Mele, Eugene J.
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Publication Orientational Phases for M3C60(1993-10-15) Yildirim, Taner; Harris, A. Brooks; Mele, Eugene J; Hong, SuklyunThe mechanism of the orientational ordering of C60 in alkali-metal-doped fullerenes M3C60 is studied. Since the M-C60 (M=K,Rb) interactions cause the C60 molecules to assume one of two standard orientations, this model is equivalent to a generalized Ising model on a fcc lattice. The Ising interactions depend on two type of energies: (1) the direct interaction, i.e., the orientationally dependent part of interactions between nearest-neighboring C60 molecules (each carrying charge -3e), and (2) the band energy of the electrons transferred from M+ ions to the C603- ions. It is shown that the contribution to the pairwise interaction from the direct orientational interaction is ferromagnetic and dominantly nearest neighbor. However, contributions from the band (kinetic) energy of the conduction electrons are found to be antiferromagnetic for first- and third-nearest neighbors, ferromagnetic for second- and fourth-nearest neighbors, and negligible for further neighbors. The total first-neighbor interaction is probably antiferromagnetic. a non-negligible four-spin interaction is also obtained. The implication of these results for the orientational structure is discussed.Publication Flux Phases in Two-Dimensional Tight-Binding Models(1989-08-01) Harris, A. Brooks; Lubensky, Tom C; Mele, Eugene JUsing a gauge-invariant tight-binding model on a rigid square lattice, we discuss the transition between a low-temperature flux phase in which orbital magnetic moments alternate antiferromagnetically in sign from plaquette to plaquette and a normal metallic phase. The order parameter, which may be chosen to be the magnetic flux penetrating a plaquette, goes continuously to zero at the transition. We also consider similar phases in a model with m spin colors antiferromagnetically exchange coupled.Publication Mean-Field Theory for Interchain Orientational Ordering of Conjugated Polymers(1989-08-15) Harris, A. Brooks; Choi, Han-Yong; Mele, Eugene J.We consider a generalized anisotropic planar-rotor model on a triangular lattice for interchain orientational ordering of undoped and doped polyacetylene, and investigate the effects of various terms on the symmetry and the range of stability of the observed herringbone (HB) phases. Dipole, quadrupole, and octopole interactions are included in the model with sixfold crystal-field anisotropy and are analyzed within the mean-field theory. The relative strength of these interactions can be estimated from the observed setting angle of the HB phase with the help of the smallness of crystal-field anisotropy. A model where the polymer chain is represented by a ‘‘quadrupolar’’ mass density only has various phases as the temperature and the interaction parameters are varied. Among them, the HB phase is found below a critical temperature Tc for some range of the parameter space, and the setting angle of the HB phase is 45° and independent of temperature. Competition between quadrupole and other interactions such as dipole or octopole, parametrized by the ratio of interaction strengths λ, results in an additional phase transition at T’c(λ) and makes the setting angle vary with the temperature below T’c(λ). For a model with quadrupole and octopole terms, there are two degenerate states of the setting angle related by θ’=π/2-θ. This degeneracy does not reflect a symmetry of the system and is lifted by the dipole terms. For a model with quadrupole and dipole interactions, the setting angle increases as the temperature is reduced below T’c(λ). From these results, we conclude that quadrupole and dipole interactions are important terms to explain experimental observations. Effects of crystal-field anisotropy resolve the twofold degeneracy, destroy the critical behavior associated with T’c(λ), and make the setting angle temperature dependent over the entire range of temperature below Tc. Crucial information on the interaction parameters of the model can be obtained through the temperature dependence of the setting angle of the HB phase.Publication Dirac Semimetal in Three Dimensions(2012-04-06) Young, Steve M; Kane, Charles L; Zaheer, Saad; Mele, Eugene J.; Teo, Jeffrey C; Rappe, A MWe show that the pseudorelativistic physics of graphene near the Fermi level can be extended to three dimensional (3D) materials. Unlike in phase transitions from inversion symmetric topological to normal insulators, we show that particular space groups also allow 3D Dirac points as symmetry protected degeneracies. We provide criteria necessary to identify these groups and, as an example, present ab initio calculations of β-cristobalite BiO2 which exhibits three Dirac points at the Fermi level. We find that β-cristobalite BiO2 is metastable, so it can be physically realized as a 3D analog to graphene.Publication Topological Insulators in Three Dimensions(2007-03-07) Kane, Charles L; Fu, Liang; Mele, Eugene JWe study three-dimensional generalizations of the quantum spin Hall (QSH) effect. Unlike two dimensions, where a single Z2 topological invariant governs the effect, in three dimensions there are 4 invariants distinguishing 16 phases