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S Ciraci - One of the best experts on this subject based on the ideXlab platform.
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functionalization of single layer mos2 Honeycomb Structures
Journal of Physical Chemistry C, 2011Co-Authors: Can Ataca, S CiraciAbstract:Based on first-principles plane-wave calculations, we studied the functionalization of the two-dimensional single-layer MoS2 structure through adatom adsorption and vacancy defect creation. Minimum-energy adsorption sites were determined for 16 different adatoms, each of which gives rise to diverse properties. Bare, single-layer MoS2, which is normally a nonmagnetic, direct-band-gap semiconductor, attains a net magnetic moment upon adsorption of specific transition-metal atoms, as well as silicon and germanium atoms. The localized donor and acceptor states in the band gap expand the utilization of MoS2 in nanoelectronics and spintronics. Specific adatoms, such as C and O, attain significant excess charge upon adsorption onto single-layer MoS2, which might be useful for tribological applications. Each MoS2 triple vacancy created in a single layer of MoS2 gives rise to a net magnetic moment, whereas other vacancy defects related to Mo and S atoms do not influence the nonmagnetic ground state. The present re...
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armchair nanoribbons of silicon and germanium Honeycomb Structures
Physical Review B, 2010Co-Authors: Seymur Cahangirov, Mehmet Topsakal, S CiraciAbstract:We present a first-principles study of bare and hydrogen passivated armchair nanoribbons of the puckered single layer Honeycomb Structures of silicon and germanium. Our study includes optimization of atomic structure, stability analysis based on the calculation of phonon dispersions, electronic structure and the variation of band gap with the width of the ribbon. The band gaps of silicon and germanium nanoribbons exhibit family behavior similar to those of graphene nanoribbons. The edges of bare nanoribbons are sharply reconstructed, which can be eliminated by the hydrogen termination of dangling bonds at the edges. Periodic modulation of the nanoribbon width results in a superlattice structure which can act as a multiple quantum wells. Specific electronic states are confined in these wells. Confinement trends are qualitatively explained by including the effects of the interface. In order to investigate wide and long superlattice Structures we also performed empirical tight binding calculations with parameters determined from \textit{ab initio} calculations.
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first principles study of defects and adatoms in silicon carbide Honeycomb Structures
Physical Review B, 2010Co-Authors: E. Bekaroglu, Seymur Cahangirov, Mehmet Topsakal, S CiraciAbstract:We present a study of mechanical, electronic and magnetic properties of two-dimensional (2D), monolayer of silicon carbide (SiC) in Honeycomb structure and its quasi-one-dimensional (quasi-1D) armchair nanoribbons using first-principles plane-wave method. In order to reveal dimensionality effects, a brief study of three-dimensional (3D) bulk and 1D atomic chain of SiC are also included. Calculated bond-lengths, cohesive energies, charge transfers and band gaps display a clear dimensionality effect. The stability analysis based on the calculation of phonon frequencies indicates that 2D SiC monolayer is stable in planar geometry. We found that 2D SiC monolayer in Honeycomb structure and its bare and hydrogen passivated nanoribbons are ionic, nonmagnetic, wide band gap semiconductors. The band gap is further increased upon self-energy corrections. The mechanical properties are investigated using the strain energy calculations. The effect of various vacancy defects, adatoms, and substitutional impurities on electronic and magnetic properties in 2D SiC monolayer and in its armchair nanoribbons is also investigated. Some of these vacancy defects and impurities, which are found to influence physical properties and attain magnetic moments, can be used to functionalize SiC Honeycomb Structures.
