Strain-engineered Graphene Research Articles

Time-dependent spin and charge transport in a strain-engineered graphene sheet coupled to a single-molecular magnet

Abstract Recent confirmation shows that graphene is the toughest substance on record and can withstand elastic and reversible deformations exceeding 20%. In this article, we focus on the effect of homogeneous axial tension on graphene-based junctions, where a molecular magnet is coupled to a graphene sheet connected to ferromagnetic leads. We demonstrate that a homogeneous longitudinal strain enhances the oscillatory variations in the spin and charge currents at the time, gate, and bias voltages. In particular, we demonstrate that applying strain makes it possible to control the switching time between the minimum and maximum spin and charge currents. These results can be employed in spintronic devices based on graphene to enhance the control of the device features.

High-harmonic generation from strain-engineered graphene for polarization tailoring

High-harmonic generation from strain-engineered graphene for polarization tailoring

Electrical manipulation of lightwaves in the uniaxially strained photonic honeycomb lattices under a pseudomagnetic field

The realization of pseudomagnetic fields for lightwaves has attained great attention in the field of nanophotonics. Like real magnetic fields, Landau quantization could be induced by pseudomagnetic fields in the strain-engineered graphene. We demonstrated that pseudomagnetic fields can also be introduced to photonic crystals by exerting a linear parabolic deformation onto the honeycomb lattices, giving rise to degenerate energy states and flat plateaus in the photonic band structures. We successfully inspire the photonic snake modes corresponding to the helical state in the synthetic magnetic heterostructure by adopting a microdisk for the unidirectional coupling. By integrating heat electrodes, we can further electrically manipulate the photonic density of states for the uniaxially strained photonic crystal. This offers an unprecedented opportunity to obtain on-chip robust optical transports under the electrical tunable pseudomagnetic fields, opening the possibility to design Si-based functional topological photonic devices.

A strain-engineered graphene qubit in a nanobubble

We propose a controllable qubit in a graphene nanobubble (NB) with emergent two-level systems (TLSs) induced by pseudo-magnetic fields (PMFs). We found that double quantum dots can be created by the strain-induced PMFs of a NB, and also that their quantum states can be manipulated by either local gate potentials or the PMFs. Graphene qubits clearly exhibit avoided crossing behavior as electrical detuning, with energy splittings of about few meV. We show a remarkable tunability of our device design that allows a fine control of the Landau–Zener transition probability by strain engineering of the NB, showing half-and-half splitting at the avoided crossing point. Further, we demonstrate that the TLSs in the NB exhibit Rabi oscillations near the avoided crossing point, resulting in very fast Rabi cycles of a few ps.

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.

Frequency-tunable terahertz graphene laser enabled by pseudomagnetic fields in strain-engineered graphene.

Graphene-based optoelectronic devices have recently attracted much attention for the next-generation electronic-photonic integrated circuits. However, it remains elusive whether it is feasible to create graphene-based lasers at the chip scale, hindering the realization of such a disruptive technology. In this work, we theoretically propose that Landau-quantized graphene enabled by strain-induced pseudomagnetic field can become an excellent gain medium that supports lasing action without requiring an external magnetic field. Tight-binding theory is employed for calculating electronic states in highly strained graphene while analytical and numerical analyses based on many-particle Hamiltonian allow studying detailed microscopic mechanisms of zero-field graphene Landau level laser dynamics. Our proposed laser presents unique features including a convenient, wide-range tuning of output laser frequency enabled by changing the level of strain in graphene gain media. The chip-scale graphene laser may open new possibilities for graphene-based electronic-photonic integrated circuits.

Computational Study on Strain-Engineered Graphene Nanopores for Selective Gas Separation

Precise fine-tuning of gas transport across nanopores is highly desirable in numerous industrial applications. In this work, we perform a computational study to investigate the strain engineering o...

Quantized Transport, Strain-Induced Perfectly Conducting Modes, and Valley Filtering on Shape-Optimized Graphene Corbino Devices.

The extreme mechanical resilience of graphene and the peculiar coupling it hosts between lattice and electronic degrees of freedom have spawned a strong impetus toward strain-engineered graphene where, on the one hand, strain augments the richness of its phenomenology and makes possible new concepts for electronic devices, and on the other hand, new and extreme physics might take place. Here, we demonstrate that the shape of substrates supporting graphene sheets can be optimized for approachable experiments where strain-induced pseudomagnetic fields (PMF) can be tailored by pressure for directionally selective electronic transmission and pinching-off of current flow down to the quantum channel limit. The Corbino-type layout explored here furthermore allows filtering of charge carriers according to valley and current direction, which can be used to inject or collect valley-polarized currents, thus realizing one of the basic elements required for valleytronics. Our results are based on a framework developed to realistically determine the combination of strain, external parameters, and geometry optimally compatible with the target spatial profile of a desired physical property-the PMF in this case. Characteristic conductance profiles are analyzed through quantum transport calculations on large graphene devices having the optimal shape.

