Klein quantum dot (KQD) refers to a QD with quasi-bound states and a finite trapping time, which has been observed in experiments focused on graphene recently. In this paper, we develop a numerical method to calculate local density of states (LDOS) of KQD and apply it to monolayer graphene. By investigating the variation of LDOS in a circular quantum dot, we obtain the dependence of the quasi-bound states on the quantum dot parameters (e.g. the electron energy, radius, confined potential, etc). Based on these results, not only can we well explain the experimental phenomena, but also demonstrate how quasi-bound states turn to real bound states when intervalley scattering is taken into considered. We further study the evolution of the LDOS for KQD varying from a circle shape to a semicircle shape, which reveals the mechanism of whispering gallery mode on the quasi-bound states.
Klein tunneling in gapless bilayer graphene, perfect reflection of electrons injecting normal to a pn junction, is expected to disappear in the presence of energy band gap induced by external gates. We theoretically show that the Klein effect still exists in gapped bilayer graphene, provided that the gaps in the n and p regions are balanced such that the polarization of electron pseudospin has the same normal component to the bilayer plane in the regions. We attribute the Klein effect to Berry phase $π$ (rather than the conventional value $2 π$ of bilayer graphene) and to electron-hole and tim…
Hydrogenated graphene edges are assumed to be either armchair, zigzag or a combination of the two. We show that the zigzag is not the most stable fully hydrogenated structure along the <2-1-10> direction. Instead hydrogenated Klein and reconstructed Klein based edges are found to be energetically more favourable, with stabilities approaching that of armchair edges. These new structures "unify" graphene edge topology, the most stable flat hydrogenated graphene edges always consisting of pairwise bonded C2H4 edge groups, irrespective the edge orientation. When edge rippling is included, CH3 edge…
We report a theoretical/experimental study of current-voltage characteristics (I-V) of graphene devices near the Dirac point. The I-V can be described by a power law (I \propto V^α, with 1< α<= 1.5). The exponent is higher when the mobility is lower. This superlinear I-V is interpreted in terms of the interplay between Zener-Klein transport, that is tunneling between different energy bands, and defect scattering. Surprisingly, the Zener-Klein tunneling is made visible by the presence of defects.
We have carried out first-principles calculations on electronic properties of graphene quantum dots embedded in hexagonal boron nitride monolayer sheets. The calculations with density functional theory show that the band gaps of quantum dots are determined by the quantum confinement effects and the hybridization of π orbitals from B, N and C atoms. The energy states near the Fermi level are found to be strongly localized within and in the vicinity of the quantum dots.
Massless Dirac particles cannot be confined by an electrostatic potential. This is a problem for making graphene quantum dots but confinement can be achieved with a magnetic field and here, general conditions for confined and deconfined states are derived. There is a class of potentials for which the character of the state can be controlled at will. Then a confinement-deconfinement transition occurs which allows the Klein paradox to be probed experimentally in graphene dots.
Using ab initio methods we have investigated the fluorination of graphene and find that different stoichiometric phases can be formed without a nucleation barrier, with the complete "2D-Teflon" CF phase being thermodynamically most stable. The fluorinated graphene is an insulator and turns out to be a perfect matrix-host for patterning nanoroads and quantum dots of pristine graphene. The electronic and magnetic properties of the nanoroads can be tuned by varying the edge orientation and width. The energy gaps between the highest occupied and lowest unoccupied molecular orbitals (HOMO-LUMO) of …
Electrons in graphene, behaving as massless relativistic Dirac particles, provide a new perspective on the relation between condensed matter and high-energy physics. We discuss atomic collapse, a novel state of superheavy atoms stripped of their discrete energy levels, which are transformed into resonant states. Charge impurities in graphene provide a convenient condensed matter system in which this effect can be explored. Relativistic dynamics also manifests itself in another system, graphene p-n junctions. We show how the transport problem in the presence of magnetic field can be solved with…
We investigate theoretically the magnetic levels and optical properties of zigzag- and armchair-edged hexagonal graphene quantum dots (GQDs) utilizing the tight-binding method. A new bound edge state at zero energy appears for the zigzag GQDs in the absence of a magnetic field. The magnetic levels of GQDs exhibit a Hofstadter-butterfly spectrum and approach the Landau levels of two-dimensional graphene as the magnetic field increases. The optical properties are tuned by the size, the type of the edge, and the external magnetic field.