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first principles study of zinc oxide Honeycomb Structures
Physical Review B, 2009Co-Authors: Mehmet Topsakal, Seymur Cahangirov, E. Bekaroglu, S CiraciAbstract:We present a first-principles study of the atomic, electronic, and magnetic properties of two-dimensional (2D), single and bilayer ZnO in Honeycomb structure and its armchair and zigzag nanoribbons. In order to reveal the dimensionality effects, our study includes also bulk ZnO in wurtzite, zincblende, and hexagonal Structures. The stability of 2D ZnO, its nanoribbons and flakes are analyzed by phonon frequency, as well as by finite temperature ab initio molecular-dynamics calculations. 2D ZnO in Honeycomb structure and its armchair nanoribbons are nonmagnetic semiconductors but acquire net magnetic moment upon the creation of zinc-vacancy defect. Zigzag ZnO nanoribbons are ferromagnetic metals with spins localized at the oxygen atoms at the edges and have high spin polarization at the Fermi level. However, they change to nonmagnetic metal upon termination of their edges with hydrogen atoms. From the phonon calculations, the fourth acoustical mode specified as twisting mode is also revealed for armchair nanoribbon. Under tensile stress the nanoribbons are deformed elastically maintaining Honeycomblike structure but yield at high strains. Beyond yielding point Honeycomblike structure undergo a structural change and deform plastically by forming large polygons. The variation in the electronic and magnetic properties of these nanoribbons have been examined under strain. It appears that plastically deformed nanoribbons may offer a new class of materials with diverse properties.
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two and one dimensional Honeycomb Structures of silicon and germanium
Physical Review Letters, 2009Co-Authors: Seymur Cahangirov, Mehmet Topsakal, E Akturk, H Sahin, S CiraciAbstract:First-principles calculations of structure optimization, phonon modes, and finite temperature molecular dynamics predict that silicon and germanium can have stable, two-dimensional, low-buckled, Honeycomb Structures. Similar to graphene, these puckered Structures are ambipolar and their charge carriers can behave like a massless Dirac fermion due to their pi and pi(*) bands which are crossed linearly at the Fermi level. In addition to these fundamental properties, bare and hydrogen passivated nanoribbons of Si and Ge show remarkable electronic and magnetic properties, which are size and orientation dependent. These properties offer interesting alternatives for the engineering of diverse nanodevices.
Mehmet Topsakal - One of the best experts on this subject based on the ideXlab platform.
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armchair nanoribbons of silicon and germanium Honeycomb Structures
Physical Review B, 2010Co-Authors: Seymur Cahangirov, Mehmet Topsakal, S CiraciAbstract:We present a first-principles study of bare and hydrogen passivated armchair nanoribbons of the puckered single layer Honeycomb Structures of silicon and germanium. Our study includes optimization of atomic structure, stability analysis based on the calculation of phonon dispersions, electronic structure and the variation of band gap with the width of the ribbon. The band gaps of silicon and germanium nanoribbons exhibit family behavior similar to those of graphene nanoribbons. The edges of bare nanoribbons are sharply reconstructed, which can be eliminated by the hydrogen termination of dangling bonds at the edges. Periodic modulation of the nanoribbon width results in a superlattice structure which can act as a multiple quantum wells. Specific electronic states are confined in these wells. Confinement trends are qualitatively explained by including the effects of the interface. In order to investigate wide and long superlattice Structures we also performed empirical tight binding calculations with parameters determined from \textit{ab initio} calculations.
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first principles study of defects and adatoms in silicon carbide Honeycomb Structures
Physical Review B, 2010Co-Authors: E. Bekaroglu, Seymur Cahangirov, Mehmet Topsakal, S CiraciAbstract:We present a study of mechanical, electronic and magnetic properties of two-dimensional (2D), monolayer of silicon carbide (SiC) in Honeycomb structure and its quasi-one-dimensional (quasi-1D) armchair nanoribbons using first-principles plane-wave method. In order to reveal dimensionality effects, a brief study of three-dimensional (3D) bulk and 1D atomic chain of SiC are also included. Calculated bond-lengths, cohesive energies, charge transfers and band gaps display a clear dimensionality effect. The stability analysis based on the calculation of phonon frequencies indicates that 2D SiC monolayer is stable in planar geometry. We found that 2D SiC monolayer in Honeycomb structure and its bare and hydrogen passivated nanoribbons are ionic, nonmagnetic, wide band gap semiconductors. The band gap is further increased upon self-energy corrections. The mechanical properties are investigated using the strain energy calculations. The effect of various vacancy defects, adatoms, and substitutional impurities on electronic and magnetic properties in 2D SiC monolayer and in its armchair nanoribbons is also investigated. Some of these vacancy defects and impurities, which are found to influence physical properties and attain magnetic moments, can be used to functionalize SiC Honeycomb Structures.
