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Grain boundaries play a major role for electron transport in graphene sheets grown by chemical vapor deposition. Here we investigate the electronic structure and transport properties of idealized graphene grain boundaries (GBs) in bi-crystals using first principles density functional theory (DFT) and non-equilibrium Greens functions (NEGF). We generated 150 different grain boundaries using an automated workflow where their geometry is relaxed with DFT. We find that the GBs generally show a quasi-1D bandstructure along the GB. We group the GBs in four classes based on their conductive properties: transparent, opaque, insulating, and spin-polarizing and show how this is related to angular mismatch, quantum mechanical interference, and out-of-plane buckling. Especially, we find that spin-polarization in the GB correlates with out-of-plane buckling. We further investigate the characteristics of these classes in simulated scanning tunnelling spectroscopy and diffusive transport along the GB which demonstrate how current can be guided along the GB.

Terahertz (THz) field pulses can now be applied in Scanning Tunnelling Microscopy (THz-STM) junction experiments to study time resolved dynamics. The relatively slow pulse compared to the typical electronic time-scale calls for approximations based on a time-scale separation. Here, we contrast three methods based on non-equilibrium Green's functions (NEGF): (i) the steady-state, adiabatic results, (ii) the lowest order dynamic expansion in the time-variation (DE), and (iii) the auxiliary mode (AM) propagation method without approximations in the time-variation. We consider a concrete THz-STM junction setup involving a hydrogen adsorbate on graphene where the localized spin polarization can be manipulated on/off by a local field from the tip electrode and/or a back-gate affecting the in-plane transport. We use steady-state NEGF combined with Density Functional Theory (DFT-NEGF) to obtain a Hubbard model for the study of the junction dynamics. Solving the Hubbard model in a mean-field approximation, we find that the near-adiabatic first order dynamical expansion provides a good description for STM voltage pulses up to the 1 V range., Comment: The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fphy.2023.1237383/ full#supplementary-material

Massive Dirac fermions are low-energy electronic excitations characterized by a hyperbolic band dispersion. They play a central role in several emerging physical phenomena such as topological phase transitions, anomalous Hall effects and superconductivity. This work demonstrates that massive Dirac fermions can be controllably induced by lithographically patterning superstructures of nanoscale holes in a graphene device. Their band dispersion is systematically visualized using angle-resolved photoemission spectroscopy with nanoscale spatial resolution. A linear scaling of effective mass with feature sizes is discovered, underlining the Dirac nature of the superstructures. In situ electrostatic doping dramatically enhances the effective hole mass and leads to the direct observation of an electronic band gap that results in a peak-to-peak band separation of (0.64 $\pm$ 0.03) eV, which is shown via first-principles calculations to be strongly renormalized by carrier-induced screening. The presented methodology outlines a new approach for band structure engineering guided by directly viewing structurally- and electrically-tunable massive Dirac quasiparticles in lithographic superstructures at the nanoscale., Comment: 37 pages, 12 figures (includes supporting information). A revised version has been published in ACS Nano

Josephson junctions based on quantum dots offer a convenient tunability by means of local gates. Here we analyze a Josephson junction based on a serial double quantum dot in which the two dots are individually gated by phase-shifted microwave tones of equal frequency. We calculate the time-averaged current across the junction and determine how the phase shift between the drives modifies the current-phase relation of the junction. Breaking particle-hole symmetry on the dots is found to give rise to a finite average anomalous Josephson current with phase bias between the superconductors fixed to zero. This microwave gated weak link thus realizes a tunable "Floquet $\varphi_{0}$-junction" with maximum critical current achieved for driving frequencies slightly off-resonance with the energy cost of exciting a sub-gap state on each dot. We provide numerical results supported by an analytical analysis for infinite superconducting gap and weak inter-dot coupling. We identify an interaction driven $0-\pi$ transition of anomalous Josephson current as a function of driving phase difference. Finally, we show that this junction can be tuned so as to provide for complete rectification of the time-averaged Josephson current phase relation., Comment: 16 pages, 12 figures

We provide a critical discussion concerning the claim of topological valley currents, driven by a global Berry curvature and valley Hall effect proposed in recent literature. After pointing out a major inconsistency of the theoretical scenario proposed to interpret giant nonlocal resistance, we discuss various possible alternative explanations and open directions of research to solve the mystery of nonlocal transport in graphene superlattices., Comment: 3 pages, 1 figure

Encapsulating graphene in hexagonal Boron Nitride has several advantages: the highest mobilities reported to date are achieved in this way, and precise nanostructuring of graphene becomes feasible through the protective hBN layers. Nevertheless, subtle effects may arise due to the differing lattice constants of graphene and hBN, and due to the twist angle between the graphene and hBN lattices. Here, we use a recently developed model which allows us to perform band structure and magnetotransport calculations of such structures, and show that with a proper account of the moir\'e physics an excellent agreement with experiments can be achieved, even for complicated structures such as disordered graphene, or antidot lattices on a monolayer hBN with a relative twist angle. Calculations of this kind are essential to a quantitative modeling of twistronic devices.

