Topological insulator in the core of the superconducting vortex in graphene
Igor F. Herbut
备注：
Four revtex pages. New discussion on competition between core orders, extension to finite-T added, typos corrected, new references, streamlined presentation. Published version
The core of the vortex in a general superconducting order parameter in graphene is argued to be ordered, with the possible order parameters forming the algebra U(1) X Cl(3), where Cl(3) is the three dimensional Clifford algebra. A sufficiently strong Zeeman coupling of the magnetic field of the vortex to the electron spin breaks the degeneracy in the core in favor of the anomalous quantum Hall state. I consider a variety of superconducting condensates on the honeycomb lattice and demonstrate the surprising universality of this result. A way to experimentally determine the outcome of the possible competition between different types of orders in the core is proposed.
The Dirac mass-vortex at the surface of a topological insulator or in graphene is considered. Within the linear approximation for the vortex amplitude's radial dependence, the spectrum is a series of degenerate bound states, which can be classified by a set of accidental SU(2) and supersymmetry generators (I. F. Herbut and C.-K. Lu, Phys. Rev. B 83 125412 (2011)). Here we discuss further the properties and manifestations of the supersymmetry of the vortex Hamiltonian, and point out some interesting analogies to the Runge-Lenz-Pauli vector in the non-relativistic hydrogen atom. Symmetry breakin…
We show that the intrinsic chiral $d_{x^2-y^2} \pm id_{xy}$-wave superconducting pairing in doped graphene is significantly strengthened in the core region of a doubly quantized s-wave superconducting vortex produced in a graphene-superconductor hybrid structure. The chiral d-wave state is induced by proximity effect, which transfers the center-of-mass angular momentum of the s-wave vortex to the orbital angular momentum of the chiral d-wave Cooper pairs. The proximity effect is enhanced by the circular geometry of the vortex and we find a $[1 + (T-T_{c,J})^2]^{-1}$ temperature dependence for …
Using Ginzburg-Landau approach we show that the strain of the nematic superconductor can generate a specific (nematic) vorticity. In the case of doped topological insulators that vorticity forms a spin vortex. We find two types of topologically different spin vortices that either enhance (type I) or suppress (type II) superconductivity far from the vortex core. We apply Bogoliubov-de Geunnes equations to study electronic states in the nematic superconductor with spin vortices. We find that in the case of the vortex of type I, zero-energy states are localized near the vortex core. These states …
The interplay of time-reversal and $n$-fold rotation symmetries ($n=2,4,6$) is known to bring a new class of topological crystalline insulators (TCIs) having $n$ surface Dirac cones due to surface rotation anomaly. We show that the proximity-induced $s$-wave superconductivity on the surface of these TCIs yields a topological superconducting phase in which two Majorana zero modes are bound to a vortex, and that $n$-fold rotation symmetry ($n=2,4,6$) enriches the topological classification of a superconducting vortex from $\mathbb{Z}_2$ to $\mathbb{Z}_2\times\mathbb{Z}_2$. Using a model of a thr…
We investigate scattering of the topological surface state of a three-dimensional time-reversal invariant topological insulator when graphene is deposited on the topological-insulator surface. Specifically, we consider the (111) surface of a Bi$_2$Se$_3$-like topological insulator. We present a low-energy model for the bulk graphene-topological insulator heterostructure and we calculate the transmission probability at zigzag and armchair edges of the deposited graphene, and the conductance through graphene nanoribbon barriers and show that its features can be understood from antiresonances in …
We show that the existence of a pair of zero-energy modes bound to a vortex carrying a pi-flux is a generic feature of the topologically non-trivial phase of the M-B model, which was introduced to describe the topological band insulator in HgTe quantum wells. We explicitly find the form of the zero-energy states of the corresponding Dirac equation, which contains a novel momentum-dependent mass term and describes a generic topological transition in a band insulator. The obtained modes are exponentially localized in the vortex-core, with the dependence of characteristic length on the parameters…