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first principles study of zinc oxide Honeycomb Structures
Physical Review B, 2009Co-Authors: Mehmet Topsakal, Seymur Cahangirov, E. Bekaroglu, S CiraciAbstract:We present a first-principles study of the atomic, electronic, and magnetic properties of two-dimensional (2D), single and bilayer ZnO in Honeycomb structure and its armchair and zigzag nanoribbons. In order to reveal the dimensionality effects, our study includes also bulk ZnO in wurtzite, zincblende, and hexagonal Structures. The stability of 2D ZnO, its nanoribbons and flakes are analyzed by phonon frequency, as well as by finite temperature ab initio molecular-dynamics calculations. 2D ZnO in Honeycomb structure and its armchair nanoribbons are nonmagnetic semiconductors but acquire net magnetic moment upon the creation of zinc-vacancy defect. Zigzag ZnO nanoribbons are ferromagnetic metals with spins localized at the oxygen atoms at the edges and have high spin polarization at the Fermi level. However, they change to nonmagnetic metal upon termination of their edges with hydrogen atoms. From the phonon calculations, the fourth acoustical mode specified as twisting mode is also revealed for armchair nanoribbon. Under tensile stress the nanoribbons are deformed elastically maintaining Honeycomblike structure but yield at high strains. Beyond yielding point Honeycomblike structure undergo a structural change and deform plastically by forming large polygons. The variation in the electronic and magnetic properties of these nanoribbons have been examined under strain. It appears that plastically deformed nanoribbons may offer a new class of materials with diverse properties.
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Monolayer Honeycomb Structures of group-IV elements and III-V binary compounds: First-principles calculations
Physical Review B, 2009Co-Authors: H Sahin, Seymur Cahangirov, Mehmet Topsakal, E. Bekaroglu, Ethem Aktürk, R. T. Senger, Salim CiraciAbstract:Using first-principles plane wave calculations, we investigate two dimensional Honeycomb structure of Group IV elements and their binary compounds, as well as the compounds of Group III-V elements. Based on structure optimization and phonon mode calculations, we determine that 22 different Honeycomb materials are stable and correspond to local minima on the Born-Oppenheimer surface. We also find that all the binary compounds containing one of the first row elements, B, C or N have planar stable Structures. On the other hand, in the Honeycomb Structures of Si, Ge and other binary compounds the alternating atoms of hexagons are buckled, since the stability is maintained by puckering. For those Honeycomb materials which were found stable, we calculated optimized Structures, cohesive energies, phonon modes, electronic band Structures, effective cation and anion charges, and some elastic constants. The band gaps calculated within Density Functional Theory using Local Density Approximation are corrected by GW0 method. Si and Ge in Honeycomb structure are semimetal and have linear band crossing at the Fermi level which attributes massless Fermion character to charge carriers as in graphene. However, all binary compounds are found to be semiconductor with band gaps depending on the constituent atoms. We present a method to reveal elastic constants of 2D Honeycomb Structures from the strain energy and calculate the Poisson’s ratio as well as in-plane stiffness values. Preliminary results show that the nearly lattice matched heteroStructures of these compounds can offer new alternatives for nanoscale electronic devices. Similar to those of the three-dimensional Group IV and Group III-V compound semiconductors, one deduces interesting correlations among the calculated properties of present Honeycomb Structures. PACS numbers: 73.22.-f, 61.48.De, 63.22.-m, 62.23.Kn
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two and one dimensional Honeycomb Structures of silicon and germanium
Physical Review Letters, 2009Co-Authors: Seymur Cahangirov, Mehmet Topsakal, E Akturk, H Sahin, S CiraciAbstract:First-principles calculations of structure optimization, phonon modes, and finite temperature molecular dynamics predict that silicon and germanium can have stable, two-dimensional, low-buckled, Honeycomb Structures. Similar to graphene, these puckered Structures are ambipolar and their charge carriers can behave like a massless Dirac fermion due to their pi and pi(*) bands which are crossed linearly at the Fermi level. In addition to these fundamental properties, bare and hydrogen passivated nanoribbons of Si and Ge show remarkable electronic and magnetic properties, which are size and orientation dependent. These properties offer interesting alternatives for the engineering of diverse nanodevices.
