we observe buckling-induced ripples in the central portion and large upward buckling of the free edges, which arises from graphene's large negative thermal expansion coefficient.

Deformation and scattering in graphene over substrate steps

The electrical properties of graphene depend sensitively on the substrate. For example, recent measurements of epitaxial graphene on SiC show resistance arising from steps on the substrate. Here we calculate the deformation of graphene at substrate steps, and the resulting electrical resistance, over a wide range of step heights. The elastic deformations contribute only a very small resistance at the step. However, for graphene on SiC(0001) there is strong substrate-induced doping, and this is substantially reduced on the lower side of the step where graphene pulls away from the substrate. The resulting resistance explains the experimental measurements.

Engineered piezoelectricity in graphene

We discover that piezoelectric effects can be engineered into nonpiezoelectric graphene through the selective surface adsorption of atoms. Our calculations show that doping a single sheet of graphene with atoms on one side results in the generation of piezoelectricity by breaking inversion symmetry. Despite their 2D nature, piezoelectric magnitudes are found to be comparable to those in 3D piezoelectric materials. Our results elucidate a designer piezoelectric phenomenon, unique to the nanoscale, that has potential to bring dynamical control to nanoscale electromechanical devices.

Electron pumping in graphene mechanical resonators

The combination of high-frequency vibrations and metallic transport in graphene makes it a unique material for nanoelectromechanical devices. In this Letter, we show that graphene-based nanoelectromechanical devices are extremely well suited for charge pumping due to the sensitivity of its transport coefficients to perturbations in electrostatic potential and mechanical deformations, with the potential for novel small scale devices with useful applications.

A valley-filtering switch based on strained graphene

We investigate valley-dependent transport through a graphene sheet modulated by both the substrate strain and the fringe field of two parallel ferromagnetic metal (FM) stripes. When the magnetizations of the two FM stripes are switched from the parallel to the antiparallel alignment, the total conductance, valley polarization and valley conductance excess change greatly over a wide range of Fermi energy, which results from the dependence of the valley-related transmission suppression on the polarity configuration of inhomogeneous magnetic fields. Thus the proposed structure exhibits the significant features of a valley-filtering switch and a magnetoresistance device.

Magnetoconductance oscillations and evidence for fractional quantum Hall states in suspended bilayer and trilayer graphene

We report pronounced magnetoconductance oscillations observed on suspended bilayer and trilayer graphene devices with mobilities up to 270,000 cm²/V s. For bilayer devices, we observe conductance minima at all integer filling factors ν between 0 and -8, as well as a small plateau at ν=1/3. For trilayer devices, we observe features at ν=-1, -2, -3, and -4, and at ν∼0.5 that persist to 4.5 K at B=8 T. All of these features persist for all accessible values of Vg and B, and could suggest the onset of symmetry breaking of the first few Landau levels and fractional quantum Hall states.

Scaling and interaction-assisted transport in graphene with one-dimensional defects

We analyze the scattering from one-dimensional defects in intrinsic graphene. The Coulomb repulsion between electrons is found to be able to induce singularities of such scattering at zero temperature as in one-dimensional conductors. In striking contrast to electrons in one space dimension, however, repulsive interactions here can enhance transport. We present explicit calculations for the scattering from vector potentials that appear when strips of the material are under strain. There the predicted effects are exponentially large for strong scatterers.

Probing strain-induced electronic structure change in graphene by Raman spectroscopy

Two-phonon Raman scattering in graphitic materials provides a distinctive approach to probing the material's electronic structure through the spectroscopy of phonons. Here we report studies of Raman scattering of the two-dimensional mode of single-layer graphene under uniaxial stress and which implicates two types of modification of the low-energy electronic structure of graphene: a deformation of the Dirac cone and its displacement away from the K point.

Controlling energy gap of bilayer graphene by strain

Using the first principles calculations, we show that mechanically tunable electronic energy gap is realizable in bilayer graphene if different homogeneous strains are applied to the two layers. It is shown that the size of the energy gap can be simply controlled by adjusting the strength and direction of these strains. We also show that the effect originates from the occurrence of strain-induced pseudoscalar potentials in graphene. When homogeneous strains with different strengths are applied to each layer of bilayer graphene, transverse electric fields across the two layers can be generated without any external electronic sources, thereby opening an energy gap. The results demonstrate a simple mechanical method of realizing pseudoelectromagnetism in graphene and suggest a maneuverable approach to fabrication of electromechanical devices based on bilayer graphene.

Strain-induced pseudomagnetic field for novel graphene electronics

Particular strain geometry in graphene could lead to a uniform pseudomagnetic field of order 10T and might open up interesting applications in graphene nanoelectronics. Through quantum transport calculations of realistic strained graphene flakes of sizes of 100 nm, we examine possible means of exploiting this effect for practical electronics and valleytronics devices. First, we found that elastic backscattering at rough edges leads to the formation of well-defined transport gaps of order 100 meV under moderate maximum strain of 10%. Second, the application of a real magnetic field induced a separation, in space and energy, of the states arising from different valleys, leading to a way of inducing bulk valley polarization which is insensitive to short-range scattering.

Tuning the conductance of dirac fermions on the surface of a topological insulator

We study the transport properties of the Dirac fermions with a Fermi velocity v{F} on the surface of a topological insulator across a ferromagnetic strip providing an exchange field J over a region of width d. We show that the conductance of such a junction, in the clean limit and at low temperature, changes from oscillatory to a monotonically decreasing function of d beyond a critical J. This leads to the possible realization of a magnetic switch using these junctions. We also study the conductance of these Dirac fermions across a potential barrier of width d and potential V0 in the presence of such a ferromagnetic strip and show that beyond a critical J, the criteria of conductance maxima changes from chi=eV{0}d/variant Planck's over v{F}=npi to chi=(n+1/2)pi for integer n. We point out that these novel phenomena have no analogs in graphene and suggest experiments which can probe them.

Strain engineering of graphene's electronic structure

We explore the influence of local strain on the electronic structure of graphene. We show that strain can be easily tailored to generate electron beam collimation, 1D channels, surface states, and confinement. These can be seen as basic elements for all-graphene electronics which, by suitable engineering of local strain profiles, could be integrated on a single graphene sheet. In addition this proposal has the advantage that patterning can be made on substrates rather than on graphene, thereby protecting the integrity of the latter.