Intervalley scattering, long-range disorder, and effective time-reversal symmetry breaking in graphene

Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update

This is an update of a previous review (Naumiset al2017Rep. Prog. Phys.80096501). Experimental and theoretical advances for straining graphene and other metallic, insulating, ferroelectric, ferroelastic, ferromagnetic and multiferroic 2D materials were considered. We surveyed (i) methods to induce valley and sublattice polarisation (P) in graphene, (ii) time-dependent strain and its impact on graphene's electronic properties, (iii) the role of local and global strain on superconductivity and other highly correlated and/or topological phases of graphene, (iv) inducing polarisationPon hexagonal boron nitride monolayers via strain, (v) modifying the optoelectronic properties of transition metal dichalcogenide monolayers through strain, (vi) ferroic 2D materials with intrinsic elastic (σ), electric (P) and magnetic (M) polarisation under strain, as well as incipient 2D multiferroics and (vii) moiré bilayers exhibiting flat electronic bands and exotic quantum phase diagrams, and other bilayer or few-layer systems exhibiting ferroic orders tunable by rotations and shear strain. The update features the experimental realisations of a tunable two-dimensional Quantum Spin Hall effect in germanene, of elemental 2D ferroelectric bismuth, and 2D multiferroic NiI2. The document was structured for a discussion of effects taking place in monolayers first, followed by discussions concerning bilayers and few-layers, and it represents an up-to-date overview of exciting and newest developments on the fast-paced field of 2D materials.

Optical valley separation in two-dimensional semimetals with tilted Dirac cones

Quasiparticles emerging in crystalline materials can possess a binary flavor known as the valley quantum number which can be used as a basis to encode information in an emerging class of valleytronic devices. Here we show that two-dimensional semimetals with tilted Dirac cones in the electronic band structure exhibit spatial separation of carriers belonging to different valleys under illumination. In stark contrast to gapped Dirac materials this optovalleytronic phenomenon occurs in systems with intact inversion and time-reversal symmetry that host gapless Dirac cones in the band structure, thereby retaining the exceptional graphene-like transport properties. We thus demonstrate that optical valley separation is possible at arbitrarily low photon frequencies including the deep infrared and terahertz regimes with full gate tunability via Pauli blocking. As a specific example of our theory, we predict tunable valley separation in the proposed two-dimensional tilted Dirac cone semimetal 8-Pmmn borophene for incident infrared photons at room temperature. This work highlights the potential of two-dimensional tilted Dirac cone materials as a platform for tunable broadband optovalleytronic applications.

Ballistic transport spectroscopy of spin-orbit-coupled bands in monolayer graphene on WSe2

Van der Waals interactions with transition metal dichalcogenides were shown to induce strong spin-orbit coupling (SOC) in graphene, offering great promises to combine large experimental flexibility of graphene with unique tuning capabilities of the SOC. Here, we probe SOC-driven band splitting and electron dynamics in graphene on WSe2 by measuring ballistic transverse magnetic focusing. We found a clear splitting in the first focusing peak whose evolution in charge density and magnetic field is well reproduced by calculations using the SOC strength of ~ 13 meV, and no splitting in the second peak that indicates stronger Rashba SOC. Possible suppression of electron-electron scatterings was found in temperature dependence measurement. Further, we found that Shubnikov-de Haas oscillations exhibit a weaker band splitting, suggesting that it probes different electron dynamics, calling for a new theory. Our study demonstrates an interesting possibility to exploit ballistic electron motion pronounced in graphene for emerging spin-orbitronics.

Topological quantum devices: a review

The introduction of the concept of topology into condensed matter physics has greatly deepened our fundamental understanding of transport properties of electrons as well as all other forms of quasi particles in solid materials. It has also fostered a paradigm shift from conventional electronic/optoelectronic devices to novel quantum devices based on topology-enabled quantum device functionalities that transfer energy and information with unprecedented precision, robustness, and efficiency. In this article, the recent research progress in topological quantum devices is reviewed. We first outline the topological spintronic devices underlined by the spin-momentum locking property of topology. We then highlight the topological electronic devices based on quantized electron and dissipationless spin conductivity protected by topology. Finally, we discuss quantum optoelectronic devices with topology-redefined photoexcitation and emission. The field of topological quantum devices is only in its infancy, we envision many significant advances in the near future.

