We consider the Ising phase of the antiferromagnetic XXZ Heisenberg chain on a finite-size lattic... more We consider the Ising phase of the antiferromagnetic XXZ Heisenberg chain on a finite-size lattice with N sites. We compute the large N behavior of the spin stiffness, obtaining the correlation length ξ. We use our results to discuss the scaling behavior of metal-insulator transitions in 1D systems, taking into account the mapping between the XXZ Heisenberg chain and the spinless fermion model and known results for the Hubbard model. We study the scaling properties of both the Hubbard model and the XXZ Heisenberg chain, by solving numerically the Bethe Ansatz equations. We find that for some range of values of ξ/N the scaling behavior may be observed for the Hubbard model but not for the XXZ Heisenserg chain. We show how ξ can be obtained from the scaling properties of the spin stiffness for small system sizes. This method can be applied to models having not an exact solution, illuminating their transport properties.
Core tip: While intravenous thrombolysis has gained wide acceptance as a major breakthrough for t... more Core tip: While intravenous thrombolysis has gained wide acceptance as a major breakthrough for the acute treatment of stroke, interventional and diagnostic neuroradiology tools have also evolved at a very high rate, providing us with very sophisticated techniques to demonstrate brain tissue damage and revascularization techniques. However, these methods have not been evaluated properly until recently and have been adopted quickly by part of the clinical neuroscience community. A number of recent studies question the impact of these techniques.
As the thinnest atomic membrane, graphene presents an opportunity to combine geometry, elasticity... more As the thinnest atomic membrane, graphene presents an opportunity to combine geometry, elasticity and electronics at the limits of their validity. The availability of reliable atomistic potentials for graphene allows unprecedented precise simulations of the mechanical response of atomic membranes. Here we describe the transport and electronic structure in the neighbourhood of conical singularities, the elementary excitations of the ubiquitous wrinkled and crumpled graphene that occur in non-epitaxial suspended samples where shear stresses are unavoidable. We use a combination of atomistic mechanical simulations, analytical geometry and transport calculations in curved graphene, and exact diagonalization of the electronic spectrum to calculate the effects of geometry on electronic structure, transport and mobility in suspended samples. We also point out how the geometry-generated pseudo-magnetic/electric fields might disrupt Landau quantization under a magnetic field.
We study the distribution of vacuum polarization charge induced by a Coulomb impurity in massive ... more We study the distribution of vacuum polarization charge induced by a Coulomb impurity in massive graphene. By analytically computing the polarization function, we show that the charge density is distributed in space in a non-trivial fashion, and on a characteristic length-scale set by the effective Compton wavelength. The density crosses over from a logarithmic behavior below this scale, to a power law variation above it. Our results in the continuum limit are confirmed by explicit diagonalization of the corresponding tight-binding model on a finite-size lattice. Electron-electron interaction effects are also discussed.
We review the problem of electron-electron interactions in graphene. Starting from the screening ... more We review the problem of electron-electron interactions in graphene. Starting from the screening of long range interactions in these systems, we discuss the existence of an emerging Dirac liquid of Lorentz invariant quasi-particles in the weak coupling regime, and strongly correlated electronic states in the strong coupling regime. We also analyze the analogy and connections between the many-body problem and the Coulomb impurity problem. The problem of the magnetic instability and Kondo effect of impurities and/or adatoms in graphene is also discussed in analogy with classical models of many-body effects in ordinary metals. We show that Lorentz invariance plays a fundamental role and leads to effects that span the whole spectrum, from the ultraviolet to the infrared. The effect of an emerging Lorentz invariance is also discussed in the context of finite size and edge effects as well as mesoscopic physics. We also briefly discuss the effects of strong magnetic fields in single layers and review some of the main aspects of the many-body problem in graphene bilayers. In addition to reviewing the fully understood aspects of the many-body problem in graphene, we show that a plethora of interesting issues remain open, both theoretically and experimentally, and that the field of graphene research is still exciting and vibrant.