with two general classes: weak (WTI) and strong (STI) topological insulators. The WTI are like layered 2D QSH states, but are destroyed by disorder. The STI are robust and lead to novel ‘‘topological metal’’ surface states. We introduce a tight binding model which realizes the WTI and STI phases, and we discuss its relevance to real materials, including bismuth.Publication Surface State Magnetization and Chiral Edge States on Topological Insulators(2013-01-25) Kane, Charles L; Zhang, Fan; Mele, Eugene J.We study the interaction between a ferromagnetically ordered medium and the surface states of a topological insulator with a general surface termination that were identified recently [F. Zhang et al.Phys. Rev. B 86 081303(R) (2012)]. This interaction is strongly crystal face dependent and can generate chiral states along edges between crystal facets even for a uniform magnetization. While magnetization parallel to quintuple layers shifts the momentum of the Dirac point, perpendicular magnetization lifts the Kramers degeneracy at any Dirac points except on the side face, where the spectrum remains gapless and the Hall conductivity switches sign. Chiral states can be found at any edge that reverses the projection of the surface normal to the stacking direction of quintuple layers. Magnetization also weakly hybridizes noncleavage surfaces.Publication Formation of Subgap States in Carbon Nanotubes Due to a Local Transverse Electric Field(2007-11-27) Kinder, Jesse M.; Mele, Eugene JWe introduce two simple models to study the effect of a spatially localized transverse electric field on the low-energy electronic structure of semiconducting carbon nanotubes. Starting from the Dirac Hamiltonian for the low-energy states of a carbon nanotube, we use scattering theory to show that an arbitrarily weak field leads to the formation of localized electronic states inside the free nanotube band gap. We study the binding energy of these subgap states as a function of the range and strength of the electrostatic potential. When the range of the potential is held constant and the strength is varied, the binding energy shows crossover behavior: the states lie close to the free nanotube band edge until the potential exceeds a threshold value, after which the binding energy increases rapidly. When the potential strength is held constant and the range is varied, we find resonant behavior: the binding energy passes through a maximum as the range of the potential is increased. Large electric fields confined to a small region of the nanotube are required to create localized states far from the band edge.Publication Nanoparticle Shape Selection by Repulsive Interactions: Metal Islands on Few-Layer Graphene(2010-01-01) Somers, Luke A; Johnson, Charlie; Mele, Eugene J; Zimbovskaya, Natalya AMetal atoms adsorbed on few-layer graphenes condense to form nanometer-size droplets whose growth is size limited by a competition between the surface tension and repulsive electrostatic interactions from charge transfer between the metal droplet and the graphene. For situations where the work-function mismatch is large and the droplet surface tension is small, a growing droplet can be unstable to a family of shape instabilities. We observe this phenomenon for Yb deposited and annealed on few-layer graphenes and develop a theoretical model to describe it by studying the renormalization of the line tension of a two-dimensional droplet by repulsive interparticle interactions. Our model describes the onset of shape instabilities for nanoparticles where the growth is size limited by a generic repulsive potential and provides a good account of the experimentally observed structures for Yb on graphene.Publication Commensuration and Interlayer Coherence in Twisted Bilayer Graphene(2010-04-12) Mele, Eugene JThe low-energy electronic spectra of rotationally faulted graphene bilayers are studied using a longwavelength theory applicable to general commensurate fault angles. Lattice commensuration requires lowenergy electronic coherence across a fault and pre-empts massless Dirac behavior near the neutrality point. Sublattice exchange symmetry distinguishes two families of commensurate faults that have distinct low-energy spectra which can be interpreted as energy-renormalized forms of the spectra for the limiting Bernal and AA stacked structures. Sublattice-symmetric faults are generically fully gapped systems due to a pseudospin-orbit coupling appearing in their effective low-energy Hamiltonians.Publication A Block Slipping on a Sphere with Friction: Exact and Perturbative Solutions(2006-11-16) Prior, Tom; Mele, Eugene JA well studied problem in elementary mechanics is the location of the release point of a particle that slides on the surface of a frictionless sphere when it is released from rest at the top. We generalize this problem to include the effects of sliding friction and solve it by a perturbation expansion in the coefficient of sliding friction and by an exact integration of the equation of motion. A comparison of the two solutions identifies a parameter range where the perturbation series accurately represents the motion of the particle and another range where the perturbative solution fails qualitatively to describe the motion of the particle.