Determining spin-orbit coupling in graphene by quasiparticle interference imaging

Inducing and controlling spin-orbit coupling (SOC) in graphene is key to create topological states of matter, and for the realization of spintronic devices. Placing graphene onto a transition metal dichalcogenide is currently the most successful strategy to achieve this goal, but there is no consensus as to the nature and the magnitude of the induced SOC. Here, we show that the presence of backscattering in graphene-on-WSe₂ heterostructures can be used to probe SOC and to determine its strength quantitatively, by imaging quasiparticle interference with a scanning tunneling microscope. A detailed theoretical analysis of the Fourier transform of quasiparticle interference images reveals that the induced SOC consists of a valley-Zeeman (λ_vZ ≈ 2 meV) and a Rashba (λ_R ≈ 15 meV) term, one order of magnitude larger than what theory predicts, but in excellent agreement with earlier transport experiments. The validity of our analysis is confirmed by measurements on a 30 degree twist angle heterostructure that exhibits no backscattering, as expected from symmetry considerations. Our results demonstrate a viable strategy to determine SOC quantitatively by imaging quasiparticle interference.

Characterization and Manipulation of Intervalley Scattering Induced by an Individual Monovacancy in Graphene

Intervalley scattering involves microscopic processes that electrons are scattered by atomic-scale defects on the nanoscale. Although central to our understanding of electronic properties of materials, direct characterization and manipulation of range and strength of the intervalley scattering induced by an individual atomic defect have so far been elusive. Using scanning tunneling microscope, we visualize and control intervalley scattering from an individual monovacancy in graphene. By directly imaging the affected range of monovacancy-induced intervalley scattering, we demonstrate that it is inversely proportional to the energy; i.e., it is proportional to the wavelength of massless Dirac fermions. A giant electron-hole asymmetry of the intervalley scattering is observed because the monovacancy is charged. By further charging the monovacancy, the bended electronic potential around the monovacancy softens the scattering potential, which, consequently, suppresses the intervalley scattering of the monovacancy.

Resonant Scattering in Proximity-Coupled Graphene/Superconducting Mo2 C Heterostructures

The realization of high-quality heterostructures or hybrids of graphene and superconductor is crucial for exploring various novel quantum phenomena and devices engineering. Here, the electronic transport on directly grown high-quality graphene/Mo2 C vertical heterostructures with clean and sharp interface is comprehensively investigated. Owing to the strong interface coupling, the graphene layer feels an effective confinement potential well imposed by two-dimensional (2D) Mo2 C crystal. Employing cross junction device geometry, a series of resonance-like magnetoresistance peaks are observed at low temperatures. The temperature and gate voltage dependences of the observed resonance peaks give evidence for geometric resonance of electron cyclotron orbits with the formed potential well. Moreover, it is found that both the amplitude of resonance peaks and conductance fluctuation exhibit different temperature-dependent behaviors below the superconducting transition temperature of 2D Mo2 C, indicating the correlation of quantum fluctuations and superconductivity. This study offers a promising route toward integrating graphene with 2D superconducting materials, and establishes a new way to investigate the interplay of massless Dirac fermion and superconductivity based on graphene/2D superconductor vertical heterostructures.

Electronic structure evolution of the transition metals substituted tetragonal graphene: a first-principles investigations

Motivated by the possibilities of tuning the Fermi level of the metallic band structure of the planar tetragonal graphene (T-graphene), by using the transition metals (TMs) substitution (3d, 4dand 5dseries), the electronic structure investigation has been carried out at low concentration level (≈2.7%) throughab initiodensity functional theory method. We have investigated the influence of the valence electrons of the TM on the evolution of the electronic structure and magnetization and the induced magnetic moments at the carbon atoms in the T-graphene network. The investigations also explored the possibilities of inducing long-range magnetic ordering. In the case of multi TMs substitutions we found the dominance signature of the antiferromagnetic correlations for most of the TM substituted cases. The critical analysis of the magnetization densities indicated the important role of the hybridization between the carbonπandσorbitals with the TM-dstates. We explored that the observed non-monotonic nature of the magnetization and evolution of electronic structure was due to the competing energy scales of electronic correlation, hybridization and crystal field splitting. This study opens up the route for further investigations towards the possibilities of using T-graphene as a potential polymorph of graphene for device applications.

Spontaneous Valley Spirals in Magnetically Encapsulated Twisted Bilayer Graphene

Van der Waals heterostructures provide a rich platform for emergent physics due to their tunable hybridization of layers, orbitals, and spin. Here, we find that twisted bilayer graphene stacked between antialigned ferromagnetic insulators can feature flat electronic bands due to the interplay between twist, exchange proximity, and spin-orbit coupling. These flat bands are nearly degenerate in valley only and are effectively described by a triangular superlattice model. At half filling, we find that interactions induce spontaneous valley correlations that favor spiral order and derive a low-energy valley-Heisenberg model with symmetric and antisymmetric exchange couplings. We also show how electric interlayer bias broadens the bands and tunes these couplings. Our results put forward magnetic van der Waals heterostructures as a platform to explore valley-correlated states.