We present a study of different models of local disorder in graphene. Our focus is on the main ef... more We present a study of different models of local disorder in graphene. Our focus is on the main effects that vacancies -- random, compensated and uncompensated --, local impurities and substitutional impurities bring into the electronic structure of graphene. By exploring these types of disorder and their connections, we show that they introduce dramatic changes in the low energy spectrum of graphene, viz. localized zero modes, strong resonances, gap and pseudogap behavior, and non-dispersive midgap zero modes.
We study the problem of Coulomb field-induced charging of the ground state in a system of 2D mass... more We study the problem of Coulomb field-induced charging of the ground state in a system of 2D massive Dirac particles -gapped graphene. As in its 3D QED counterpart, the critical Coulomb coupling is renormalized to higher values, compared to the massless case. We find that in gapped graphene a novel supercritical regime is possible, where the screening charge is comparable to the impurity charge, thus leading to suppression of the Coulomb field at nanometer scales. We corroborate this with numerical solution of the tight-binding problem on the honeycomb lattice.
We address the problem of an unscreened Coulomb charge in graphene, and calculate the local densi... more We address the problem of an unscreened Coulomb charge in graphene, and calculate the local density of states and displaced charge as a function of energy and distance from the impurity. This is done non-perturbatively in two different ways: (1) solving the problem exactly by studying numerically the tight-binding model on the lattice; (2) using the continuum description in terms of the 2D Dirac equation. We show that the Dirac equation, when properly regularized, provides a qualitative and quantitative low energy description of the problem. The lattice solution shows extra features that cannot be described by the Dirac equation, namely bound state formation and strong renormalization of the van Hove singularities.
A microscopic theory for rare-earth ferromagnetic hexaborides, such as Eu(1-x)Ca(x)B6, is propose... more A microscopic theory for rare-earth ferromagnetic hexaborides, such as Eu(1-x)Ca(x)B6, is proposed on the basis of the double-exchange Hamiltonian. In these systems, the reduced carrier concentrations place the Fermi level near the mobility edge, introduced in the spectral density by the disordered spin background. We show that the transport properties such as Hall effect, magnetoresitance, frequency dependent conductivity, and DC resistivity can be quantitatively described within the model. We also make specific predictions for the behavior of the Curie temperature, Tc, as a function of the plasma frequency, omega_p.
We propose a route to all-graphene integrated electronic devices by exploring the influence of st... more We propose a route to all-graphene integrated electronic devices by exploring the influence of strain on the electronic structure of graphene. We show that strain can be easily tailored to generate electron beam collimation, 1D channels, surface states and confinement, the basic elements for all-graphene electronics. In addition this proposal has the advantage that patterning can be made on substrates rather than on the graphene sheet, thereby protecting the integrity of the latter.