We construct the general extension of the four-dimensional Jackiw-Rossi-Dirac Hamiltonian that preserves the antilinear reflection symmetry between the positive and negative energy eigenstates. Among other systems, the resulting Hamiltonian describes the s-wave superconducting vortex at the surface of the topological insulator, at a finite chemical potential, and in the presence of both Zeeman and orbital couplings to the external magnetic field. Here we find that the bound zero-mode exists only when the Zeeman term is below a critical value. Other physical realizations pertaining to graphene …
We investigate magnetoplasmon dynamics localized on the edges of graphene vortex Hall fluid. The vortex matter captures an anomalous term that causes vortex localization near fluid boundary and creates a double boundary layer, $Δ_0\propto (β-1)\ell_B$ with $β$ being filling factor. The term also has qualitative effect on resonant excitations of edge magnetoplasmons. We found that for sharp edges under experimental conditions, graphene Edge Magnetoplasmon (EMP) resonances have similar behavior as in recent experiments. Gradual distinctions arise for smooth edges in the presence of the anomalous…
Magnetic-Field-Driven Insulator-Superconductor Transition in Rhombohedral Graphene
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；National Institute for Material Sciences（国立材料研究所）；Hefei National Laboratory（合肥国家实验室）；Interdisciplinary Institute of Light-Element Quantum Materials and Research Center for Light-Element Advanced Materials, Peking University（北京大学轻元素量子材料交叉研究所及轻元素先进材料研究中心）；Collaborative Innovation Center of Quantum Matter, Beijing（北京量子物质协同创新中心）
Following the recent realization of an artificial version of Graphene in the electronic surface states of copper with judiciously placed carbon monoxide molecules inducing the honeycomb lattice symmetry (K. K. Gomes et al., Nature 483, 306 (2012)), we demonstrate that these can be used to realize a vortex in a Kekule texture of the honeycomb lattice. The Kekule texture is mathematically analogous to a superconducting order parameter, opening a spectral gap in the massless Dirac point spectrum of the Graphene structure. The core of a vortex in the texture order parameter, supports subgap states…
We investigate mesoscopic Josephson junction arrays created by patterning superconducting disks on monolayer graphene, concentrating on the high-$T/T_c$ regime of these devices and the phenomena which contribute to the superconducting glass state in diffusive arrays. We observe features in the magnetoconductance at rational fractions of flux quanta per array unit cell, which we attribute to the formation of flux-quantized vortices. The applied fields at which the features occur are well described by Ginzburg-Landau simulations that take into account the number of unit cells in the array. We fi…
In two-dimensional (2D) twisted bilayers, the van der Waals (vdW) interlayer interaction introduces atomic-scale reconstruction at interface by locally rotating lattice to form strain-field vortex networks in their moiré superlattice. However, direct imaging the tiny local lattice rotation of the strain-field vortex requires extremely high spatial resolution and is an outstanding challenge in experiment. Here, a topmost small-period graphene moiré pattern is introduced to magnify sub-Angstrom distortions of the lattice and tiny local lattice rotation in underlying twisted bilayer graphene (TBG…
We study temperature effect on anomalous viscosity of Graphene Hall fluid within quantum many-vortex hydrodynamics. The commonly observed filling fractions, $ν$ in the range $0 < ν< 2$ is considered. An expression for anomalous viscosity dependent on a geometric parameter-Hall expansion coefficient, is obtained at finite temperatures. It arises from strained induced pseudo-magnetic field in addition to an anomalous term in vortex velocity, which is responsible for re-normalization of vortex-vortex interactions. We observed that both terms greatly modify the anomalous viscosity as well as an en…
We study the bound state spectrum and the conditions for entering a supercritical regime in graphene with strong intrinsic and Rashba spin-orbit interactions within the topological insulator phase. Explicit results are provided for a disk-shaped potential well and for the Coulomb center problem
In this paper we consider modification of electronic properties of graphene-based topological insulator in the presence of wedge disclination and magnetic field by adopting the Kane-Mele model with intrinsic spin-orbit coupling. Using the properly defined Dirac-Weyl equation for this system, an exact solution for the Landau levels is obtained. The influence of the topological defect on the evolution of Landau levels is discussed.