Negative-curvature spacetime solutions for graphene

We provide a detailed analysis of the electronic properties of graphene-like materials with charge carriers living on a curved substrate, focusing in particular on constant negative-curvature spacetime. An explicit parametrization is also worked out in the remarkable case of Beltrami geometry, with an analytic solution for the pseudoparticles modes living on the curved bidimensional surface. We will then exploit the correspondent massless Dirac description, to determine how it affects the sample local density of states.

Dirac Fermion Kinetics in 3D Curved Graphene

3D integration of graphene has attracted attention for realizing carbon-based electronic devices. While the 3D integration can amplify various excellent properties of graphene, the influence of 3D curved surfaces on the fundamental physical properties of graphene has not been clarified. The electronic properties of 3D nanoporous graphene with a curvature radius down to 25-50 nm are systematically investigated and the ambipolar electronic states of Dirac fermions are essentially preserved in the 3D graphene nanoarchitectures, while the 3D curvature can effectively suppress the slope of the linear density of states of Dirac fermion near the Fermi level are demonstrated. Importantly, the 3D curvature can be utilized to tune the back-scattering-suppressed electrical transport of Dirac fermions and enhance both electron localization and electron-electron interaction. As a result, nanoscale curvature provides a new degree of freedom to manipulate 3D graphene electrical properties, which may pave a new way to design new 3D graphene devices with preserved 2D electronic properties and novel functionalities.

Hybrid topological guiding mechanisms for photonic crystal fibers

We create hybrid topological-photonic localisation of light by introducing concepts from the field of topological matter to that of photonic crystal fiber arrays. S-polarized obliquely propagating electromagnetic waves are guided by hexagonal, and square, lattice topological systems along an array of infinitely conducting fibers. The theory utilises perfectly periodic arrays that, in frequency space, have gapped Dirac cones producing band gaps demarcated by pronounced valleys locally imbued with a nonzero local topological quantity. These broken symmetry-induced stop-bands allow for localised guidance of electromagnetic edge-waves along the crystal fiber axis. Finite element simulations, complemented by asymptotic techniques, demonstrate the effectiveness of the proposed designs for localising energy in finite arrays in a robust manner.

Weak localization in graphene sandwiched by aligned h-BN flakes

Charge carriers in graphene exhibit distinct characteristics from those in other two-dimensional materials because of their chiral nature. Additionally, multiple Dirac cones that emerge in graphene superlattices have been regarded as an interesting point in condensed-matter physics in recent years. Here, we report an investigation of the magneto-conductance in graphene encapsulated on the top and bottom by aligned h-BN. The bottom h-BN is precisely aligned with graphene, while the top h-BN is rotated a very small angle relative to it. Such a heterostructure could spoil the commensurate state existing in precisely aligned graphene while the giant moiré superlattice remains. A clear signature of weak localization and weak anti-localization is observed at multiple Dirac cones. Both the weak (anti)localization and the universal conductance fluctuations exhibit strong dependencies on the carrier density, temperature and channel length. This artificial heterostructure allows one to explore quantum interference in graphene with a wide spectrum of electronic properties.

Universal scaling of weak localization in graphene due to bias-induced dispersion decoherence

The differential conductance of graphene is shown to exhibit a zero-bias anomaly at low temperatures, arising from a suppression of the quantum corrections due to weak localization and electron interactions. A simple rescaling of these data, free of any adjustable parameters, shows that this anomaly exhibits a universal, temperature- (T) independent form. According to this, the differential conductance is approximately constant at small voltages (V < kBT/e), while at larger voltages it increases logarithmically with the applied bias. For theoretical insight into the origins of this behaviour, which is inconsistent with electron heating, we formulate a model for weak-localization in the presence of nonequilibrium transport. According to this model, the applied voltage causes unavoidable dispersion decoherence, which arises as diffusing electron partial waves, with a spread of energies defined by the value of the applied voltage, gradually decohere with one another as they diffuse through the system. The decoherence yields a universal scaling of the conductance as a function of eV/kBT, with a logarithmic variation for eV/kBT > 1, variations in accordance with the results of experiment. Our theoretical description of nonequilibrium transport in the presence of this source of decoherence exhibits strong similarities with the results of experiment, including the aforementioned rescaling of the conductance and its logarithmic variation as a function of the applied voltage.