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

Scientific Reports 6: Article number: 22440; Published online: 01 March 2016; Updated: 02 June 2016 The following statement has been omitted from the ‘Additional Information’ section of the HTML version of this Article: “Data Availability: The images and spectra on which this paper is based may be publicly accessed and are stored at 10.

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.

Third-order intermodulation distortion in graphene resonant channel transistors

Third-order intermodulation distortion (IM3) is an important metric for electromechanical resonators used in radio frequency signal processing applications since it characterizes the nonlinearity of the device, and the amount of in-band interference it generates when subject to unwanted, out-of-band signals. In this letter, we measure and model IM3 in a strain-engineered graphene mechanical resonator operated as a graphene resonant channel transistor (G-RCT). The device analyzed in this work has a voltage third-order intercept point (VIIP3) of 69.5 dBm V at a gate-to-source DC bias (Vgs) of 2.5 V, which drops to 52.1 dBm V at Vgs = 4.5 V when driven with two out-of-band input tones spaced 5 and 10 MHz from the resonant frequency. The decrease in the VIIP3 with Vgs coincides with an increase in the transmission response (S21) of the device, illustrating a trade-off between transduction efficiency and linearity. In addition, we find that conventional micro-electro-mechanical systems theory for IM3 calculation does not accurately describe our measurement data. To resolve this discrepancy, we develop a model for IM3 in G-RCTs that takes into account all of the output current terms present in the embedded transistor structure, as well as an effective Duffing parameter (αeff).

Pseudomagnetic fields in graphene nanobubbles of constrained geometry: A molecular dynamics study

Analysis of the strain-induced pseudomagnetic fields generated in graphene nanobulges under three different substrate scenarios shows that, in addition to the shape, the graphene-substrate interaction can crucially determine the overall distribution and magnitude of strain and those fields, in and outside the bulge region. We utilize a combination of classical molecular dynamics, continuum mechanics, and tight-binding electronic structure calculations as an unbiased means of studying pressure-induced deformations and the resulting pseudomagnetic field distribution in graphene nanobubbles of various geometries. The geometry is defined by inflating graphene against a rigid aperture of a specified shape in the substrate. The interplay among substrate aperture geometry, lattice orientation, internal gas pressure, and substrate type is analyzed in view of the prospect of using strain-engineered graphene nanostructures capable of confining and/or guiding electrons at low energies. Except in highly anisotropic geometries, the magnitude of the pseudomagnetic field is generally significant only near the boundaries of the aperture and rapidly decays towards the center of the bubble because under gas pressure at the scales considered here there is considerable bending at the edges and the central region of the nanobubble displays nearly isotropic strain. When the deflection conditions lead to sharp bends at the edges of the bubble, curvature and the tilting of the ${p}_{z}$ orbitals cannot be ignored and contributes substantially to the total field. The strong and localized nature of the pseudomagnetic field at the boundaries and its polarity-changing profile can be exploited as a means of trapping electrons inside the bubble region or of guiding them in channellike geometries defined by nanoblister edges. However, we establish that slippage of graphene against the substrate is an important factor in determining the degree of concentration of pseudomagnetic fields in or around the bulge since it can lead to considerable softening of the strain gradients there. The nature of the substrate emerges thus as a decisive factor determining the effectiveness of nanoscale pseudomagnetic field tailoring in graphene.

Tailoring electronic properties of 2D crystals by strain engineering

One of the enticing features common to most of the two-dimensional electronic systems that, in the wake of (and in parallel with) graphene, 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 (or, at least, perturbed) electronic properties. Graphene, in particular, on account of its exceptional range of elastic deformation, complemented by an unusual electron-phonon coupling that can be captured by the concept of a fictitious or pseudo-magnetic field (PMF), has taught us that its intrinsic electronic properties can be molded by many more, and much richer, approaches that can be applied to 3D bulk solids. The ability to manipulate the local strain distribution in graphene opens the enticing prospect of strain-engineering its electronic and optical properties, as well as of enhancing interaction and correlation effects. I will describe some examples of how strain-engineered graphene can have richer spectral, transport, and optical properties, or how it allows potentially novel device functionalities and tunability. Some concepts will be discussed in parallel with a summary of selected experimental work. A general optimization framework for tailoring physical properties of 2D crystals by manipulating the state of local strain, and allowing a one-step route from their design to experimental implementation, will be presented, together with a discussion of examples of its application in the design of nanoscale transport devices.

Delay time and Hartman effect in strain engineered graphene

Tunneling times, including group delay and dwell time, are studied for massless Dirac electrons transmitting through a one-dimensional barrier in strain-engineered graphene. The Hartman effect, the independence of group delay on barrier length, is induced by the strain effect, and associated with the transmission gap and the evanescent mode. The influence of barrier height/length and strain modulus/direction on the group delay is also discussed, which provides the flexibility to control the group delay with applications in graphene-based devices. The relationship between group delay and dwell time is finally derived to clarify the nature of the Hartman effect.