While graphene is a semi-metal, recently synthesized hydrogenated graphene called graphane, turns out to be an insulator. We have probed the metal insulator Transition in graphene-graphane system within the framework of density functional theory. By analysing the evolutionary trends in the electronic structure for fifteen different hydrogen concentrations on graphene, we unravel some novel features of this transition. As hydrogen coverage increases the semi-metal turns first into a metal, then transforms into an insulator. The metallic phase is spatially inhomogeneous in the sense, it contains…
The strong Coulomb interaction between massless Dirac fermions can drive a semimetal-insulator transition in single-layer graphene by dynamically generating an excitonic fermion gap. There is a critical interaction strength $λ_c$ that separates the semimetal phase from the insulator phase. We calculate the specific heat and susceptibility of the system and show that they exhibit distinct behaviors in the semimetal and insulator phases.
The control of a ferromagnet's magnetization via only electric currents requires the efficient generation of current-driven spin-torques. In magnetic structures based on topological insulators (TIs) current-induced spin-orbit torques can be generated. Here we show that the addition of graphene, or bilayer graphene, to a TI-based magnetic structure greatly enhances the current-induced spin density accumulation and significantly reduces the amount of power dissipated. We find that this enhancement can be as high as a factor of 100, giving rise to a giant Edelstein effect. Such a large enhancemen…
We formulate a continuum model to study the low-energy electronic structure of heterostructures formed by graphene on a strong three-dimensional topological insulator (TI) for the case of both commensurate and incommensurate stacking. The incommensurability can be due to a twist angle between graphene and the TI surface or a lattice mismatch between the two systems. We find that the proximity of the TI induces in graphene a strong enhancement of the spin-orbit coupling that can be tuned via the twist angle.
The two-dimensional electron systems in graphene and in topological insulators are described by massless Dirac equations. Although the two systems have similar Hamiltonians, they are polar opposites in terms of spin-orbit coupling strength. We briefly review the status of efforts to achieve long spin relaxation times in graphene with its weak spin-orbit coupling, and to achieve large current-induced spin polarizations in topological-insulator surface states that have strong spin-orbit coupling. We also comment on differences between the magnetic responses and dilute-moment coupling properties …
The electronic structures of graphene systems and topological insulators have closely-related features, such as quantized Berry phase and zero-energy edge states. The reason for these analogies is that in both systems there are two relevant orbital bands, which generate the pseudo-spin degree of freedom, and, less obviously, there is a correspondence between the valley degree of freedom in graphene and electron spin in topological insulators. Despite the similarities, there are also several important distinctions, both for the bulk topological properties and for their implications for the edge…
We determine the structure of band and gaps in graphene encapsulated in hexagonal boron nitride and subjected to magnetic field of Abrikosov lattice of vortices in the underlying superconducting film. The spectrum features one non-dispersive magnetic miniband at zero energy, separated by the largest gaps in the miniband spectrum from a pair of minibands resembling slightly broadened first Landau levels in graphene, suggesting the persistence of $ν= \pm 2$ quantum Hall effect states. Also, we identify occasional merging point of magnetic minibands which feature Dirac-type dispersion at the cons…
Laboratory for Solid State Physics, ETH Zurich（苏黎世联邦理工学院固体物理实验室）；Quantum Center, ETH Zurich（苏黎世联邦理工学院量子中心）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（国家材料科学研究所材料纳米架构研究中心）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（国家材料科学研究所电子与光学材料研究中心）；Institute for Theoretical Physics, ETH Zurich（苏黎世联邦理工学院理论物理研究所）
While the experimental progress on three dimensional topological insulators is rapid, the development of their two dimensional counterparts has been comparatively slow, despite their technological promise. The main reason is materials challenges of the to date only realizations of two-dimensional topological insulators, in semiconductor quantum wells. Here we identify a two dimensional topological insulator in a material which does not face similar challenges and which is by now most widely available and well-charaterized: graphene. For certain commensurate interlayer twists graphene multilaye…