The Josephson current is investigated in a superconducting graphene bilayer where pristine graphene sheets can make in-plane or out-of-plane displacements with respect to each other. The superconductivity can be of an intrinsic nature, or due to a proximity effect. The results demonstrate that the supercurrent responds qualitatively differently to relative displacement if the superconductivity is due to either intralayer or interlayer spin-singlet electron-electron pairing, thus providing a tool to distinguish between the two mechanisms. Specifically, both the AA and AB stacking orders are studied with antiferromagnetic spin alignment. For the AA stacking order with intralayer and on-site pairing no current reversal is found. In contrast, the supercurrent may switch its direction as a function of the in-plane displacement and out-of-plane interlayer coupling for the cases of AA ordering with interlayer pairing and AB ordering with either intralayer or interlayer pairing. In addition to sign reversal, the Josephson signal displays many characteristic fingerprints which derive directly from the pairing mechanism. Thus, measurements of the Josephson current as a function of the graphene bilayer displacement open up the means achieve deeper insights into the superconducting pairing mechanism., Comment: 6 pages, 3 figures

A quantitative understanding of the electromagnetic response of materials is essential for the precise engineering of maximal, versatile, and controllable light--matter interactions. Material surfaces, in particular, are prominent platforms for enhancing electromagnetic interactions and for tailoring chemical processes. However, at the deep nanoscale, the electromagnetic response of electron systems is significantly impacted by quantum surface-response at material interfaces, which is challenging to probe using standard optical techniques. Here, we show how ultra-confined acoustic graphene plasmons (AGPs) in graphene--dielectric--metal structures can be used to probe the quantum surface-response functions of nearby metals, here encoded through the so-called Feibelman $d$-parameters. Based on our theoretical formalism, we introduce a concrete proposal for experimentally inferring the low-frequency quantum response of metals from quantum shifts of the AGPs' dispersion, and demonstrate that the high field confinement of AGPs can resolve intrinsically quantum mechanical electronic length-scales with subnanometer resolution. Our findings reveal a promising scheme to probe the quantum response of metals, and further suggest the utilization of AGPs as plasmon rulers with \r{a}ngstr\"{o}m-scale accuracy., Comment: 7 pages, 4 figures

We demonstrate terahertz time-domain spectroscopy (THz-TDS) to be an accurate, rapid and scalable method to probe the interaction-induced Fermi velocity renormalization {\nu}F^* of charge carriers in graphene. This allows the quantitative extraction of all electrical parameters (DC conductivity {\sigma}DC, carrier density n, and carrier mobility {\mu}) of large-scale graphene films placed on arbitrary substrates via THz-TDS. Particularly relevant are substrates with low relative permittivity (< 5) such as polymeric films, where notable renormalization effects are observed even at relatively large carrier densities (> 10^12 cm-2, Fermi level > 0.1 eV). From an application point of view, the ability to rapidly and non-destructively quantify and map the electrical ({\sigma}DC, n, {\mu}) and electronic ({\nu}F^* ) properties of large-scale graphene on generic substrates is key to utilize this material in applications such as metrology, flexible electronics as well as to monitor graphene transfers using polymers as handling layers., Comment: 23 pages, 8 figures

The recent generalised nonlocal optical response (GNOR) theory for plasmonics is analysed, and its main input parameter, namely the complex hydrodynamic convection-diffusion constant, is quantified in terms of enhanced Landau damping due to diffusive surface scattering of electrons at the surface of the metal. GNOR has been successful in describing plasmon damping effects, in addition to the frequency shifts originating from induced-charge screening, through a phenomenological electron diffusion term implemented into the traditional hydrodynamic Drude model of nonlocal plasmonics. Nevertheless, its microscopic derivation and justification is still missing. Here we discuss how the inclusion of a diffusion-like term in standard hydrodynamics can serve as an efficient vehicle to describe Landau damping without resorting to computationally demanding quantum-mechanical calculations, and establish a direct link between this term and the Feibelman $d$ parameter for the centroid of charge. Our approach provides a recipe to connect the phenomenological fundamental GNOR parameter to a frequency-dependent microscopic surface-response function. We therefore tackle one of the principal limitations of the model, and further elucidate its range of validity and limitations, thus facilitating its proper application in the framework of nonclassical plasmonics.

Finite graphene nanoribbon (GNR) heterostructures host intriguing topological in-gap states (Rizzo, D. J. et al.~\textit{Nature} \textbf{2018}, \textit{560}, 204]). These states may be localized either at the bulk edges, or at the ends of the structure. Here we show that correlation effects (not included in previous density functional simulations) play a key role in these systems: they result in increased magnetic moments at the ribbon edges accompanied by a significant energy renormalization of the topological end states -- even in the presence of a metallic substrate. Our computed results are in excellent agreement with the experiments. Furthermore, we discover a striking, novel mechanism that causes an energy splitting of the non-zero-energy topological end states for a weakly screened system. We predict that similar effects should be observable in other GNR heterostructures as well.