We review the problem of electron-electron interactions in graphene. Starting from the screening ... more We review the problem of electron-electron interactions in graphene. Starting from the screening of long range interactions in these systems, we discuss the existence of an emerging Dirac liquid of Lorentz invariant quasi-particles in the weak coupling regime, and strongly correlated electronic states in the strong coupling regime. We also analyze the analogy and connections between the many-body problem and the Coulomb impurity problem. The problem of the magnetic instability and Kondo effect of impurities and/or adatoms in graphene is also discussed in analogy with classical models of many-body effects in ordinary metals. We show that Lorentz invariance plays a fundamental role and leads to effects that span the whole spectrum, from the ultraviolet to the infrared. The effect of an emerging Lorentz invariance is also discussed in the context of finite size and edge effects as well as mesoscopic physics. We also briefly discuss the effects of strong magnetic fields in single layers and review some of the main aspects of the many-body problem in graphene bilayers. In addition to reviewing the fully understood aspects of the many-body problem in graphene, we show that a plethora of interesting issues remain open, both theoretically and experimentally, and that the field of graphene research is still exciting and vibrant. d /ǫ 0 . Thus, the ratio of Coulomb to kinetic energy is given by E C /E K ∝ (n 0 /n d ) 1/d , where n 0 = [m * e 2 /( 2 ǫ 0 )] d depends only on material properties. Therefore, at high electron densities, n d ≫ n 0 , the kinetic energy dominates over the Coulomb energy, which can be disregarded, and the Fermi liquid description is safe. At low densities, n d ≪ n 0 the Coulomb energy is dominant and new electronic phases, such as ferromagnetism and Wigner crystallization, can
We address the problem of an unscreened Coulomb charge in graphene and calculate the local densit... more We address the problem of an unscreened Coulomb charge in graphene and calculate the local density of states and displaced charge as a function of energy and distance from the impurity. This is done nonperturbatively in two different ways: (1) solving the problem exactly by studying numerically the tight-binding model on the lattice and (2) using the continuum description in terms of the 2D Dirac equation. We show that the Dirac equation, when properly regularized, provides a qualitative and quantitative low energy description of the problem. The lattice solution shows extra features that cannot be described by the Dirac equation: namely, bound state formation and strong renormalization of the van Hove singularities.
As the thinnest atomic membrane, graphene presents an opportunity to combine geometry, elasticity... more As the thinnest atomic membrane, graphene presents an opportunity to combine geometry, elasticity and electronics at the limits of their validity. The availability of reliable atomistic potentials for graphene allows unprecedented precise simulations of the mechanical response of atomic membranes. Here we describe the transport and electronic structure in the neighbourhood of conical singularities, the elementary excitations of the ubiquitous wrinkled and crumpled graphene that occur in non-epitaxial suspended samples where shear stresses are unavoidable. We use a combination of atomistic mechanical simulations, analytical geometry and transport calculations in curved graphene, and exact diagonalization of the electronic spectrum to calculate the effects of geometry on electronic structure, transport and mobility in suspended samples. We also point out how the geometry-generated pseudo-magnetic/electric fields might disrupt Landau quantization under a magnetic field.
We propose a route to all-graphene integrated electronic devices by exploring the influence of st... more We propose a route to all-graphene integrated electronic devices by exploring the influence of strain on the electronic structure of graphene. We show that strain can be easily tailored to generate electron beam collimation, 1D channels, surface states and confinement, the basic elements for allgraphene electronics. In addition this proposal has the advantage that patterning can be made on substrates rather than on the graphene sheet, thereby protecting the integrity of the latter. PACS numbers: 81.05.Uw,85.30.Mn,73.90.+f 1 arXiv:0810.4539v3 [cond-mat.mes-hall]
We consider the electronic structure near vacancies in the half-filled honeycomb lattice. It is s... more We consider the electronic structure near vacancies in the half-filled honeycomb lattice. It is shown that vacancies induce the formation of localized states. When particle-hole symmetry is broken, localized states become resonances close to the Fermi level. We also study the problem of a finite density of vacancies, obtaining the electronic density of states, and discussing the issue of electronic localization in these systems. Our results have also relevance for the problem of disorder in d-wave superconductors.
We consider the electronic structure near vacancies in the half-filled honeycomb lattice. It is s... more We consider the electronic structure near vacancies in the half-filled honeycomb lattice. It is shown that vacancies induce the formation of localized states. When particle-hole symmetry is broken, localized states become resonances close to the Fermi level. We also study the problem of a finite density of vacancies, obtaining the electronic density of states, and discussing the issue of electronic localization in these systems. Our results have also relevance for the problem of disorder in d-wave superconductors.
We study the magnetization of square and hexagonal graphene dots. It is shown that two classes of... more 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 , whose 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 that the overall effect is an enhancement of magnetization with strain. The enhancement can be as large as 100% for strain of the order of 20%. Additionally, stress induces a spatial displacement of the magnetization over the dot, moving it from the zig-zag to the armchair edges.