Topological insulators (TIs) having intrinsic or proximity-coupled s-wave superconductivity host Majorana zero modes (MZMs) at the ends of vortex lines. The MZMs survive up to a critical doping of the TI at which there is a vortex phase transition that eliminates the MZMs. In this work, we show that the phenomenology in higher-order topological insulators (HOTIs) can be qualitatively distinct. In particular, we find two distinct features. (i) We find that vortices placed on the gapped (side) surfaces of the HOTI, exhibit a pair of phase transitions as a function of doping. The first transition…
Majorana fermions have been intensively studied in recent years for their importance to both fundamental science and potential applications in topological quantum computing1,2. Majorana fermions are predicted to exist in a vortex core of superconducting topological insulators3. However, they are extremely difficult to be distinguished experimentally from other quasiparticle states for the tiny energy difference between Majorana fermions and these states, which is beyond the energy resolution of most available techniques. Here, we overcome the problem by systematically investigating the spatial…
The characteristics of tunnel junctions formed between n- and p-doped graphene are investigated theoretically. The single-particle tunnel current that flows between the two-dimensional electronic states of the graphene (2D-2D tunneling) is evaluated. At a voltage bias such that the Dirac points of the two electrodes are aligned, a large resonant current peak is produced. The magnitude and width of this peak is computed, and its use for devices is discussed. The influence of both rotational alignment of the graphene electrodes and structural perfection of the graphene is discussed.
Surface plasmons in graphene may provide an attractive alternative to noble-metal plasmons due to their tighter confinement, peculiar dispersion, and longer propagation distance. We present theoretical studies of the nonlinear difference frequency generation of terahertz surface plasmon modes supported by two-dimensional layers of massless Dirac electrons, which includes graphene and surface states in topological insulators. Our results demonstrate strong enhancement of the DFG efficiency near the plasmon resonance and the feasibility of phase-matched nonlinear generation of plasmons over a br…
The low energy physics of both graphene and surface states of three-dimensional topological insulators is described by gapless Dirac fermions with linear dispersion. In this work, we predict the emergence of a "heavy" Dirac fermion in a graphene/topological insulator hetero-junction, where the linear term almost vanishes and the corresponding energy dispersion becomes highly non-linear. By combining {\it ab initio} calculations and an effective low-energy model, we show explicitly how strong hybridization between Dirac fermions in graphene and the surface states of topological insulators can r…
We propose realizing the quantum anomalous Hall effect by proximity coupling graphene to an antiferromagnetic insulator that provides both broken time-reversal symmetry and spin-orbit coupling. We illustrate our idea by performing ab initio calculations for graphene adsorbed on the (111) surface of BiFeO3. In this case, we find that the proximity-induced exchange field in graphene is about 70 meV, and that a topologically nontrivial band gap is opened by Rashba spin-orbit coupling. The size of the gap depends on the separation between the graphene and the thin film substrate, which can be tune…
The question of whether electron-electron interactions can drive a metal to insulator transition in graphene under realistic experimental conditions is addressed. Using three representative methods to calculate the effective long-range Coulomb interaction between $π$-electrons in graphene and solving for the ground state using quantum Monte Carlo methods, we argue that without strain, graphene remains metallic and changing the substrate from SiO$_2$ to suspended samples hardly makes any difference. In contrast, applying a rather large -- but experimentally realistic -- uniform and isotropic st…
We establish the correspondence between the fractional charge bound to a vortex in a textured lattice and the relevant bulk band topology in two-dimensional (2D) topological crystalline insulators. As a representative example, we consider the Kekule textured graphene whose bulk band topology is characterized by a 2D $\mathbb{Z}_{2}$ topological invariant $ν_{\rm 2D}$ protected by inversion symmetry. The fractional charge localized at a vortex in the Kekule texture is shown to be related to the change in the bulk topological invariant $ν_{\rm 2D}$ around the vortex, as in the case of the Su-Sch…