Robust weak antilocalization due to spin-orbital entanglement in Dirac material Sr3SnO

The presence of both inversion (P) and time-reversal (T) symmetries in solids leads to a double degeneracy of the electronic bands (Kramers degeneracy). By lifting the degeneracy, spin textures manifest themselves in momentum space, as in topological insulators or in strong Rashba materials. The existence of spin textures with Kramers degeneracy, however, is difficult to observe directly. Here, we use quantum interference measurements to provide evidence for the existence of hidden entanglement between spin and momentum in the antiperovskite-type Dirac material Sr3SnO. We find robust weak antilocalization (WAL) independent of the position of EF. The observed WAL is fitted using a single interference channel at low doping, which implies that the different Dirac valleys are mixed by disorder. Notably, this mixing does not suppress WAL, suggesting contrasting interference physics compared to graphene. We identify scattering among axially spin-momentum locked states as a key process that leads to a spin-orbital entanglement.

Electric-Controlled Valley Pseudomagnetoresistance in Graphene with Y-Shaped Kekulé Lattice Distortion

We propose a new method for regulating valley pseudomagnetoresistance in ballistic graphene-based valley field-effect transistors by taking into account the Y-shaped Kekulé lattice distortion and electric barrier. The device involves valley injection and valley detection by ferromagnetic-strain source and drain. The valley manipulation in the channel is achieved via the Y-shaped Kekulé lattice distortion and electric barrier. The central mechanism of these devices lies on Y-shaped Kekulé lattice distortion in graphene can induce a valley precession, thus controlling the valley orientation of channel electrons and hence the current collected at the drain. We found that the tuning external bias voltage makes the valley pseudomagnetoresistance oscillate between positive and negative values and colossal tunneling valley pseudomagnetoresistance of over 30,000% can be achieved. Our results suggest that the synergy of valleytronics and digital logics may provide new paradigms for valleytronic-based information processing and reversible computing.

Quantum Hall Response to Time-Dependent Strain Gradients in Graphene

Mechanical deformations of graphene induce a term in the Dirac Hamiltonian that is reminiscent of an electromagnetic vector potential. Strain gradients along particular lattice directions induce local pseudomagnetic fields and substantial energy gaps as indeed observed experimentally. Expanding this analogy, we propose to complement the pseudomagnetic field by a pseudoelectric field, generated by a time-dependent oscillating stress applied to a graphene ribbon. The joint Hall-like response to these crossed fields results in a strain-induced charge current along the ribbon. We analyze in detail a particular experimental implementation in the (pseudo)quantum Hall regime with weak intervalley scattering. This allows us to predict an (approximately) quantized Hall current that is unaffected by screening due to diffusion currents.

Tunable three-way topological energy-splitter

Strategically combining four structured domains creates the first ever three-way topological energy-splitter; remarkably, this is only possible using a square, or rectangular, lattice, and not the graphene-like structures more commonly used in valleytronics. To achieve this effect, the two mirror symmetries, present within all fully-symmetric square structures, are broken; this leads to two nondistinct interfaces upon which valley-Hall states reside. These interfaces are related to each other via the time-reversal operator and it is this subtlety that allows us to ignite the third outgoing lead. The geometrical construction of our structured medium allows for the three-way splitter to be adiabatically converted into a wave steerer around sharp bends. Due to the tunability of the energies directionality by geometry, our results have far-reaching implications for applications such as beam-splitters, switches and filters across wave physics.

Programmable graphene nanobubbles with three-fold symmetric pseudo-magnetic fields

Graphene nanobubbles (GNBs) have attracted much attention due to the ability to generate large pseudo-magnetic fields unattainable by ordinary laboratory magnets. However, GNBs are always randomly produced by the reported protocols, therefore, their size and location are difficult to manipulate, which restricts their potential applications. Here, using the functional atomic force microscopy (AFM), we demonstrate the ability to form programmable GNBs. The precision of AFM facilitates the location definition of GNBs, and their size and shape are tuned by the stimulus bias of AFM tip. With tuning the tip voltage, the bubble contour can gradually transit from parabolic to Gaussian profile. Moreover, the unique three-fold symmetric pseudo-magnetic field pattern with monotonous regularity, which is only theoretically predicted previously, is directly observed in the GNB with an approximately parabolic profile. Our study may provide an opportunity to study high magnetic field regimes with the designed periodicity in two dimensional materials.