Strain-engineered graphene through a nanostructured substrate. II. Pseudomagnetic fields

The strain induced pseudo-magnetic field in supported graphene deposited on top of a nanostructured substrate is investigated by using atomistic simulations. Step, elongated trench, one dimensional barrier, spherical bubbles, Gaussian bump and Gaussian depression are considered as support structures for graphene. From the obtained optimum configurations we found very strong induced pseudo-magnetic fields which can reach up to $\sim$ 1000\,T due to the strain-induced deformations in the supported graphene. Different magnetic confinements with controllable geometries are found by tuning the pattern of the substrate. The resulting induced magnetic fields for graphene on top of a step, barrier and trench are calculated. In contrast to the step and trench the middle part of graphene on top of a barrier has zero pseudo-magnetic field. This study provides a theoretical background for designing magnetic structures in graphene by nanostructuring substrates. We found that altering the radial symmetry of the deformation, changes the six-fold symmetry of the induced pseudo-magnetic field.

Strain-engineered graphene through a nanostructured substrate. I. Deformations

Using atomistic simulations we investigate the morphological properties of graphene deposited on top of a nanostructured substrate. Sinusoidally corrugated surfaces, steps, elongated trenches, one dimensional and cubic barriers, spherical bubbles, Gaussian bump and Gaussian depression are considered as support structures for graphene. The graphene-substrate interaction is governed by van der Waals forces and the profile of the graphene layer is determined by minimizing the energy using molecular dynamics simulations. Based on the obtained optimum configurations, we found that: (i) for graphene placed over sinusoidally corrugated substrates with corrugation wave lengths longer than 2\,nm, the graphene sheet follows the substrate pattern while for supported graphene it is always suspended across the peaks of the substrate, (ii) the conformation of graphene to the substrate topography is enhanced when increasing the energy parameter in the van der Waals model, (iii) the adhesion of graphene into the trenches depends on the width of the trench and on graphene's orientation, i.e. in contrast to a small width (3 nm) nanoribbon with armchair edges, the one with zig-zag edges follows the substrate profile, (iv) atomic scale graphene follows a Gaussian bump substrate but not the substrate with a Gaussian depression, and (v) the adhesion energy due to van der Waals interaction varies in the range [0.1-0.4] J/m^2.

Strain-induced switching of magnetoresistance and perfect spin-valley filtering in graphene

We study spin-dependent valley currents and magnetoresistance (TMR) in double magnetic layer graphene-based N/ F 1/St/ F 2/ N junction where N, F 1,2 and St are normal, ferromagnetic and strain-engineered graphene, respectively. Local strain in the St region causes a pseudo-vector potential with the same magnitude for the K- and K′-valleys but different sign, leading to valley polarization when applying real vector potential into the junction. The F layers cause the Zeeman field for controlling spin current and can be orientated either parallel ( P) or anti parallel ( AP). As an effect of the interplay of the Zeeman field and the strain field, the current in the junction is split into four current groups, I k↑ , I k↓ , I k′↑ and I k′↓ , called spin-valley currents. We find that, the interplay of the Zeeman and strain field causes a perfect spin-valley filtering in the angular space only for the P configuration. Large TMR and switching of TMR triggered by a very small strain are also predicted. Our work reveals the potential of the interplay of the Zeeman and the strain field for application of spin-valley-based nanoelectronics and the switching effect induced by a very small strain should be applicable for strain sensor device.

Control of Spin-Valley Current in Strain-Engineered Graphene Magnetic Junction

We investigate the spin-valley current in a strain-engineered graphene magnetic system, normal region (N)/strain region(S)/ferromagnetic region (F)/normal region (N) junction. Locally strained region S leads to valley-dependent current, and ferromagnetic region F leads to the spin-dependent current. We find that pure valley current can be created easily by applying the real-vector potential that is equal to the pseudo-vector potential caused by strains in the S-region. In this work, we focus on the spin current in each valley when exchange field is applied in the F-region, and find that the linear control of spin-valley polarization by gate potential is possible. It is also found that when the current is carried only by the carriers in one valley (pure valley current), pure spin-up current can be linearly altered to pure spin-down current by tuning the gate potential, in the case of very large-F-thickness junction. Our work is applicable for devising controllable spin-valley-current electronics circuits.

Dirac-Kronig-Penney model for strain-engineered graphene

Motivated by recent proposals on strain-engineering of graphene electronic circuits we calculate conductivity, shot-noise and the density of states in periodically deformed graphene. We provide the solution to the Dirac-Kronig-Penney model, which describes the phase-coherent transport in clean monolayer samples with an one-dimensional modulation of the strain and the electrostatic potentials. We compare the exact results to a qualitative band-structure analysis. We find that periodic strains induce large pseudo-gaps and suppress charge transport in the direction of strain modulation. The strain-induced minima in the gate-voltage dependence of the conductivity characterize the quality of graphene superstructures. The effect is especially strong if the variation of inter-atomic distance exceeds the value a^2/l, where a is the lattice spacing of free graphene and l is the period of the superlattice. A similar effect induced by a periodic electrostatic potential is weakened due to Klein tunnelling.