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.

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

Graphene-analogous low-dimensional materials

The chemical stability of graphene and other free-standing two-dimensional crystals means that they can be stacked in different combinations to produce a new class of functional materials, designed for specific device applications. Here we report resonant tunnelling of Dirac fermions through a boron nitride barrier, a few atomic layers thick, sandwiched between two graphene electrodes. The resonance occurs when the electronic spectra of the two electrodes are aligned. The resulting negative differential conductance in the device characteristics persists up to room temperature and is gate voltage-tuneable due to graphene’s unique Dirac-like spectrum. Although conventional resonant tunnelling devices comprising a quantum well sandwiched between two tunnel barriers are tens of nanometres thick, the tunnelling carriers in our devices cross only a few atomic layers, offering the prospect of ultra-fast transit times. This feature, combined with the multi-valued form of the device characteristics, has potential for applications in high-frequency and logic devices.

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Resonant tunnelling and negative differential conductance in graphene transistors

We report a new solution deposition method to synthesize an unprecedented type of two-dimensional ordered mesoporous carbon nanosheets via a controlled low-concentration monomicelle close-packing assembly approach. These obtained carbon nanosheets possess only one layer of ordered mesopores on the surface of a substrate, typically the inner walls of anodic aluminum oxide pore channels, and can be further converted into mesoporous graphene nanosheets by carbonization. The atomically flat graphene layers with mesopores provide high surface area for lithium ion adsorption and intercalation, while the ordered mesopores perpendicular to the graphene layer enable efficient ion transport as well as volume expansion flexibility, thus representing a unique orthogonal architecture for excellent lithium ion storage capacity and cycling performance. Lithium ion battery anodes made of the mesoporous graphene nanosheets have exhibited an excellent reversible capacity of 1040 mAh/g at 100 mA/g, and they can retain at 833 mAh/g even after numerous cycles at varied current densities. Even at a large current density of 5 A/g, the reversible capacity is retained around 255 mAh/g, larger than for most other porous carbon-based anodes previously reported, suggesting a remarkably promising candidate for energy storage.

Two-dimensional mesoporous carbon nanosheets and their derived graphene nanosheets: synthesis and efficient lithium ion storage.

Properties of phonons-quanta of the crystal lattice vibrations-in graphene have recently attracted significant attention from the physics and engineering communities. Acoustic phonons are the main heat carriers in graphene near room temperature, while optical phonons are used for counting the number of atomic planes in Raman experiments with few-layer graphene. It was shown both theoretically and experimentally that transport properties of phonons, i.e. energy dispersion and scattering rates, are substantially different in a quasi-two-dimensional system such as graphene compared to the basal planes in graphite or three-dimensional bulk crystals. The unique nature of two-dimensional phonon transport translates into unusual heat conduction in graphene and related materials. In this review, we outline different theoretical approaches developed for phonon transport in graphene, discuss contributions of the in-plane and cross-plane phonon modes, and provide comparison with available experimental thermal conductivity data. Particular attention is given to analysis of recent results for the phonon thermal conductivity of single-layer graphene and few-layer graphene, and the effects of the strain, defects, and isotopes on phonon transport in these systems.

https://iopscience.iop.org/article/10.1088/0953-8984/24/23/233203/pdf

Two-dimensional phonon transport in graphene

Strongly enhanced thermoelectric properties are predicted for graphene nanoribbons (GNRs) with optimized pattern By means of nonequilibrium Green's function atomistic simulation of electron and phonon transport, we analyze the thermal and electrical properties of perfect GNRs as a function of their width and their edge orientation to identify a strategy likely to degrade the thermal conductance while retaining high electronic conductance and thermopower An effect of resonant tunneling of electrons is detected in mixed GNRs consisting of alternate zigzag and armchair sections To fully benefit from this effect and from strongly reduced phonon thermal conductance, a structure with armchair and zigzag sections of different widths is proposed It is shown to provide a high thermoelectric factor of merit $\mathit{ZT}$ exceeding unity at room temperature