Landau Quantization of a Narrow Doubly-Folded Wrinkle in Monolayer Graphene

Folding can be an effective way to tailor the electronic properties of graphene and has attracted wide study interest in finding its novel properties. Here we present the experimental characterizations of the structural and electronic properties of a narrow graphene wrinkle on a SiO₂/Si substrate using scanning tunneling microscopy/spectroscopy. Pronounced and nearly equally separated conductance peaks are observed in the d I/d V spectra of the wrinkle. We attribute these peaks to pseudo-Landau levels (PLLs) that are caused by a gradient-strain-induced pseudomagnetic field up to about 42 T in the narrow wrinkle. The introduction of the gradient strain and thus the pseudomagnetic field can be ascribed to the lattice deformation. A doubly-folded structure of the wrinkle is suggested. Our density functional theory calculations show that the band structure of the doubly folded graphene wrinkle has a parabolic dispersion, which can well explain the equally separated PLLs. The effective mass of carriers is obtained to be about 0.02 m_e ( m_e: the rest mass of electron), and interestingly, it is revealed that there exists valley polarization in the wrinkle. Such properties of the strained doubly folded wrinkle may provide a platform to explore some exciting phenomena in graphene, like zero-field quantum valley Hall effect.

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.

Localization of Interacting Dirac Fermions

Using exact quantum Monte Carlo calculations, we examine the interplay between localization of electronic states driven by many-body correlations and that by randomness in a two-dimensional system featuring linearly vanishing density of states at the Fermi level. A novel disorder-induced nonmagnetic insulating phase is found to emerge from the zero-temperature quantum critical point separating a semimetal and a Mott insulator. Within this phase, a phase transition from a gapless Anderson-like insulator to a gapped Mott-like insulator is identified. Implications of the phase diagram are also discussed.

Substantially Enhancing Quantum Coherence of Electrons in Graphene via Electron-Plasmon Coupling

The interplays between different quasiparticles in solids lay the foundation for a wide spectrum of intriguing quantum effects, yet how the collective plasmon excitations affect the quantum transport of electrons remains largely unexplored. Here we provide the first demonstration that when the electron-plasmon coupling is introduced, the quantum coherence of electrons in graphene is substantially enhanced with the quantum coherence length almost tripled. We further develop a microscopic model to interpret the striking observations, emphasizing the vital role of the graphene plasmons in suppressing electron-electron dephasing. The novel and transformative concept of plasmon-enhanced quantum coherence sheds new insight into interquasiparticle interactions, and further extends a new dimension to exploit nontrivial quantum phenomena and devices in solid systems.

Valley filter and valve effect by strong electrostatic potentials in graphene

We report a theoretical study on the valley-filter and valley-valve effects in the monolayer graphene system by using electrostatic potentials, which are assumed to be electrically controllable. Based on a lattice model, we find that a single extremely strong electrostatic-potential barrier, with its strength exceeding the hopping energy of electrons, will significantly block one valley but allow the opposite valley flowing in the system, and this is dependent on the sign of the potential barrier as well as the flowing direction of electrons. In a valley-valve device composed of two independent potential barriers, the valley-valve efficiency can even amount to 100% that the electronic current is entirely prohibited or allowed by reversing the sign of one of potential barriers. The physics origin is attributed to the valley mixing effect in the strong potential barrier region. Our findings provide a simple electric way of controlling the valley transport in the monolayer graphene system.

Valley-filtered edge states and quantum valley Hall effect in gated bilayer graphene

Electron edge states in gated bilayer graphene in the quantum valley Hall (QVH) effect regime can carry both charge and valley currents. We show that an interlayer potential splits the zero-energy level and opens a bulk gap, yielding counter-propagating edge modes with different valleys. A rich variety of valley current states can be obtained by tuning the applied boundary potential and lead to the QVH effect, as well as to the unbalanced QVH effect. A method to individually manipulate the edge states by the boundary potentials is proposed.

Emergent Gauge Fields from Curvature in Single Layers of Transition-Metal Dichalcogenides

We analyze the electron dynamics in corrugated layers of transition-metal dichalcogenides. Due to the strong spin-orbit coupling, the intrinsic (Gaussian) curvature leads to an emergent gauge field associated with the Berry connection of the spinor wave function. We discuss the gauge field created by topological defects of the lattice, namely, tetragonal and octogonal disclinations and edge dislocations. Ripples and topological disorder induce the same dephasing effects as a random magnetic field, suppressing the weak localization effects. This geometric magnetic field can be detected in an Aharonov-Bohm interferometry experiment by measuring the local density of states in the vicinity of corrugations.

Topological phases in two-dimensional materials: a review

Topological phases with insulating bulk and gapless surface or edge modes have attracted intensive attention because of their fundamental physics implications and potential applications in dissipationless electronics and spintronics. In this review, we mainly focus on recent progress in the engineering of topologically nontrivial phases (such as [Formula: see text] topological insulators, quantum anomalous Hall effects, quantum valley Hall effects etc) in two-dimensional systems, including quantum wells, atomic crystal layers of elements from group III to group VII, and the transition metal compounds.