We report on the emergence of bulk, valley-polarized currents in graphene-based devices, driven by spatially varying regions of broken sublattice symmetry, and revealed by non-local resistance ($R_\mathrm{NL}$) fingerprints. By using a combination of quantum transport formalisms, giving access to bulk properties as well as multi-terminal device responses, the presence of a non-uniform local bandgap is shown to give rise to valley-dependent scattering and a finite Fermi surface contribution to the valley Hall conductivity, related to characteristics of $R_\mathrm{NL}$. These features are robust against disorder and provide a plausible interpretation of controversial experiments in graphene/hBN superlattices. Our findings suggest both an alternative mechanism for the generation of valley Hall effect in graphene, and a route towards valley-dependent electron optics, by materials and device engineering., Comment: 6 pages, 4 figures

Bottom-up prepared carbon nanostructures appear as promising platforms for future carbon-based nanoelectronics, due to their atomically precise and versatile structure. An important breakthrough is the recent preparation of nanoporous graphene (NPG) as an ordered covalent array of graphene nanoribbons (GNRs). Within NPG, the GNRs may be thought of as 1D electronic nanochannels through which electrons preferentially move, highlighting NPG's potential for carbon nanocircuitry. However, the {\pi}-conjugated bonds bridging the GNRs give rise to electronic cross-talk between the individual 1D channels, leading to spatially dispersing electronic currents. Here, we propose a chemical design of the bridges resulting in destructive quantum interference, which blocks the cross-talk between GNRs in NPG, electronically isolating them. Our multiscale calculations reveal that injected currents can remain confined within a single, 0.7 nm wide, GNR channel for distances as long as 100 nm. The concepts developed in this work thus provide an important ingredient for the quantum design of future carbon nanocircuitry.

We theoretically investigate gate-defined graphene superlattices with broken inversion symmetry as a platform for realizing tunable valley dependent transport. Our analysis is motivated by recent experiments [C. Forsythe et al., Nat. Nanotechnol. 13, 566 (2018)] wherein gate-tunable superlattice potentials have been induced on graphene by nanostructuring a dielectric in the graphene/patterneddielectric/gate structure. We demonstrate how the electronic tight-binding structure of the superlattice system resembles a gapped Dirac model with associated valley dependent transport using an unfolding procedure. In this manner we obtain the valley Hall conductivities from the Berry curvature distribution in the superlattice Brillouin zone, and demonstrate the tunability of this conductivity by the superlattice potential. Finally, we calculate the valley Hall angle relating the transverse valley current and longitudinal charge current and demonstrate the robustness of the valley currents against irregularities in the patterned dielectric., Comment: 12 pages, 11 figures

We experimentally investigate the charge induction mechanism across gated, narrow, ballistic graphene devices with different degrees of edge disorder. By using magnetoconductance measurements as the probing technique, we demonstrate that devices with large edge disorder exhibit a nearly homogeneous capacitance profile across the device channel, close to the case of an infinitely large graphene sheet. In contrast, devices with lower edge disorder (< 1 nm roughness) are strongly influenced by the fringing electrostatic field at graphene boundaries, in quantitative agreement with theoretical calculations for pristine systems. Specifically, devices with low edge disorder present a large effective capacitance variation across the device channel with a nontrivial, inhomogeneous profile due not only to classical electrostatics but also to quantum mechanical effects. We show that such quantum capacitance contribution, occurring due to the low density of states (DOS) across the device in the presence of an external magnetic field, is considerably altered as a result of the gate electrostatics in the ballistic graphene device. Our conclusions can be extended to any two dimensional (2D) electronic system confined by a hard-wall potential and are important for understanding the electronic structure and device applications of conducting 2D materials., Comment: 3 figures

Plasmon-emitter interactions are of paramount importance in modern nanoplasmonics and are generally maximal at short emitter-surface separations. However, when the separation falls below 10-20 nm, the classical theory progressively deteriorates due to its neglect of quantum mechanical effects such as nonlocality, electronic spill-out, and Landau damping. Here, we show how this neglect can be remedied by presenting a unified theoretical treatment of mesoscopic electrodynamics grounded on the framework of Feibelman $d$-parameters. Crucially, our technique naturally incorporates nonclassical resonance shifts and surface-enabled Landau damping - a nonlocal damping effect - which have a dramatic impact on the amplitude and spectral distribution of plasmon-emitter interactions. We consider a broad array of plasmon-emitter interactions ranging from dipolar and multipolar spontaneous emission enhancement, to plasmon-assisted energy transfer and enhancement of two-photon transitions. The formalism presented here gives a complete account of both plasmons and plasmon-emitter interactions at the nanoscale, constituting a simple yet rigorous and general platform to incorporate nonclassical effects in plasmon-empowered nanophotonic phenomena., Comment: 12 pages, 6 figures

We study the spectral function and quasiparticle scattering in Li-decorated graphene (Li@graphene) with an atomistic $T$-matrix formalism and uncover adatom-induced spectral effects which shed light on experimentally observed angle-resolved photoemission spectroscopy (ARPES) features. From transport studies, alkali adatoms are known to introduce charged-impurity scattering limiting the carrier mobility. Here, we demonstrate that Li adatoms furthermore give rise to a low-energy impurity band centered at the $\Gamma$ point which originates from the hybridization between the atomic 2s state of the Li adatoms and graphene "surface" states. We show that the impurity band is strongly dependent on the concentration $c_\mathrm{Li}$ of Li adatoms, and aligns with the Li-induced Fermi level on the Dirac cone at $c_\mathrm{Li}\sim 8\,\%$ ($E_F\approx 1.1\,\mathrm{eV}$). Finally, we show that adatom-induced quasiparticle scattering increases dramatically at energies above $\sim 1\,\mathrm{eV}$ close to the van Hove singularity in the graphene density of states (DOS), giving rise to a large linewidth broadening on the Dirac cone with a concomitant downshift and a characteristic kink in the conduction band. Our findings are highly relevant for future studies of ARPES, transport, and superconductivity in adatom-doped graphene., Comment: 6 pages, 4 figures, and supplemental material. Published version