We show that in gapped bilayer graphene, quasiparticle tunneling and the corresponding Berry phase can be controlled such that it exhibits features of single layer graphene such as Klein tunneling. The Berry phase is detected by a high-quality Fabry-Pérot interferometer based on bilayer graphene. By raising the Fermi energy of the charge carriers, we find that the Berry phase can be continuously tuned from $2π$ down to $0.68π$ in gapped bilayer graphene, in contrast to the constant Berry phase of $2π$ in pristine bilayer graphene. Particularly, we observe a Berry phase of $π$, the standard val…
We study the magnetization of square and hexagonal graphene dots. It is shown that two classes of hexagonal dots have a second order phase transition at a critical Hubbard energy $U$, whoose value is similar to the one in bulk graphene, albeit the dots do not have a density of states proportional to the absolute value of the energy, relatively to the Dirac point. Furthermore, we show that a particular class of hexagonal dots having zig-zag edges, does not exhibit zero energy edge states. We also study the effect of uniaxial strain on the evolution of the magnetization of square dots, and find …
We analyse the electronic and optical properties of graphene quantum dots (GQD) using accurate \textit{ab initio} many-body $GW$ and Bethe-Salpeter calculations. We show that most pristine GQD, including structures with irregular shapes, are characterized by dark low energy singlet excitations that quench fluorescence. We rationalizqe this property by exploiting the chiral symmetry of the low energy electronic states in graphene. Edge \textit{sp}$^3$ functionalization is shown to efficiently brighten these low lying excitations by distorting the \textit{sp}$^2$ backbone planar symmetry. Such f…
Employing a combination of many-body configuration interaction method described by extended Hubbard model along with first principle calculations we predict the emergence of high oscillator strength at near-IR region which originates from the Davydov type of splitting in doped graphene quantum dots (GQD). Incorporation of strain in GQD promotes closely spaced bright states inciting for coherent excitation. Controlling the destructive interference of the functionalized nano graphene quantum states, the dark states can be tuned towards red end ensuing the system as a good candidate for photocell…
In the present work, we investigate how structural defects in graphene can change its transport properties. In particular, we show that breaking of the sublattice symmetry in a graphene monolayer overcomes the Klein effect, leading to confined states of massless Dirac fermions. Experimentally, this corresponds to chemical bonding of foreign atoms to carbon atoms, which attach themselves to preferential positions on one of the two sublattices. In addition, we consider the scattering off a tensor barrier, which describes the rotation of the honeycomb cells of a given region around an axis perpen…
Superconductivity can be induced in a normal material via the leakage of superconducting pairs of charge carriers from an adjacent superconductor. This so-called proximity effect is markedly influenced by graphene unique electronic structure, both in fundamental and technologically relevant ways. These include an unconventional form of the leakage mechanism the Andreev reflection and the potential of supercurrent modulation through electrical gating. Despite the interest of high-temperature superconductors in that context, realizations have been exclusively based on low-temperature ones. Here …
Transmission of low-energetic electrons through two-dimensional materials leads to unique scattering resonances. These resonances contribute to photoemission from occupied bands where they appear as strongly dispersive features of suppressed photoelectron intensity. Using angle-resolved photoemission we have systematically studied scattering resonances in epitaxial graphene grown on the chemically differing substrates Ir(111), Bi/Ir, Ni(111) as well as in graphene/Ir(111) nanopatterned with a superlattice of uniform Ir quantum dots. While the strength of the chemical interaction with the subst…
We analyze the bound-state spectra of mass-profile quantum dots in graphene, a system at current experimental reach. Homogeneous perpendicular magnetic fields are also considered which result in breaking the valley degeneracy. The spectra show rich features, arising from the chiral band structure of graphene and its Landau levels and we identify three different regimes depending on the ratio between the radius of the dot and the magnetic length. We further carry out a comparison with potential-well quantum dots discussed in [Recher et al, Phys. Rev. B 79, 085407 (2009)] and conclude that mass …
We introduce a generalized Hamiltonian describing not only all topological phases observed experimentally in Kekulé graphene (KekGr) but predicting also new ones. These phases show features like a quadratic band crossing point, valley splitting, or the crossing of conduction bands, typically induced by Rashba spin-orbit interactions or Zeeman fields. The electrons in KekGr behave as Dirac fermions and follow pseudo-relativistic dispersion relations with Fermi velocities, rest masses, and valley-dependent self-gating. Transitions between the topological phases can be induced by tuning these par…
Electronic properties of quantum dots (QDs) depend sensitively on their parent materials. Therefore, confined electronic states in graphene QDs (GQDs) of monolayer and Bernal-stacked bilayer graphene are quite different. Twisted bilayer graphene (TBG) is distinct from monolayer and Bernal-stacked bilayer graphene because of the new degree of freedom: twist angle. In the past few years, numerous efforts have been made to realize the GQDs of monolayer and Bernal-stacked bilayer graphene and achieved great success. Thus far, however, strategies for realizing GQDs of TBG have been elusive. Here, w…
An electrostatic quantum dot cannot be formed in monolayer graphene, because of the Klein tunnelling. However, a dot can be formed with the help of a uniform magnetic field. As shown here, a spatial modulation of the Dirac gap leads to confined states with discrete energy levels, thus defining a dot, without applying external electric and magnetic fields. Gap-induced dot states can coexist and couple with states introduced by an electrostatic potential. This property allows the region in which the resulting states are localized to be tuned with the potential.