Colossal magnetoresistance in amino-functionalized graphene quantum dots at room temperature: manifestation of weak anti-localization and doorway to spintronics

In this work, we have demonstrated the signatures of localized surface distortions and disorders in functionalized graphene quantum dots (fGQD) and consequences in magneto-transport under weak field regime (∼1 Tesla) at room temperature. Observed positive colossal magnetoresistance (MR) and its suppression is primarily explained by weak anti-localization phenomenon where competitive valley (inter and intra) dependent scattering takes place at room temperature under low magnetic field; analogous to low mobility disordered graphene samples. Furthermore, using ab-initio analysis we show that sub-lattice sensitive spin-polarized ground state exists in the GQD as a result of pz orbital asymmetry in GQD carbon atoms with amino functional groups. This spin polarized ground state is believed to help the weak anti-localization dependent magneto transport by generating more disorder and strain in a GQD lattice under applied magnetic field and lays the premise for future graphene quantum dot based spintronic applications.

Spin rectification by orbital polarization in Bi-bilayer nanoribbons

We investigate the edge states of quantum spin-Hall phase Bi(111) bilayer nano-ribbons (BNRs) and their spin-rectifying effect using first-principles calculations and a non-equilibrium transport method. As low-dimensional materials, BNRs have tunable electronic properties, which are not only dependent on the edge shape, chemical passivation, or external electric fields but also governed by geometrical deformation. Depending on the passivation types, the interaction of the helical edge states in BNRs exhibits various patterns, enabling the valley engineering of the Dirac cones. In addition, the spin texture of the Dirac state is significantly tuned by edge passivation, external electric fields and geometric deformations. We demonstrate that curved BNRs can be used as the spin valves to rectify the electric currents via the edge states. Our results provide a practical way of utilizing two-dimensional topological insulator Bi bilayers for spintronic devices.

Mechanisms governing phonon scattering by topological defects in graphene nanoribbons

Understanding phonon scattering by topological defects in graphene is of particular interest for thermal management in graphene-based devices. We present a study that quantifies the roles of the different mechanisms governing defect phonon scattering by comparing the effects of ten different defect structures using molecular dynamics. Our results show that phonon scattering is mainly influenced by mass density difference, with general trends governed by the defect formation energy and typical softening behaviors in the phonon density of state. The phonon scattering cross-section is found to be far larger than that geometrically occupied by the defects. We also show that the lattice thermal conductivity can be reduced by a factor of up to ~30 in the presence of the grain boundaries formed by these defects.

Sound waves induce Volkov-like states, band structure and collimation effect in graphene

We find exact states of graphene quasiparticles under a time-dependent deformation (sound wave), whose propagation velocity is smaller than the Fermi velocity. To solve the corresponding effective Dirac equation, we adapt the Volkov-like solutions for relativistic fermions in a medium under a plane electromagnetic wave. The corresponding electron-deformation quasiparticle spectrum is determined by the solutions of a Mathieu equation resulting in band tongues warped in the surface of the Dirac cones. This leads to a collimation effect of electron conduction due to strain waves.

Growth mode and structures of magnetic Mn clusters on graphene

Lowest-energy geometries of Mn clusters on graphene. Blue and pink balls represent Mn atoms with negative and positive magnetic moments.

Strong interface-induced spin-orbit interaction in graphene on WS2

Interfacial interactions allow the electronic properties of graphene to be modified, as recently demonstrated by the appearance of satellite Dirac cones in graphene on hexagonal boron nitride substrates. Ongoing research strives to explore interfacial interactions with other materials to engineer targeted electronic properties. Here we show that with a tungsten disulfide (WS2) substrate, the strength of the spin-orbit interaction (SOI) in graphene is very strongly enhanced. The induced SOI leads to a pronounced low-temperature weak anti-localization effect and to a spin-relaxation time two to three orders of magnitude smaller than in graphene on conventional substrates. To interpret our findings we have performed first-principle electronic structure calculations, which confirm that carriers in graphene on WS2 experience a strong SOI and allow us to extract a spin-dependent low-energy effective Hamiltonian. Our analysis shows that the use of WS2 substrates opens a possible new route to access topological states of matter in graphene-based systems.

Energy flows in graphene: hot carrier dynamics and cooling

Long lifetimes of hot carriers can lead to qualitatively new types of responses in materials. The magnitude and time scales for these responses reflect the mechanisms governing energy flows. We examine the microscopics of two processes which are key for energy transport, focusing on the unusual behavior arising due to graphene's unique combination of material properties. One is hot carrier generation in its photoexcitation dynamics, where hot carriers multiply through an Auger type carrier-carrier scattering cascade. The hot-carrier generation manifests itself through elevated electronic temperatures which can be accessed in a variety of ways, in particular optical conductivity measurements. Another process of high interest is electron-lattice cooling. We survey different cooling pathways and discuss the cooling bottleneck arising for the momentum-conserving electron-phonon scattering pathway. We show how this bottleneck can be relieved by higher-order collisions—supercollisions—and examine the variety of supercollision processes that can occur in graphene.