Using a Green's function approach, we study phonon-mediated superconducting pairing symmetries that may arise in bilayer graphene where the monolayers are displaced in-plane with respect to each other. We consider a generic coupling potential between the displaced graphene monolayers, which is applicable to both shifted and commensurate twisted graphene layers; study intralayer and interlayer phonon-mediated BCS pairings; and investigate AA and AB(AC) stacking orders. Our findings demonstrate that at the charge neutrality point, the dominant pairings in both AA and AB stackings with intralayer and interlayer electron-electron couplings can have even-parity $s$-wave class and odd-parity $p$-wave class of symmetries with the possibility of invoking equal-pseudospin and odd-frequency pair correlations. At a finite doping, however, the AB (and equivalently AC) stacking can develop pseudospin-singlet and pseudospin-triplet $d$-wave symmetry, in addition to $s$-wave, $p$-wave, $f$-wave, and their combinations, while the AA stacking order, similar to the undoped case, is unable to host the $d$-wave symmetry. When we introduce a generic coupling potential, applicable to commensurate twisted and shifted bilayers of graphene, $d$-wave symmetry can also appear at the charge neutrality point. Inspired by a recent experiment where two phonon modes were observed in a twisted bilayer graphene, we also discuss the possibility of the existence of two-gap superconductivity, where the intralayer and interlayer phonon-mediated BCS picture is responsible for superconductivity. These analyses may provide a useful tool in determining the superconducting pairing symmetries and mechanism in bilayer graphene systems.

Coulomb drag between nanoscale conductors is of both fundamental and practical interest. Here, we theoretically study drag in a double quantum-dot (QD) system consisting of a biased drive QD and an unbiased drag QD coupled via a direct interdot Coulomb interaction. We demonstrate that the Coulomb drag is driven by the charge fluctuations in the drive QD, and show how the properties of the associated quantum noise allow to distinguish it from, e.g., shot-noise driven drag in circuits of weakly interacting quantum conductors. In the strong-interaction regime exhibiting an orbital ("pseudospin") Kondo effect, the drag is governed by charge fluctuations induced by pseudospin-flip cotunneling processes. The quenching of pseudospin-flip processes by Kondo correlations are found to suppress the drag at low bias and introduce a zero-bias anomaly in the second-order differential transconductance. Finally, we show that the drag is maximized for values of the interdot interaction matching the lead couplings. Our findings are relevant for the understanding of drag in QD systems and provide experimentally testable predictions in different transport regimes., Comment: Published version: 6 pages, 5 figures, and supplemental material

Motivated by recent experimental progress, we study the effect of mechanical deformations on the superconducting pairing symmetries in monolayer black phosphorus (MBP). Starting with phonon-mediated intervalley spin-singlet electron-electron pairing and making use of realistic band parameters obtained through first-principles calculations, we show that the application of weak mechanical strain in the plane of MBP can change the effective $s$-wave and $p$-wave symmetry of the superconducting correlations into effective $d$-wave and $f$-wave symmetries, respectively. This prediction of a change in the pairing symmetries might be experimentally confirmed through angular dependence high-resolution tunneling spectroscopy, the Meissner effect, and critical temperature experiments. The idea of manipulating the superconducting symmetry class by applying planar mechanical strain can be extended to other anisotropic materials as well, and may help in providing important information of the symmetries of the order parameter, perhaps even in some high-$T_c$ superconductors.

Leonid Keldysh -- one of the most influential theoretical physicists of the 20th century -- passed away in November 2016. Keldysh is best known for the diagrammatic formulation of real-time (nonequilibrium) Green functions theory and for the theory of strong field ionization of atoms. Both theories profoundly changed large areas of theoretical physics and stimulated important experiments. Both these discoveries emerged almost simultaneously -- like Einstein, also Keldysh had his \textit{annus mirabilis} -- the year 1964. But the list of his theoretical developments is much broader and is briefly reviewed here.