Tunable and highly reproducible metal-insulator transitions have been observed in bilayer graphene upon thermal annealing at 400 K under high vacuum conditions. Before annealing, the sample is metallic in the whole temperature regime of study. Upon annealing, the conductivity changes from metallic to that of an insulator and the transition temperature is a function of annealing time. The pristine metallic state can be reinstated by exposing to air thereby inducing changes in the electronic properties by adsorbing water vapor, which makes graphene a technologically promising material for sensor…
We present numerical and analytical results for the optical and acoustic plasmon collective modes of coupled massless-Dirac two-dimensional electron systems. Our results apply to topological insulator (TI) thin films and to two graphene sheets separated by a thin dielectric barrier layer. We find that because of strong bulk dielectric screening TI acoustic modes are locked to the top of the particle-hole continuum and therefore probably unobservable.
Zero energy states in the Dirac spectrum with U(1) symmetric massive vortices of various underlying insulating orders in strained graphene are constructed in the presence of the magnetic field. An easy plane vortex of antiferromagnet and quantum spin Hall orders host two zero energy states, however, with two different length scales. Such inequivalent zero modes can lead to oscillatory charge and magnetization, and their usual quantizations get restored only far from the vortex core. Otherwise, these zero modes can be delocalized from each other by tuning the mutual strength of two fields. One …
We compute the renormalization group flow of the long-ranged electron-electron interaction at the Gross-Neveu quantum critical point between the semimetal and the excitonic insulator in graphene, perturbatively in the small parameter $ε=d-1$, with $d$ as the spatial dimension. The $O(ε)$ correction to the usual beta-function makes the long-range interaction only more irrelevant at the critical than at the Gaussian fixed point. A weak long-range tail of the Coulomb interaction is found to be marginally irrelevant also in arbitrary dimension when the number of Dirac fermions is large. Its ultima…
The quantum Hall effect in a single-layer graphene sample is studied in strong magnetic fields up to 28 T. Our measurements reveal the existence of a metal- insulator transition from filling factor $ν=-2$ to $ν=0$. The value of the universal scaling exponent is found to be $κ=0.57 $ in graphene and therefore in a truly two-dimensional system. This value of $κ$ is in agreement with the accepted universal value for the plateau-insulator transitions in standard quasi two-dimensional electron and hole gases.
Exact stationary solutions of the electron-photon Dirac equation are obtained to describe the strong interaction between massless Dirac fermions in graphene and circularly polarized photons. It follows from them that this interaction forms bound electron-photon states which should be considered as a kind of charged quasiparticles. The energy spectrum of the quasiparticles is of dielectric type and characterized by an energy gap between the valence and conductivity bands. Therefore the electron-photon interaction results in metal-insulator transition in graphene. The stationary energy gap, indu…
Higher-order topological insulators are newly proposed topological phases of matter, whose bulk topology manifests as localized modes at two- or higher-dimensional lower boundaries. In this work, we propose the twisted bilayer graphenes with large angles as higher-order topological insulators, hosting topological corner charges. At large commensurate angles, the intervalley scattering opens up the bulk gap and the corner states occur at half filling. Based on both first-principles calculations and analytic analysis, we show the striking results that the emergence of the corner states do not de…
Graphene-based materials show promise for spintronic applications due to their potentially large spin coherence length. On the other hand, because of their small intrinsic spin-orbit interaction, an external magnetic source is desirable in order to perform spin manipulation. Because of the flat nature of graphene, the proximity interaction with a ferromagnetic insulator (FI) surface seems a natural way to introduce magnetic properties into graphene. Exploiting the peculiar electronic properties of bilayer graphene coupled with FIs, we show that it is possible to devise very efficient gate-tuna…
In this paper we investigate quasiparticles in graphene-based topological insulator with a wedge disclination in the presence of a uniform magnetic field. In particular, we consider a massive spinless model. The Landau levels are analytically found for the described system. We show that the Landau levels are lifted for a specific range of the parameter ν. In addition, we also show that, for appropriate parameter values, one finds gapless and gapped states.