We consider the Ising phase of the antiferromagnetic XXZ Heisenberg chain on a finite-size lattic... more We consider the Ising phase of the antiferromagnetic XXZ Heisenberg chain on a finite-size lattice with N sites. We compute the large N behavior of the spin stiffness, obtaining the correlation length ξ. We use our results to discuss the scaling behavior of metal-insulator transitions in 1D systems, taking into account the mapping between the XXZ Heisenberg chain and the spinless fermion model and known results for the Hubbard model. We study the scaling properties of both the Hubbard model and the XXZ Heisenberg chain, by solving numerically the Bethe Ansatz equations. We find that for some range of values of ξ/N the scaling behavior may be observed for the Hubbard model but not for the XXZ Heisenserg chain. We show how ξ can be obtained from the scaling properties of the spin stiffness for small system sizes. This method can be applied to models having not an exact solution, illuminating their transport properties.
Core tip: While intravenous thrombolysis has gained wide acceptance as a major breakthrough for t... more Core tip: While intravenous thrombolysis has gained wide acceptance as a major breakthrough for the acute treatment of stroke, interventional and diagnostic neuroradiology tools have also evolved at a very high rate, providing us with very sophisticated techniques to demonstrate brain tissue damage and revascularization techniques. However, these methods have not been evaluated properly until recently and have been adopted quickly by part of the clinical neuroscience community. A number of recent studies question the impact of these techniques.
As the thinnest atomic membrane, graphene presents an opportunity to combine geometry, elasticity... more As the thinnest atomic membrane, graphene presents an opportunity to combine geometry, elasticity and electronics at the limits of their validity. The availability of reliable atomistic potentials for graphene allows unprecedented precise simulations of the mechanical response of atomic membranes. Here we describe the transport and electronic structure in the neighbourhood of conical singularities, the elementary excitations of the ubiquitous wrinkled and crumpled graphene that occur in non-epitaxial suspended samples where shear stresses are unavoidable. We use a combination of atomistic mechanical simulations, analytical geometry and transport calculations in curved graphene, and exact diagonalization of the electronic spectrum to calculate the effects of geometry on electronic structure, transport and mobility in suspended samples. We also point out how the geometry-generated pseudo-magnetic/electric fields might disrupt Landau quantization under a magnetic field.
We study the distribution of vacuum polarization charge induced by a Coulomb impurity in massive ... more We study the distribution of vacuum polarization charge induced by a Coulomb impurity in massive graphene. By analytically computing the polarization function, we show that the charge density is distributed in space in a non-trivial fashion, and on a characteristic length-scale set by the effective Compton wavelength. The density crosses over from a logarithmic behavior below this scale, to a power law variation above it. Our results in the continuum limit are confirmed by explicit diagonalization of the corresponding tight-binding model on a finite-size lattice. Electron-electron interaction effects are also discussed.
We review the problem of electron-electron interactions in graphene. Starting from the screening ... more We review the problem of electron-electron interactions in graphene. Starting from the screening of long range interactions in these systems, we discuss the existence of an emerging Dirac liquid of Lorentz invariant quasi-particles in the weak coupling regime, and strongly correlated electronic states in the strong coupling regime. We also analyze the analogy and connections between the many-body problem and the Coulomb impurity problem. The problem of the magnetic instability and Kondo effect of impurities and/or adatoms in graphene is also discussed in analogy with classical models of many-body effects in ordinary metals. We show that Lorentz invariance plays a fundamental role and leads to effects that span the whole spectrum, from the ultraviolet to the infrared. The effect of an emerging Lorentz invariance is also discussed in the context of finite size and edge effects as well as mesoscopic physics. We also briefly discuss the effects of strong magnetic fields in single layers and review some of the main aspects of the many-body problem in graphene bilayers. In addition to reviewing the fully understood aspects of the many-body problem in graphene, we show that a plethora of interesting issues remain open, both theoretically and experimentally, and that the field of graphene research is still exciting and vibrant.