This work analyzes carrier transport, the relaxation of non-equilibrium charge, and the electronic structure of fluorinated graphene (FG) films with graphene quantum dots (GQDs). The FG films with GQDs were fabricated by means of chemical functionalization in an aqueous solution of hydrofluoric acid. High fluctuations of potential relief inside the FG barriers have been detected in the range of up to 200 mV. A phenomenological expression that describes the dependence of the time of non-equilibrium charge emission from GQDs on quantum confinement levels and film thickness (potential barrier par…
The observation of quantum conductance oscillations in mesoscopic systems has traditionally required the confinement of the carriers to a phase space of reduced dimensionality. While electron optics such as lensing and focusing have been demonstrated experimentally, building a collimated electron interferometer in two unconfined dimensions has remained a challenge due to the difficulty of creating electrostatic barriers that are sharp on the order of the electron wavelength. Here, we report the observation of conductance oscillations in extremely narrow graphene heterostructures where a resona…
We calculate the transmission coefficient for a particle crossing a potential barrier in monolayer graphene with Rashba spin-orbit coupling and in bilayer graphene. We show that in both the cases one can go from Klein tunneling regime, characterized by perfect normal transmission, to anti-Klein tunneling regime, with perfect normal reflection, by tuning the Rashba spin-orbit coupling for a monolayer or the interplane coupling for a bilayer graphene. We show that the intermediate regime is characterized by a non-monotonic behavior with oscillations and resonances in the normal transmission ampl…
An armchair graphene ribbon switch has been designed based on the principle of the Klein paradox. The resulting switch displays an excellent on-off ratio performance. Anomalous tunneling phenomena are observed in our numerical simulations. According to our analytical results, selective tunneling rule is proposed to explain this interesting transport behavior. The switch design enriches the phenomenon of the Klein paradox and also provides a platform to study the paradox.
The band modulation of the silicene and graphene quantum dots is investigated by a first-principles method. This study includes the ordinary silicene and graphene quantum dots and the embedded quantum dots in the hydrogenated silicene and graphene. The shapes and sizes of quantum dots are recognized as important factors for the electronic properties. We studied several types of quantum dots: triangular, parallelogram, rectangular, hexagonal dots. It demonstrates the energy gap of the quantum dot can be tuned by the dot size, the larger of the dot the smaller the energy gap. Moreover, the shape…
We study by first-principles calculations a densely packed island of organic molecules (F4TCNQ) adsorbed on graphene. We find that with electron doping the island naturally forms a p-n junction in the graphene sheet. For example, a doping level of ~ 3 * 10^{13} electrons per cm^2 results in a p-n junction with 800 meV electrostatic potential barrier. Unlike in a conventional p-n junction in graphene, in the case of the junction formed by an adsorbed organic molecular island we expect that the Klein tunneling is inhibited, even without an applied external magnetic field. Here Klein tunneling is…
Higher harmonic generation in plane graphene quantum dots initiated by intense coherent radiation is investigated, using dynamical Hartree-Fock mean-field theory. A microscopic theory describing the extreme nonlinear optical response of plane graphene quantum dots is developed. The closed set of differential equations for the single-particle density matrix at the graphene quantum dots-strong laser field multiphoton interaction is solved numerically. The obtained solutions indicate the significance of the type of edge and lateral size, and bandgap and laser field strength in the high harmonic g…
We present Coulomb blockade measurements in a graphene double dot system. The coupling of the dots to the leads and between the dots can be tuned by graphene in-plane gates. The coupling is a non-monotonic function of the gate voltage. Using a purely capacitive model, we extract all relevant energy scales of the double dot system.