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Enhanced thermoelectric properties in graphene nanoribbons by resonant tunneling of electrons

In this letter, we propose the resonant tunneling diode (RTD) based on a double-barrier graphene/boron nitride (BN) heterostructure as device suitable to take advantage of the elaboration of atomic sheets containing different domains of BN and C phases within a hexagonal lattice. The device operation and performance are investigated by means of a self- consistent model within the non-equilibrium Green's function formalism on a tight-binding Hamiltonian. This RTD exhibits a negative differential conductance effect which involves the resonant tunneling through both the electron and hole bound states of the graphene quantum well. It is shown that the peak- to-valley ratio can reach the value of 4 at room temperature for gapless graphene and the value of 13 for a bandgap of 50 meV.

Resonant tunneling diode based on graphene/h-BN heterostructure

In this work, we propose a resonant tunnelling diode (RTD) based on a double-barrier graphene/boron nitride (BN) heterostructure as a device suitable to take advantage of the elaboration of atomic sheets containing different domains of BN and C phases within a hexagonal lattice. The device operation and performance are investigated by means of a self-consistent solution within the non-equilibrium Green's function formalism on a tight-binding Hamiltonian. This RTD exhibits a negative differential conductance effect, which involves the resonant tunnelling through both the electron and hole bound states in the graphene quantum well. It is shown that the peak-to-valley ratio reaches a value of ?4 at room temperature even for zero bandgap and can be higher than 10 when a finite gap opens in the graphene channel.

https://iopscience.iop.org/article/10.1088/0022-3727/45/32/325104/pdf

Resonant tunnelling diodes based on graphene/h-BN heterostructure

Using atomistic quantum simulation based on a tight binding model, we have investigated the transport characteristics of graphene nanomesh-based devices and evaluated the possibilities of observing negative differential conductance. It is shown that by taking advantage of bandgap opening in the graphene nanomesh lattice, a strong negative differential conductance effect can be achieved at room temperature in pn junctions and n-doped structures. Remarkably, the effect is improved very significantly (with a peak-to-valley current ratio of a few hundred) and appears to be weakly sensitive to the transition length in graphene nanomesh pn hetero-junctions when inserting a pristine (gapless) graphene section in the transition region between n and p zones. The study therefore suggests new design strategies for graphene electronic devices which may offer strong advantages in terms of performance and processing over the devices studied previously.

https://iopscience.iop.org/article/10.1088/0957-4484/23/6/065201/pdf

Graphene nanomesh-based devices exhibiting a strong negative differential conductance effect.

The thermoelectric properties of defected graphene nanoribbons (GNRs) and multi-junction (MJ) GNRs coupling periodic armchair sections of different width are analyzed by means of Green's function techniques to simulate electron and phonon transport. Among the different strategies likely to enhance the thermoelectric performance, the effects of edge disorder and random vacancies are shown to be small since they lead to the concomitant degradation of the phonon thermal conductance and of the electronic conductance, which finally reduces the thermoelectric factor ZT. However, the periodic distribution of vacancies and the structuring of GNRs in MJ-GNRs both lead to the enhancement of the figure of merit ZT. In the latter case, in addition to the strong reduction of the phonon thermal conductance, an effect of resonant tunneling of electrons allows retaining high electronic conductance and enhancing significantly the thermopower. Finally, by introducing a periodic distribution of vacancies in the MJ-GNR, the maximum value ZT=0.4 is reached at room temperature.

Fulvio Mazzamuto

Papers

Enhanced thermoelectric properties in graphene nanoribbons by resonant tunneling of electrons

Resonant tunneling diode based on graphene/h-BN heterostructure

Resonant tunnelling diodes based on graphene/h-BN heterostructure

Graphene nanomesh-based devices exhibiting a strong negative differential conductance effect.

Thermoelectric performance of disordered and nanostructured graphene ribbons using Green's function method