Ballistic bipolar junctions in chemically gated graphene ribbons

The realization of ballistic graphene pn-junctions is an essential task in order to study Klein tunneling phenomena. Here we show that intercalation of Ge under the buffer layer of pre-structured SiC-samples succeeds to make truly nano-scaled pn-junctions. By means of local tunneling spectroscopy the junction width is found to be as narrow as 5 nm which is a hundred times smaller compared to electrically gated structures. The ballistic transmission across the junction is directly proven by systematic transport measurements with a 4-tip STM. Various npn- and pnp-junctions are studied with respect to the barrier length. The pn-junctions are shown to act as polarizer and analyzer with the second junction becoming transparent in case of a fully ballistic barrier. This can be attributed to the almost full suppression of electron transmission through the junction away from normal incidence.

Density of states in a two-dimensional chiral metal with vacancies

We study quantum interference effects in a two-dimensional chiral metal (bipartite lattice) with vacancies. We demonstrate that randomly distributed vacancies constitute a peculiar type of chiral disorder leading to strong modifications of critical properties at zero energy as compared to those of conventional chiral metals. In particular, the average density of states diverges as ρ∝E(-1)|lnE|(-3/2) and the correlation length L(c)∝√[|lnE|] in the limit E→0. When the average density of vacancies is different in the two sublattices, a finite concentration of zero modes emerges and a gap in the quasiclassical density of states opens around zero energy. Interference effects smear this gap, resulting in exponentially small tails at low energies.

Topological signatures in the electronic structure of graphene spirals

Topology is familiar mostly from mathematics, but also natural sciences have found its concepts useful. Those concepts have been used to explain several natural phenomena in biology and physics, and they are particularly relevant for the electronic structure description of topological insulators and graphene systems. Here, we introduce topologically distinct graphene forms - graphene spirals - and employ density-functional theory to investigate their geometric and electronic properties. We found that the spiral topology gives rise to an intrinsic Rashba spin-orbit splitting. Through a Hamiltonian constrained by space curvature, graphene spirals have topologically protected states due to time-reversal symmetry. In addition, we argue that the synthesis of such graphene spirals is feasible and can be achieved through advanced bottom-up experimental routes that we indicate in this work.

Purification/annealing of graphene with 100-MeV Ag ion irradiation

Studies on interaction of graphene with radiation are important because of nanolithographic processes in graphene-based electronic devices and for space applications. Since the electronic properties of graphene are highly sensitive to the defects and number of layers in graphene sample, it is desirable to develop tools to engineer these two parameters. We report swift heavy ion (SHI) irradiation-induced annealing and purification effects in graphene films, similar to that observed in our studies on fullerenes and carbon nanotubes (CNTs). Raman studies after irradiation with 100-MeV Ag ions (fluences from 3 × 10(10) to 1 × 10(14) ions/cm(2)) show that the disorder parameter α, defined by I D/I G ratio, decreases at lower fluences but increases at higher fluences beyond 1 × 10(12) ions/cm(2). This indicates that SHI induces annealing effects at lower fluences. We also observe that the number of graphene layers is reduced at fluences higher than 1 × 10(13) ions/cm(2). Using inelastic thermal spike model calculations, we estimate a radius of 2.6 nm for ion track core surrounded by a halo extending up to 11.6 nm. The transient temperature above the melting point in the track core results in damage, whereas lower temperature in the track halo is responsible for annealing. The results suggest that SHI irradiation fluence may be used as one of the tools for defect annealing and manipulation of the number of graphene layers.

PACS

60.80.x; 81.05.ue.

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.

Spin-controlled superconductivity and tunable triplet correlations in graphene nanostructures

We study graphene ferromagnet/superconductor/ferromagnet (F/S/F) nanostructures via a microscopic self-consistent Dirac Bogoliubov-de Gennes formalism. We show that as a result of proximity effects, experimentally accessible spin switching phenomena can occur as one tunes the Fermi level μF of the F regions or varies the angle θ between exchange field orientations. Superconductivity can then be switched on and off by varying either θ or μF (a spin-controlled superconducting graphene switch). The induced equal-spin triplet correlations in S can be controlled by tuning μF, effectively making a graphene based two-dimensional spin-triplet valve.