Anisotropic electronic transport is a possible route towards nanoscale circuitry design, particularly in two-dimensional materials. Proposals to introduce such a feature in patterned graphene have to date relied on large-scale structural inhomogeneities. Here we theoretically explore how a random, yet homogeneous, distribution of zigzag-edged triangular perforations can generate spatial anisotropies in both charge and spin transport. Anisotropic electronic transport is found to persist under considerable disordering of the perforation edges, suggesting its viability under realistic experimental conditions. Furthermore, controlling the relative orientation of perforations enables spin filtering of the transmitted electrons, resulting in a half-metallic anisotropic transport regime. Our findings point towards a co-integration of charge and spin control in a two-dimensional platform of relevance for nanocircuit design. We further highlight how geometrical effects allow finite samples to display finite transverse resistances, reminiscent of Spin Hall effects, in the absence of any bulk fingerprints of such mechanisms, and explore the underlying symmetries behind this behaviour., Comment: 11 pages, 6 figures

We develop theory models for both ballistic and disordered superconducting monolayer black phosphorus devices in the presence of magnetic exchange field and strain. The ballistic case is studied through a microscopic Bogoliubov-de Gennes formalism while for the disordered case we formulate a quasiclassical model. Utilizing the two models, we theoretically study the response of supercurrent to an externally applied magnetic field in two-dimensional black phosphorus Josephson junctions. Our results demonstrate that the response of the supercurrent to a perpendicular magnetic field in ballistic samples can deviate from the standard Fraunhofer interference pattern when the Fermi level and mechanical strain are varied. This finding suggests the combination of chemical potential and strain is an efficient external knob to control the current response in highly sensitive strain-effect transistors and superconducting quantum interference devices. We also study the supercurrent in a superconductor-ferromagnet-ferromagnet-superconductor junction where the magnetizations of the two adjacent magnetized regions are uniform with misaligned orientations. We show that the magnetization misalignment can control the excitation of harmonics higher than the first harmonic sin(phi) (in which phi is the phase difference between the superconductors) in supercurrent and constitutes a full spin switching current element. Finally, we discuss possible experimental implementations of our findings. We foresee our models and discussions could provide guidelines to experimentalists in designing devices and future investigations., Comment: 10 pages, 4 figures, (Bogoliubov-de Gennes, Eilenberger, and Usadel Techniques)

We use confocal Raman microscopy and modified vector analysis methods to investigate the nanoscale origin of strain and carrier concentration in exfoliated graphene-hexagonal boron nitride (hBN) heterostructures on silicon dioxide (SiO2). Two types of heterostructures are studied: graphene on SiO2 partially coved by hBN, and graphene fully encapsulated between two hBN flakes. We extend the vector analysis methods to produce spatial maps of the strain and doping variation across the heterostructures. This allows us to visualise and directly quantify the much-speculated effect of the environment on carrier concentration as well as strain in graphene. Moreover, we demonstrate that variations in strain and carrier concentration in graphene arise from nanoscale features of the heterostructures such as fractures, folds and bubbles trapped between layers. For bubbles in hBN-encapsulated graphene, hydrostatic strain is shown to be greatest at bubble centres, whereas the maximum of carrier concentration is localised at bubble edges. Raman spectroscopy is shown to be a non-invasive tool for probing strain and doping in graphene, which could prove useful for engineering of two-dimensional devices., Comment: 14 pages, 5 figures

We develop a theory for strain control of Majorana zero energy modes and Josephson effect in black phosphorus (BP) devices proximity coupled to a superconductor. Employing realistic values for the band parameters subject to strain, we show that the strain closes the intrinsic band gap of BP, however the proximity effect from the superconductor reopens it and creates Dirac and Weyl nodes. Our results illustrate that Majorana zero energy flat bands connect the nodes within the band-inverted regime in which their associated density of states is localized at the edges of the device. In a ferromagnetically mediated Josephson configuration, the exchange field induces super-harmonics into the supercurrent phase relation in addition to a {\phi}0 phase shift, corresponding to a spontaneous supercurrent, and strain offers an efficient tool to control these phenomena. We analyze the experimental implications of our findings, and show that they can pave the way for creating a rich platform for studying two-dimensional Dirac and Weyl superconductivity.

In this paper we analyze the effects of nonlocality on the optical properties of a system consisting of a thin metallic film separated from a graphene sheet by a hexagonal boron nitride (hBN) layer. We show that nonlocal effects in the metal have a strong impact on the spectrum of the surface plasmon-polaritons on graphene. If the graphene sheet is shaped into a grating, we show that the extinction curves can be used to shed light on the importance of nonlocal effects in metals. Therefore, graphene surface plasmons emerge as a tool for probing nonlocal effects in metallic nanostructures, including thin metallic films. As a byproduct of our study, we show that nonlocal effects lead to smaller losses for the graphene plasmons than what is predicted by a local calculation. We show that these effects can be very well mimicked using a local theory with an effective spacer thickness larger than its actual value., Comment: 16 pages

Electron waiting times are an important concept in the analysis of quantum transport in nano-scale conductors. Here we show that the statistics of electron waiting times can be used to characterize Cooper pair splitters that create spatially separated spin-entangled electrons. A short waiting time between electrons tunneling into different leads is associated with the fast emission of a split Cooper pair, while long waiting times are governed by the slow injection of Cooper pairs from a superconductor. Experimentally, the waiting time distributions can be measured using real-time single-electron detectors in the regime of slow tunneling, where conventional current measurements are demanding. Our work is important for understanding the fundamental transport processes in Cooper pair splitters and the predictions may be verified using current technology., Comment: 6 pages, 4 figures, final version as published in Phys. Rev. Lett