We present a study of different models of local disorder in graphene. Our focus is on the main ef... more We present a study of different models of local disorder in graphene. Our focus is on the main effects that vacancies -- random, compensated and uncompensated --, local impurities and substitutional impurities bring into the electronic structure of graphene. By exploring these types of disorder and their connections, we show that they introduce dramatic changes in the low energy spectrum of graphene, viz. localized zero modes, strong resonances, gap and pseudogap behavior, and non-dispersive midgap zero modes.
We study the problem of Coulomb field-induced charging of the ground state in a system of 2D mass... more We study the problem of Coulomb field-induced charging of the ground state in a system of 2D massive Dirac particles -gapped graphene. As in its 3D QED counterpart, the critical Coulomb coupling is renormalized to higher values, compared to the massless case. We find that in gapped graphene a novel supercritical regime is possible, where the screening charge is comparable to the impurity charge, thus leading to suppression of the Coulomb field at nanometer scales. We corroborate this with numerical solution of the tight-binding problem on the honeycomb lattice.
We address the problem of an unscreened Coulomb charge in graphene, and calculate the local densi... more We address the problem of an unscreened Coulomb charge in graphene, and calculate the local density of states and displaced charge as a function of energy and distance from the impurity. This is done non-perturbatively in two different ways: (1) solving the problem exactly by studying numerically the tight-binding model on the lattice; (2) using the continuum description in terms of the 2D Dirac equation. We show that the Dirac equation, when properly regularized, provides a qualitative and quantitative low energy description of the problem. The lattice solution shows extra features that cannot be described by the Dirac equation, namely bound state formation and strong renormalization of the van Hove singularities.
A microscopic theory for rare-earth ferromagnetic hexaborides, such as Eu(1-x)Ca(x)B6, is propose... more A microscopic theory for rare-earth ferromagnetic hexaborides, such as Eu(1-x)Ca(x)B6, is proposed on the basis of the double-exchange Hamiltonian. In these systems, the reduced carrier concentrations place the Fermi level near the mobility edge, introduced in the spectral density by the disordered spin background. We show that the transport properties such as Hall effect, magnetoresitance, frequency dependent conductivity, and DC resistivity can be quantitatively described within the model. We also make specific predictions for the behavior of the Curie temperature, Tc, as a function of the plasma frequency, omega_p.
We propose a route to all-graphene integrated electronic devices by exploring the influence of st... more We propose a route to all-graphene integrated electronic devices by exploring the influence of strain on the electronic structure of graphene. We show that strain can be easily tailored to generate electron beam collimation, 1D channels, surface states and confinement, the basic elements for all-graphene electronics. In addition this proposal has the advantage that patterning can be made on substrates rather than on the graphene sheet, thereby protecting the integrity of the latter.