Measurement of filling-factor-dependent magnetophonon resonances in graphene using Raman spectroscopy

We perform polarization-resolved Raman spectroscopy on graphene in magnetic fields up to 45 T. This reveals a filling-factor-dependent, multicomponent anticrossing structure of the Raman G peak, resulting from magnetophonon resonances between magnetoexcitons and E(2g) phonons. This is explained with a model of Raman scattering taking into account the effects of spatially inhomogeneous carrier densities and strain. Random fluctuations of strain-induced pseudomagnetic fields lead to increased scattering intensity inside the anticrossing gap, consistent with the experiments.

Insulating to relativistic quantum Hall transition in disordered graphene

Quasi-particle excitations in graphene exhibit a unique behavior concerning two key phenomena of mesoscopic physics: electron localization and the quantum Hall effect. A direct transition between these two states has been found in disordered two-dimensional electron gases at low magnetic field. It has been suggested that it is a quantum phase transition, but the nature of the transition is still debated. Despite the large number of works studying either the localization or the quantum Hall regime in graphene, such a transition has not been investigated for Dirac fermions. Here we discuss measurements on low-mobility graphene where the localized state at low magnetic fields and a quantum Hall state at higher fields are observed. We find that the system undergoes a direct transition from the insulating to the Hall conductor regime. Remarkably, the transverse magneto-conductance shows a temperature independent crossing point, pointing to the existence of a genuine quantum phase transition.

The electronic properties of bilayer graphene

We review the electronic properties of bilayer graphene, beginning with a description of the tight-binding model of bilayer graphene and the derivation of the effective Hamiltonian describing massive chiral quasiparticles in two parabolic bands at low energies. We take into account five tight-binding parameters of the Slonczewski-Weiss-McClure model of bulk graphite plus intra- and interlayer asymmetry between atomic sites which induce band gaps in the low-energy spectrum. The Hartree model of screening and band-gap opening due to interlayer asymmetry in the presence of external gates is presented. The tight-binding model is used to describe optical and transport properties including the integer quantum Hall effect, and we also discuss orbital magnetism, phonons and the influence of strain on electronic properties. We conclude with an overview of electronic interaction effects.

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.

Direct observation of valley hybridization and universal symmetry of graphene with mesoscopic conductance fluctuations

In graphene, the valleys represent spinlike quantities and can act as a physical resource in valley-based electronics to produce novel quantum computation schemes. Here we demonstrate a direct route to tune and read the valley quantum states of disordered graphene by measuring the mesoscopic conductance fluctuations. We show that the conductance fluctuations in graphene at low temperatures are reduced by a factor of 4 when valley triplet states are gapped in the presence of short-range potential scatterers at high carrier densities. We also show that this implies a gate tunable universal symmetry class that outlines a fundamental feature arising from graphene's unique crystal structure.

Patterning of graphene

Two-dimensional atomic sheets of carbon (graphene, graphane, etc.) are amenable to unique patterning schemes such as cutting, bending, folding and fusion that are predicted to lead to interesting properties. In this review, we present theoretical understanding and processing routes for patterning graphene and highlight potential applications. With more precise and scalable patterning, the prospects of integrating flat carbon (graphene) with curved carbon (nanotubes and half nanotubes) and programmable graphene folding are envisioned.

Interaction-induced topological insulator states in strained graphene

The electronic properties of graphene can be manipulated via mechanical deformations, which opens prospects for both studying the Dirac fermions in new regimes and for new device applications. Certain natural configurations of strain generate large nearly uniform pseudomagnetic fields, which have opposite signs in the two valleys, and give rise to flat spin- and valley-degenerate pseudo-Landau levels (PLLs). Here we consider the effect of the Coulomb interactions in strained graphene with a uniform pseudomagnetic field. We show that the spin or valley degeneracies of the PLLs get lifted by the interactions, giving rise to topological insulator states. In particular, when a nonzero PLL is quarter or three-quarter filled, an anomalous quantum Hall state spontaneously breaking time-reversal symmetry emerges. At half-filled PLLs, a weak spin-orbital interaction stabilizes the time-reversal-symmetric quantum spin-Hall state. These many-body states are characterized by the quantized conductance and persist to a high temperature scale set by the Coulomb interactions, which we estimate to be a few hundreds Kelvin at moderate strain values. At fractional fillings, fractional quantum Hall states breaking valley symmetry emerge. These results suggest a new route to realizing robust topological states in mesoscopic graphene.

z→-z symmetry of spin-orbit coupling and weak localization in graphene

We show that the influence of spin-orbit (SO) coupling on the weak-localization effect for electrons in graphene depends on the lack or presence of z→-z symmetry in the system. While, for z→-z asymmetric SO coupling, disordered graphene should display a weak antilocalization behavior at lowest temperature, z→-z symmetric coupling leads to an effective saturation of decoherence time which can be partially lifted by an in-plane magnetic field, thus tending to restore the weak-localization effect.