Intervalley scattering by atomic defects in monolayer transition metal dichalcogenides (TDMs; MX2) presents a serious obstacle for applications exploiting their unique valley-contrasting properties. Here, we show that the symmetry of the atomic defects can give rise to an unconventional protection mechanism against intervalley scattering in monolayer TMDs. The predicted defect-dependent selection rules for intervalley scattering can be verified via Fourier transform scanning tunneling spectroscopy (FT-STS), and provide a unique identification of, e.g., atomic vacancy defects (M vs X). Our findings put the absence of the intervalley FT-STS peak in recent experiments in a different perspective., Comment: 7 pages, 4 figures + supplementary. Published version

We reveal new aspects of the interaction between plasmons and phonons in 2D materials that go beyond a mere shift and increase in plasmon width due to coupling to either intrinsic vibrational modes of the material or phonons in a supporting substrate. More precisely, we predict strong plasmon splitting due to this coupling, resulting in a characteristic avoided crossing scheme. We base our results on a computationally efficient approach consisting in including many-body interactions through the electron self-energy. We specify this formalism for a description of plasmons based upon a tight-binding electron Hamiltonian combined with the random-phase approximation. This approach is accurate provided vertex corrections can be neglected, as is is the case in conventional plasmon-supporting metals and Dirac-fermion systems. We illustrate our method by evaluating plasmonic spectra of doped graphene nanotriangles with varied size, where we predict remarkable peak splittings and other radical modifications in the spectra due to plasmons interactions with intrinsic optical phonons. Our method is equally applicable to other 2D materials and provides a simple approach for investigating coupling of plasmons to phonons, excitons, and other excitations in hybrid thin nanostructures.

We study thermoelectric effects in Coulomb-coupled quantum-dot (CCQD) systems beyond lowest-order tunneling processes and the often applied wide-band approximation. To this end, we present a master-equation (ME) approach based on a perturbative $T$-matrix calculation of the charge and heat tunneling rates and transport currents. Applying the method to transport through a non-interacting single-level QD, we demonstrate excellent agreement with the Landauer-B{\"u}ttiker theory when higher-order (cotunneling) processes are included in the ME. Next, we study the effect of cotunneling and energy-dependent lead couplings on the heat currents in a system of two Coulomb-coupled QDs. Overall, we find that cotunneling processes (i) dominate the heat currents at low temperature and bias, and (ii) give rise to a pronounced reduction of the cooling power achievable with the recently demonstrated Maxwell's demon cooling mechanism. Furthermore, we demonstrate that the cooling power can be boosted significantly by carefully engineering the energy dependence of the lead couplings to filter out undesired transport processes. Our findings emphasize the importance of considering higher-order cotunneling processes as well as the advantage of engineered energy-dependent lead couplings in the optimization of the thermoelectric performance of Coulomb-coupled QD systems.

Commensurability oscillations in the magnetotransport of periodically patterned systems, emerging from the interplay of cyclotron orbit and the pattern periodicity, are a benchmark of mesoscopic physics in electron gas systems. Exploiting similar effects in 2D materials would allow exceptional control of electron behaviour, but is hindered by the requirement to maintain ballistic transport over large length scales. Recent experiments have overcome this obstacle and observed distinct magnetoresistance commensurability peaks for perforated graphene sheets (antidot lattices). Interpreting the exact mechanisms behind these peaks is of key importance, particularly in graphene where a range of regimes are accessible by varying the electron density. In this work a fully atomistic, device-based simulation of magnetoresistance experiments allows us to analyse both the resistance peaks and the current flow at commensurability conditions. Magnetoresistance spectra are found in excellent agreement with experiment, but we show that a semi-classical analysis, in terms of simple skipping or pinned orbits, is insufficient to fully describe the corresponding electron trajectories. Instead, a generalised mechanism in terms of states bound to individual antidots, or to groups of antidots, is required. Commensurability features are shown to arise when scattering between such states is enhanced. The emergence and suppression of commensurability peaks is explored for different antidot sizes, magnetic field strengths and electron densities. The insights gained from our study will guide the design and optimization of future experiments with nanostructured graphene.

Zigzag edges of the honeycomb structure of graphene exhibit magnetic polarization making them attractive as building blocks for spintronic devices. Here, we show that devices with zigzag edged triangular antidots perform essential spintronic functionalities, such as spatial spin-splitting or spin filtering of unpolarized incoming currents. Near-perfect performance can be obtained with optimized structures. The device performance is robust against substantial disorder. The gate-voltage dependence of transverse resistance is qualitatively different for spin-polarized and spin-unpolarized devices, and can be used as a diagnostic tool. Importantly, the suggested devices are feasible within current technologies., Comment: 6 pages, 5 figures, published

Atomic disorder is a common limiting factor for the low-temperature mobility in monolayer transition-metal dichalcogenides (TMDs; MX2). Here, we study the effect of often occurring atomic vacancies on carrier scattering and transport in p- and n-type monolayer MoS2. Due to charge trapping in vacancy-induced in-gap states, both neutral and charged vacancies resembling, respectively, short-range and combined short-range and long-range Coulomb scatterers, must be considered. Using the T-matrix formalism, we demonstrate a strong renormalization of the Born description of short-range scattering, manifested in a pronounced reduction and a characteristic energy dependence of the scattering rate. As a consequence, carrier scattering in TMDs with charged vacancies is dominated by the long-range Coulomb-disorder scattering, giving rise to a strong screening-induced temperature and density dependence of the low-temperature carrier mobility. For TMDs with neutral vacancies, the absence of intrinsic Coulomb disorder results in significantly higher mobilities as well as an unusual density dependence of the mobility which decreases with the carrier density. Our work illuminates the transport-limiting effects of atomic-vacancy scattering relevant for high-mobility TMD devices., Comment: New version, 13 pages, 7 figures