The generation of highly-confined plasmons through far-field optical illumination appears to be impractical for technological applications due to their large energy-momentum mismatch with external light. Electrical generation of plasmons offers a possible solution to this problem, although its performance depends on a careful choice of material and geometrical parameters. Here we theoretically investigate graphene-based structures and show in particular the very different performance between (i) two layers of graphene separated by a dielectric and (ii) metal$|$insulator$|$graphene sandwiches a…
Heterostructures of Dirac materials such as graphene and topological insulators provide interesting platforms to explore exotic quantum states of electrons in solids. Here we study the electronic structure of graphene-Sb2Te3 heterostructure using density functional theory and tight-binding methods. We show that the epitaxial graphene on Sb2Te3 turns into quantum spin-Hall phase due to its proximity to the topological insulating Sb2Te3. It is found that the epitaxial graphene develops a giant spin-orbit gap of about ~20 meV, which is about three orders of magnitude larger than that of pristine …
Further development of the field of all-electric spintronics requires the successful integration of spin transport channels with spin injector/generator elements. While with the advent of graphene and related 2D materials high performance spin channel materials are available, the use of nanostructured spin generators remains a major challenge. Especially promising for the latter purpose are 3D topological insulators, whose 2D surface states host massless Dirac fermions with spin-momentum locking. Here, we demonstrate injection of spin-polarized current from a topological insulator into graphen…
The recent developments in the emerging field of plasmonics in graphene and other Dirac systems are reviewed and a comprehensive introduction to the standard models and techniques is given. In particular, we discuss intrinsic plasmon excitations of single and bilayer graphene via hydrodynamic equations and the random phase approximation, but also comment on double and multilayer structures. Additionally, we address Dirac systems in the retardation limit and also with large spin-orbit coupling including topological insulators. Finally, we summarize basic properties of the charge, current and ph…
Enhancing the spin-orbit interaction in graphene, via proximity effects with topological insulators, could create a novel 2D system that combines nontrivial spin textures with high electron mobility. In order to engineer practical spintronics applications with such graphene/topological insulator (Gr/TI) heterostructures, an understanding of the hybrid spin-dependent properties is essential. {However to date, despite the large number of experimental studies on Gr/TI heterostructures reporting a great variety of remarkable (spin) transport phenomena, little is known about the true nature of the …
By coating a three-dimensional topological insulator (TI) with a ferromagnetic film supporting an in-plane magnetic vortex, one breaks the time-reversal symmetry (TRS) without generating a mass gap. It rather yields electronic states bound to the vortex center which have different probabilities associated with each spin mode. In addition, its associate current (around the vortex center) is partially polarized with an energy gap separating the most excited bound state from the scattered ones. Charged zero-modes also appear as fully polarized modes localized near the vortex center. From the magn…
We study the electronic properties of Möbius graphene strip with a zigzag edge. We show that such graphene strip behaves as a topological insulator with a gapped bulk and a robust metallic surface, which enjoys some features due to its nontrivial topology of the spatial configuration, such as the existence of edge states and the non-Abelian induced gauge field. We predict that the topological properties of the Möbius graphene strip can be experimentally displayed by the destructive interference in the transmission spectrum, and the robustness of edge states under certain perturbations.