Whereas massless Dirac fermions in monolayer graphene exhibit Klein tunneling when passing through a potential barrier upon normal incidence, such a barrier totally reflects massive Dirac fermions in bilayer graphene due to difference in chirality. We show that, in the presence of magnetic barriers, such massive Dirac fermions can have transmission through even at normal incidence. The general consequence of this behaviour for multilayer graphene consisting of massless and massive modes are mentioned. We also briefly discuss the effect of a bias voltage on such magnetotransport.
The so-called Klein paradox - unimpeded penetration of relativistic particles through high and wide potential barriers - is one of the most exotic and counterintuitive consequences of quantum electrodynamics (QED). The phenomenon is discussed in many contexts in particle, nuclear and astro- physics but direct tests of the Klein paradox using elementary particles have so far proved impossible. Here we show that the effect can be tested in a conceptually simple condensed-matter experiment by using electrostatic barriers in single- and bi-layer graphene. Due to the chiral nature of their quasipar…
We present a theory of excitonic processes in gate controlled graphene quantum dots. The dependence of the energy gap on shape, size and edge for graphene quantum dots with up to a million atoms is predicted. Using a combination of tight-binding, Hartree-Fock and configuration interaction methods, we show that triangular graphene quantum dots with zigzag edges exhibit optical transitions simultaneously in the THz, visible and UV spectral ranges, determined by strong electron-electron and excitonic interactions. The relationship between optical properties and finite magnetic moment and charge d…
Charge carriers in single and multilayered graphene systems behave as chiral particles due to the particular lattice symmetry of the crystal. We show that the interplay between the meta-material properties of graphene multilayers and the pseudospinorial properties of the charge carriers result in the occurrence of Klein and anti-Klein tunneling for rhombohedral stacked multilayers. We derive an algebraic formula predicting the angles at which these phenomena occur and support this with numerical calculations for systems up to four layers. We present a decomposition of an arbitrarily stacked mu…
Using the coupled-mode theory in guided-wave optics and electronics, we explore a directional coupling structure composed of two parallel waveguides electrostatically induced by the split-gate technique in bulk graphene. Our results show that Klein tunneling can greatly enhance the coupling strength of the structure. By adjusting a gate voltage, the probability density of Dirac electron wave function initially in one waveguide can be completely transferred into the other waveguide within several hundred nanometers. Our findings could not only lead to functional coherent coupling devices for qu…
In this paper we analyse the electronic properties of Dirac electrons in finite-size ribbons and in circular and hexagonal quantum dots made of graphene.
We study and compare two analytic models of graphene quantum dots for calculating charge relaxation times due to electron-phonon interaction. Recently, charge relaxation processes in graphene quantum dots have been probed experimentally and here we provide a theoretical estimate of relaxations times. By comparing a model with pure edge confinement to a model with electrostatic confinement, we find that the latter features much larger relaxation times. Interestingly, relaxation times in electrostatically defined quantum dots are predicted to exceed the experimentally observed lower bound of ~10…
Graphene is characterized by chiral electronic excitations. As such it provides a perfect testing ground for the production of Klein pairs (electron/holes). If confirmed, the standard results for barrier phenomena must be reconsidered with, as a byproduct, the accumulation within the barrier of holes.