The classical treatment of plasmonics is insufficient at the nanometer-scale due to quantum mechanical surface phenomena. Here, an extension to the classical paradigm is reported which rigorously remedies this deficiency through the incorporation of first-principles surface response functions - the Feibelman d-parameters - in general geometries. Several analytical results for the leading-order plasmonic quantum corrections are obtained in a first-principles setting; particularly, a clear separation of the roles of shape, scale, and material is established. The utility of the formalism is illustrated by the derivation of a modified sum-rule for complementary structures, a rigorous reformulation of Kreibig's phenomenological damping prescription, and an account of the small-scale resonance-shifting of simple and noble metal nanostructures. These insights open the technological design space and deepen our fundamental understanding of nanoplasmonics beyond the classical regime., Comment: 6 pages, 3 figures, 1 table (Supporting Material included as ancillary file)

The low energy band structure of graphene has two inequivalent valleys at K and K' points of the Brillouin zone. The possibility to manipulate this valley degree of freedom defines the field of valleytronics, the valley analogue of spintronics. A key requirement for valleytronic devices is the ability to break the valley degeneracy by filtering and spatially splitting valleys to generate valley polarized currents. Here we suggest a way to obtain valley polarization using strain-induced inhomogeneous pseudomagnetic fields (PMF) which act differently on the two valleys. Notably, the suggested method does not involve external magnetic fields, or magnetic materials, as previous proposals. In our proposal the strain is due to experimentally feasible nanobubbles (but any local deformation would do): the associated PMFs lead to different real space trajectories for K and K' electrons, thus allowing the two valleys to be addressed individually. In this way, graphene nanobubbles can be exploited in both valley filtering and valley splitting devices, and our simulations reveal that a number of different functionalities are possible depending on the deformation field.

We report on mesoscopic transport fingerprints in disordered graphene caused by strain-field induced pseudomagnetic Landau levels (pLLs). Efficient numerical real space calculations of the Kubo formula are performed for an ordered network of nanobubbles in graphene, creating pseudomagnetic fields up to several hundreds of Tesla, values inaccessible by real magnetic fields. Strain-induced pLLs yield enhanced scattering effects across the energy spectrum resulting in lower mean free path and enhanced localization effects. In the vicinity of the zeroth order pLL, we demonstrate an anomalous transport regime, where the mean free paths increases with disorder. We attribute this puzzling behavior to the low-energy sub-lattice polarization induced by the zeroth order pLL, which is unique to pseudomagnetic fields preserving time-reversal symmetry. These results, combined with the experimental feasibility of reversible deformation fields, open the way to tailor a metal-insulator transition driven by pseudomagnetic fields.

Magnetic fields are often used for characterizing transport in nanoscale materials. Recent magnetotransport experiments have demonstrated that ballistic transport is possible in graphene antidot lattices (GALs). These experiments have inspired the present theoretical study of GALs in a perpendicular magnetic field. We calculate magnetotransport through graphene antidot barriers (GABs), which are finite rows of antidots arranged periodically in a pristine graphene sheet, using a tight-binding model and the Landauer-B\"uttiker formula. We show that GABs behave as ideal Dirac mass barriers for antidots smaller than the magnetic length, and demonstrate the presence of magnetic edge states, which are localized states on the periphery of the antidots due to successive reflections on the antidot edge in the presence of a magnetic field. We show that these states are robust against variations in lattice configuration and antidot edge chirality. Moreover, we calculate the transmittance of disordered GABs and find that magnetic edge states survive a moderate degree of disorder. Due to the long phase-coherence length in graphene and the robustness of these states, we expect magnetic edge states to be observable in experiments as well.

We have realized nanometer size constrictions in ballistic graphene nanoribbons grown on sidewalls of SiC mesa structures. The high quality of our devices allows the observation of a number of electronic quantum interference phenomena. The transmissions of Fabry-Perot like resonances were probed by in-situ transport measurements at various temperatures. The energies of the resonances are determined by the size of the constrictions which can be controlled precisely using STM lithography. The temperature and size dependence of the measured conductances are in quantitative agreement with tight-binding calculations. The fact that these interference effects are visible even at room temperature makes the reported devices attractive as building blocks for future carbon based electronics., Comment: to appear in Phys. Rev. Lett