We review the problem of electron-electron interactions in graphene. Starting from the screening ... more We review the problem of electron-electron interactions in graphene. Starting from the screening of long range interactions in these systems, we discuss the existence of an emerging Dirac liquid of Lorentz invariant quasi-particles in the weak coupling regime, and strongly correlated electronic states in the strong coupling regime. We also analyze the analogy and connections between the many-body problem and the Coulomb impurity problem. The problem of the magnetic instability and Kondo effect of impurities and/or adatoms in graphene is also discussed in analogy with classical models of many-body effects in ordinary metals. We show that Lorentz invariance plays a fundamental role and leads to effects that span the whole spectrum, from the ultraviolet to the infrared. The effect of an emerging Lorentz invariance is also discussed in the context of finite size and edge effects as well as mesoscopic physics. We also briefly discuss the effects of strong magnetic fields in single layers and review some of the main aspects of the many-body problem in graphene bilayers. In addition to reviewing the fully understood aspects of the many-body problem in graphene, we show that a plethora of interesting issues remain open, both theoretically and experimentally, and that the field of graphene research is still exciting and vibrant. d /ǫ 0 . Thus, the ratio of Coulomb to kinetic energy is given by E C /E K ∝ (n 0 /n d ) 1/d , where n 0 = [m * e 2 /( 2 ǫ 0 )] d depends only on material properties. Therefore, at high electron densities, n d ≫ n 0 , the kinetic energy dominates over the Coulomb energy, which can be disregarded, and the Fermi liquid description is safe. At low densities, n d ≪ n 0 the Coulomb energy is dominant and new electronic phases, such as ferromagnetism and Wigner crystallization, can
We address the problem of an unscreened Coulomb charge in graphene and calculate the local densit... more We address the problem of an unscreened Coulomb charge in graphene and calculate the local density of states and displaced charge as a function of energy and distance from the impurity. This is done nonperturbatively in two different ways: (1) solving the problem exactly by studying numerically the tight-binding model on the lattice and (2) using the continuum description in terms of the 2D Dirac equation. We show that the Dirac equation, when properly regularized, provides a qualitative and quantitative low energy description of the problem. The lattice solution shows extra features that cannot be described by the Dirac equation: namely, bound state formation and strong renormalization of the van Hove singularities.
As the thinnest atomic membrane, graphene presents an opportunity to combine geometry, elasticity... more As the thinnest atomic membrane, graphene presents an opportunity to combine geometry, elasticity and electronics at the limits of their validity. The availability of reliable atomistic potentials for graphene allows unprecedented precise simulations of the mechanical response of atomic membranes. Here we describe the transport and electronic structure in the neighbourhood of conical singularities, the elementary excitations of the ubiquitous wrinkled and crumpled graphene that occur in non-epitaxial suspended samples where shear stresses are unavoidable. We use a combination of atomistic mechanical simulations, analytical geometry and transport calculations in curved graphene, and exact diagonalization of the electronic spectrum to calculate the effects of geometry on electronic structure, transport and mobility in suspended samples. We also point out how the geometry-generated pseudo-magnetic/electric fields might disrupt Landau quantization under a magnetic field.
We propose a route to all-graphene integrated electronic devices by exploring the influence of st... more We propose a route to all-graphene integrated electronic devices by exploring the influence of strain on the electronic structure of graphene. We show that strain can be easily tailored to generate electron beam collimation, 1D channels, surface states and confinement, the basic elements for allgraphene electronics. In addition this proposal has the advantage that patterning can be made on substrates rather than on the graphene sheet, thereby protecting the integrity of the latter. PACS numbers: 81.05.Uw,85.30.Mn,73.90.+f 1 arXiv:0810.4539v3 [cond-mat.mes-hall]
We consider the electronic structure near vacancies in the half-filled honeycomb lattice. It is s... more We consider the electronic structure near vacancies in the half-filled honeycomb lattice. It is shown that vacancies induce the formation of localized states. When particle-hole symmetry is broken, localized states become resonances close to the Fermi level. We also study the problem of a finite density of vacancies, obtaining the electronic density of states, and discussing the issue of electronic localization in these systems. Our results have also relevance for the problem of disorder in d-wave superconductors.
We consider the electronic structure near vacancies in the half-filled honeycomb lattice. It is s... more We consider the electronic structure near vacancies in the half-filled honeycomb lattice. It is shown that vacancies induce the formation of localized states. When particle-hole symmetry is broken, localized states become resonances close to the Fermi level. We also study the problem of a finite density of vacancies, obtaining the electronic density of states, and discussing the issue of electronic localization in these systems. Our results have also relevance for the problem of disorder in d-wave superconductors.
We study the magnetization of square and hexagonal graphene dots. It is shown that two classes of... more 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 , whose 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 that the overall effect is an enhancement of magnetization with strain. The enhancement can be as large as 100% for strain of the order of 20%. Additionally, stress induces a spatial displacement of the magnetization over the dot, moving it from the zig-zag to the armchair edges.
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Papers by Vitor Pereira