We introduce and analyze a model that sheds light on the interplay between correlated insulating states, superconductivity, and flavor-symmetry breaking in magic angle twisted bilayer graphene. Using a variational mean-field theory, we determine the normal-state phase diagram of our model as a function of the band filling. The model features robust insulators at even integer fillings, occasional weaker insulators at odd integer fillings, and a pattern of flavor-symmetry breaking at non-integer fillings. Adding a phonon-mediated inter-valley retarded attractive interaction, we obtain strong-cou…
When bilayer graphene is rotationally faulted to an angle $θ\approx 1.1^\circ$, theory predicts the formation of a flat electronic band and correlated insulating, superconducting, and ferromagnetic states have all been observed at partial band filling. The proximity of superconductivity to correlated insulators has suggested a close relationship between these states, reminiscent of the cuprates where superconductivity arises by doping a Mott insulator. Here, we show that superconductivity can appear without correlated insulating states. While both superconductivity and correlated insulating be…
Model description of patterns of atomic displacements in twisted bilayer systems has been proposed. The model is based on the consideration of several dislocation ensembles, employing a language that is widely used for grain boundaries and film/substrate systems. We show that three ensembles of parallel screw dislocations are sufficient both to describe the rotation of the layers as a whole, and for the vortex-like displacements resulting from elastic relaxation. The results give a clear explanation of the observed features of the structural state such as vortices, accompanied by alternating s…
We show that gated bilayer graphene hosts a strong topological insulator (TI) phase in the presence of Rashba spin-orbit (SO) coupling. We find that gated bilayer graphene under preserved time-reversal symmetry is a quantum valley Hall insulator for small Rashba SO coupling $λ_{\mathrm{R}}$, and transitions to a strong TI when $λ_{\mathrm{R}} > \sqrt{U^2+t_\bot^2}$, where $U$ and $t_\bot$ are respectively the interlayer potential and tunneling energy. Different from a conventional quantum spin Hall state, the edge modes of our strong TI phase exhibit both spin and valley filtering, and thus sh…
The field theory of the semimetal-superconductor quantum phase transition for graphene and surface states of topological insulators is presented. The Lagrangian possesses the global U(1) symmetry, with the self-interacting complex bosonic order-parameter and the massless Dirac fermions coupled through a Yukawa term. The same theory also governs the quantum critical behavior of graphene near the transition towards the bond-density-wave (Kekule) insulator. The local U(1) gauged version of the theory which describes the quantum semimetal-superconductor transition in the ultimate critical regime i…
Recent experiments have demonstrated that neutral graphene sheets have an insulating ground state in the presence of an external magnetic field. We report on a $π$-band tight-binding-model Hartree-Fock calculation which examines the competition between distinct candidate insulating ground states. We conclude that for graphene sheets on substrates the ground state is most likely a field-induced spin-density-wave, and that a charge density wave state is possible for suspended samples. Neither of these density-wave states support gapless edge excitations.
Graphene ranks highly as a possible material for future high-speed and flexible electronics. Current fabrication routes, which rely on metal substrates, require post synthesis transfer of the graphene onto a Si wafer or in the case of epitaxial growth on SiC, temperatures above 1000 °C are required. Both the handling difficulty and high temperatures are not best suited to present day silicon technology. We report a facile chemical vapor deposition approach in which nano-graphene and few layer graphene is directly formed over magnesium oxide and can be achieved at temperatures as low as 325 °C.
Prototypical three-dimensional topological insulators of the Bi$_2$Se$_3$ family provide a beautiful example of the appearance of the surface states inside the bulk band gap caused by spin-orbit coupling-induced topology. The surface states are protected against back scattering by time reversal symmetry, and exhibit spin-momentum locking whereby the electron spin is polarized perpendicular to the momentum, typically in the plane of the surface. On the other hand, graphene is a prototypical two-dimensional material, with negligible spin-orbit coupling. When graphene is placed on the surface of …