Ideal graphene antidot lattices are predicted to show promising band gap behavior (i.e., $E_G\simeq 500$ meV) under carefully specified conditions. However, for the structures studied so far this behavior is critically dependent on superlattice geometry and is not robust against experimentally realistic disorders. Here we study a rectangular array of triangular antidots with zigzag edge geometries and show that their band gap behavior qualitatively differs from the standard behavior which is exhibited, e.g, by rectangular arrays of armchair-edged triangles. In the spin unpolarized case, zigzag-edged antidots give rise to large band gaps compared to armchair-edged antidots, irrespective of the rules which govern the existence of gaps in armchair-edged antidot lattices. In addition the zigzag-edged antidots appear more robust than armchair-edged antidots in the presence of geometrical disorder. The inclusion of spin polarization within a mean-field Hubbard approach gives rise to a large overall magnetic moment at each antidot due to the sublattice imbalance imposed by the triangular geometry. Half-metallic behavior arises from the formation of spin-split dispersive states near the Fermi energy, reducing the band gaps compared to the unpolarized case. This behavior is also found to be robust in the presence of disorder. Our results highlight the possibilities of using triangular perforations in graphene to open electronic band gaps in systems with experimentally realistic levels of disorder, and furthermore, of exploiting the strong spin dependence of the system for spintronic applications., Comment: 9 pages, 11 figures, published

Using ab-initio methods we investigate the possibility of three-terminal graphene "T-junction" devices and show that these all-graphene edge contacts are energetically feasible when the 1D interface itself is free from foreign atoms. We examine the energetics of various junction structures as a function of the atomic scale geometry. Three-terminal equilibrium Green's functions are used to determine the transmission spectrum and contact resistance of the system. We find that the most symmetric structures have a significant binding energy, and we determine the contact resistances in the junction to be in the range of 1-10 kOhm which is comparable to the best contact resistance reported for edge-contacted graphene-metal contacts. We conclude that conducting all-carbon T-junctions should be feasible.

We study theoretically Coulomb drag in capacitively coupled quantum dots (CQDs) -- a biasdriven dot coupled to an unbiased dot where transport is due to Coulomb mediated energy transfer drag. To this end, we introduce a master-equation approach which accounts for higher-order tunneling (cotunneling) processes as well as energy-dependent lead couplings, and identify a mesoscopic Coulomb drag mechanism driven by nonlocal multi-electron cotunneling processes. Our theory establishes the conditions for a nonzero drag as well as the direction of the drag current in terms of microscopic system parameters. Interestingly, the direction of the drag current is not determined by the drive current, but by an interplay between the energy-dependent lead couplings. Studying the drag mechanism in a graphene-based CQD heterostructure, we show that the predictions of our theory are consistent with recent experiments on Coulomb drag in CQD systems., Comment: 6 pages, 4 figures + supplementary. Published version

Strain fields in graphene giving rise to pseudomagnetic fields have received much attention due to the possibility of mimicking real magnetic fields with magnitudes of greater than 100 Tesla. We examine systems with such strains confined to finite regions ("pseudomagnetic dots") and provide a transparent explanation for the characteristic sublattice polarization occurring in the presence of pseudomagnetic field. In particular, we focus on a triaxial strain leading to a constant field in the central region of the dot. This field causes the formation of pseudo Landau levels, where the zeroth order level shows significant differences compared to the corresponding level in a real magnetic field. Analytic arguments based on the Dirac model are employed to predict the sublattice and valley dependencies of the density of states in these systems. Numerical tight binding calculations of single pseudomagnetic dots in extended graphene sheets confirm these predictions, and are also used to study the effect of the rotating the strain direction and varying the size of the pseudomagnetic dot.

We study two-stream instabilities in a non-equilibrium system in which a stream of electrons is injected into doped graphene. As with equivalent non-equilibrium parabolic band systems, we find that the graphene systems can support unstable charge-density waves whose amplitudes grow with time. We determine the range of wavevector $\boldsymbol{q}$ that are unstable, and their growth rates. We find no instability for waves with wavevectors parallel or perpendicular to the direction of the injected carriers. We find that, within the small wavevector approximation, the angle between $\boldsymbol{q}$ and the direction of the injected electrons that maximizes the growth rate increases with increasing $\boldsymbol{|q|}$. We compare the range and strength of the instability in graphene to that of two and three dimensional parabolic band systems., Comment: 21 pages, 7 figures

Strain-induced deformations in graphene are predicted to give rise to large pseudomagnetic fields. We examine theoretically the case of gas-inflated bubbles to determine whether signatures of such fields are present in the local density of states. Sharp-edged bubbles are found to induce Friedel-type oscillations which can envelope pseudo-Landau level features in certain regions of the bubble. However, bubbles which minimise interference effects are also unsuitable for pseudo-Landau level formation due to more spatially varying field profiles., Comment: Submitted to Edison19

We theoretically examine the role of Kerr nonlinearities for graphene plasmonics in nanostructures, specifically in nanoribbons. The nonlinear Kerr interaction is included semiclassically in the intraband approximation. The resulting electromagnetic problem is solved numerically by self-consistent iteration with linear steps using a real-space discretization. We derive a simple approximation for the resonance shifts in general graphene nanostructures, and obtain excellent agreement with numerics for moderately high field strengths. Near plasmonic resonances the nonlinearities are strongly enhanced due to field enhancement, and the total nonlinearity is significantly affected by the field inhomogeneity of the plasmonic excitation. Finally, we discuss the emergence of a plasmonic bistability which exists for frequencies redshifted relative to the linear resonance. Our results offer new insights into the role of nonlinear interaction in nanostructured graphene and paves the way for experimental investigation., Comment: 5 pages, 3 figures, and additional supplemental material