The conductance and the Fano factor in a graphene sheet in the ballistic regime are calculated. The electrostatic potential in the sheet is modeled by a trapezoid barrier, which allows to use the exact solution of the Dirac equation in a uniform electric field in the slope areas (the two lateral sides of the trapezoid). A special attention is devoted to asymmetry with respect to the sign of the gate voltage, which is connected with the difference between the Klein tunneling and the over-barrier reflection. The comparison of the developed theory with the experiment supports the conclusion that …
We study the dynamics of semiclassical electrons in (gapped) graphene in two complementary limits, i.e. in the Klein tunneling and valley Hall effect regimes, by scattering wave packets off armchair step potentials and by exposing wave packets to a uniform electric field, respectively. Our numerical wave packet simulation goes beyond semiclassical analytical approximations and standard Klein tunneling treatments and allows to study intra- and intervalley scattering processes. We find distinct Klein tunneling characteristics for low and tall steps, which include unusual Berry curvature induced …
We report on theoretical studies of transport through graphene quantum dots weakly coupled to external ferromagnetic leads. The calculations are performed by exact diagonalization of a tight-binding Hamiltonian with finite Coulomb correlations for graphene sheet and by using the real-time diagrammatic technique in the sequential and cotunneling regimes. The emphasis is put on the role of graphene flake shape and spontaneous edge magnetization in transport characteristics, such as the differential conductance, tunneling magnetoresistance (TMR) and the shot noise. It is shown that for certain sh…
We propose how to form spin qubits in graphene. A crucial requirement to achieve this goal is to find quantum dot states where the usual valley degeneracy in bulk graphene is lifted. We show that this problem can be avoided in quantum dots based on ribbons of graphene with semiconducting armchair boundaries. For such a setup, we find the energies and the exact wave functions of bound states, which are required for localized qubits. Additionally, we show that spin qubits in graphene can not only be coupled between nearest neighbor quantum dots via Heisenberg exchange interaction but also over l…
We study the conductance spectrum of graphene quantum dots, both single and multiple cases. The single electron tunneling phenomenon is investigated and the periodicity, amplitude and line shape of the Coulomb blockade oscillations at low temperatures are obtained. Further, we discuss the transport behavior when multiple dots are assembled in array and find a phase transition of conductance spectra from individual Coulomb blockade to collective Coulomb blockade.
The possibility to make 10 nm scale, and low-disorder, suspended graphene devices would open up many possibilities to study and make use of strongly coupled quantum electronics, quantum mechanics, and optics. We present a versatile method, based on the electromigration of gold-on-graphene bow-tie bridges, to fabricate low-disorder suspended graphene junctions and quantum dots with lengths ranging from 6 nm up to 55 nm. We control the length of the junctions, and shape of their gold contacts by adjusting the power at which the electromigration process is allowed to avalanche. Using carefully en…
Graphene and bilayer graphene quantum dots are promising hosts for spin qubits with long coherence times. Although recent technological improvements make it possible to confine single electrons electrostatically in bilayer graphene quantum dots, and their spin and valley texture of the single particle spectrum has been studied in detail, their relaxation dynamics remains still unexplored. Here, we report on transport through a high-frequency gate controlled single-electron bilayer graphene quantum dot. By transient current spectroscopy of single-electron spin states, we extract a lower bound o…
We study the transport through evanescent waves in graphene quantum dots of different geometries. The transmission is suppressed when the leads are attached to edges of the same majority sublattice. Otherwise, the transmission depends exponentially on the distance between leads in rectangular dots, and as a power law in circular dots. The transmission through junctions where the transmitted and reflected currents belong to the opposite valley as the incoming one depends on details of the lattice structure at distances comparable to the atomic spacing.
This is a review on graphene quantum dots and their use as a host for spin qubits. We discuss the advantages but also the challenges to use graphene quantum dots for spin qubits as compared to the more standard materials like GaAs. We start with an overview of this young and fascinating field and will then discuss gate-tunable quantum dots in detail. We calculate the bound states for three different quantum dot architectures where a bulk gap allows for confinement via electrostatic fields: (i) graphene nanoribbons with armchair boundary, (ii) a disc in single-layer graphene, and (iii) a disc i…
Graphene quantum dots are considered as promising alternatives to quantum dots in III-V semiconductors, e.g., for the use as spin qubits due to their consistency made of light atoms including spin-free nuclei which both imply relatively long spin decoherene times. However, this potential has not been realized in experiments so far, most likely, due to a missing control of the edge configurations of the quantum dots. Thus, a more fundamental investigation of Graphene quantum dots appears to be necessary including a full control of the wave function properties most favorably during transport spe…
The hybridization of $σ$ and $π$ orbitals of carbon atoms in graphene depends on the surface curvature. Considering a single junction between flat and rippled graphene subsystems, it is found an accumulation of charge in the rippled subsystem due to Klein penetration phenomenon that gives rise to n-p junction. Using this fact, we show that the momentum distribution of electrons in ballisitically propagating beam can be selective without a waveguide, or external electric, and/or magnetic fields in graphene strip under experimentally feasible one-dimensional periodic potential. Such a potential …
Graphene electrons feature a pair of massless Dirac cones of opposite pseudospin chirality at two valleys. Klein tunneling refers to the intriguing capability of these chiral electrons to penetrate through high and wide potential barrier. The two valleys have been treated independently in the literature, where time reversal symmetry dictates that neither the normal incidence transmission nor the angle-averaged one can have any valley polarization. Here we show that, when intervalley scattering by barrier is accounted, graphene electrons normally incident at a superlattice barrier can experienc…
We suggest a simple approach to calculate the local density of states that effectively applies to any structure created by an axially symmetric potential on a continuous graphene sheet such as circular graphene quantum dots or rings. Calculations performed for the graphene quantum dot studied in a recent scanning tunneling microscopy measurement [{\sl Gutierrez et al. Nat. Phys. \textbf{12}, 1069--1075 (2016)}] show an excellent experimental-theoretical agreement.
We present graphene quantum dots endowed with addition energies as large as 1.6 eV, fabricated by the controlled rupture of a graphene sheet subjected to a large electron current in air. The size of the quantum dot islands is estimated to be in the 1 nm range. The large addition energies allow for Coulomb blockade at room temperature, with possible application to single-electron devices.
We present a theory of quantum-coherent transport through a lateral p-n-p structure in graphene, which fully accounts for the interference of forward and backward scattering on the p-n interfaces. The backreflection amplitude changes sign at zero incidence angle because of the Klein phenomenon, adding a phase $π$ to the interference fringes. The contributions of the two p-n interfaces to the phase of the interference cancel with each other at zero magnetic field, but become imbalanced at a finite field. The resulting half a period shift in the Fabry-Perot fringe pattern, induced by a relativel…
Tunnelling of electrons in graphene-based junctions is studied theoretically. Graphene is assumed to be deposited either directly on a ferromagnetic insulator or on a few atomic layers of boron nitride which separate graphene from a metallic ferromagnetic substrate. Such junctions can be formed by appropriate external gating of the corresponding system. To describe low-energy electronic states near the Dirac points, certain effective Hamiltonians available in the relevant literature are used. These Hamiltonians include staggered potential and exchange interaction due to ferromagnetic substrate…
The Klein paradox, first introduced in relation to chiral tunneling, is also manifested in the study of bound-states in single-layer graphene with a 1D square-well potential. We derive analytic (and numerical) solutions for bound-state wavefunctions, in the absence and in the presence of an external transverse magnetic field, and calculate the corresponding dipole transition rates, which can be probed by photon absorption experiments. The role of parity and time-reversal symmetries is briefly discussed. Our results are also relevant for the physics of bound states of light in periodic optical …
We present electronic structure and quantum transport calculations that predict conducting channels induced in graphene quantum dots by lines of adsorbed hydrogen atoms to function as highly efficient, experimentally realizable valley filters, accumulators and switches. The underlying physics is a novel property of graphene Dirac point resonances (DPRs) that is revealed here, namely, that an electric current passing through a DPR-mediated conducting channel in a given direction is carried by electrons of em only one of the two graphene valleys. Our predictions apply to lines of hydrogen atoms …
We present the results of ab-initio density functional theory based calculations of the stability and reconstruction of zigzag edges in triangular graphene quantum dots. We show that, while the reconstructed pentagon-heptagon zigzag edge structure is more stable in the absence of hydrogen, ideal zigzag edges are energetically favored by hydrogen passivation. Zero-energy band exists in both structures when passivated by hydrogen, however in case of pentagon-heptagon zigzag, this band is found to have stronger dispersion, leading to the loss of net magnetization.
Within the Landauer transport formalism we demonstrate that conductance zeroes are possible in bipartite systems at half-filling when leads are contacted to different sublattice sites. In particular, we investigate the application of this theory to graphene quantum dots with leads in the armchair configuration. The obtained conductance cancellation is robust in the presence of any single-site impurity.