Michael I Weinstein - One of the best experts on this subject based on the ideXlab platform.
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high contrast elliptic operators in Honeycomb Structures
arXiv: Mathematical Physics, 2021Co-Authors: Maxence Cassier, Michael I WeinsteinAbstract:We study the band structure of self-adjoint elliptic operators $\mathbb{A}_g= -\nabla \cdot \sigma_{g} \nabla$, where $\sigma_g$ has the symmetries of a Honeycomb tiling of $\mathbb{R}^2$. We focus on the case where $\sigma_{g}$ is a real-valued scalar: $\sigma_{g}=1$ within identical, disjoint and "inclusions", centered at vertices of a Honeycomb lattice, and $\sigma_{g}=g \gg1 $ (high contrast) in the complement of the inclusion set (bulk). Such operators govern, e.g. transverse electric (TE) modes in photonic crystal media consisting of high dielectric constant inclusions (semi-conductor pillars) within a homogeneous lower contrast bulk (air), a configuration in physical studies. Our approach, which is based on monotonicity properties of the associated energy form, extends to a class of high contrast elliptic operators that model heterogeneous and anisotropic Honeycomb media. Our results concern the global behavior of dispersion surfaces, and the existence of conical crossings (Dirac points) occurring in the lowest two energy bands as well as in bands arbitrarily high in the spectrum. Dirac points are the source of important phenomena in fundamental and applied physics, e.g. graphene and its artificial analogues, and topological insulators. The key hypotheses are the non-vanishing of the Dirac (Fermi) velocity $v_D(g)$, verified numerically, and a spectral isolation condition, verified analytically in many configurations. Asymptotic expansions, to any order in $g^{-1}$, of Dirac point eigenpairs and $v_D(g)$ are derived with error bounds. Our study illuminates differences between the high contrast behavior of $\mathbb{A}_g$ and the corresponding strong binding regime for Schroedinger operators.
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bifurcations of edge states topologically protected and non protected in continuous 2d Honeycomb Structures
2D Materials, 2016Co-Authors: Charles Fefferman, James P Leethorp, Michael I WeinsteinAbstract:Edge states are time-harmonic solutions to energy-conserving wave equations, which are propagating parallel to a line-defect or 'edge' and are localized transverse to it. This paper summarizes and extends the authors' work on the bifurcation of topologically protected edge states in continuous two-dimensional (2D) Honeycomb Structures. We consider a family of Schrodinger Hamiltonians consisting of a bulk Honeycomb potential and a perturbing edge potential. The edge potential interpolates between two different periodic Structures via a domain wall. We begin by reviewing our recent bifurcation theory of edge states for continuous 2D Honeycomb Structures (http://arxiv.org/abs/1506.06111). The topologically protected edge state bifurcation is seeded by the zero-energy eigenstate of a one-dimensional Dirac operator. We contrast these protected bifurcations with (more common) non-protected bifurcations from spectral band edges, which are induced by bound states of an effective Schrodinger operator. Numerical simulations for Honeycomb Structures of varying contrasts and 'rational edges' (zigzag, armchair and others), support the following scenario: (a) for low contrast, under a sign condition on a distinguished Fourier coefficient of the bulk Honeycomb potential, there exist topologically protected edge states localized transverse to zigzag edges. Otherwise, and for general edges, we expect long lived edge quasi-modes which slowly leak energy into the bulk. (b) For an arbitrary rational edge, there is a threshold in the medium-contrast (depending on the choice of edge) above which there exist topologically protected edge states. In the special case of the armchair edge, there are two families of protected edge states; for each parallel quasimomentum (the quantum number associated with translation invariance) there are edge states which propagate in opposite directions along the armchair edge.
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bifurcations of edge states topologically protected and non protected in continuous 2d Honeycomb Structures
arXiv: Mathematical Physics, 2015Co-Authors: Charles Fefferman, James P Leethorp, Michael I WeinsteinAbstract:This paper summarizes and extends the authors' work on the bifurcation of topologically protected edge states in continuous two-dimensional Honeycomb Structures. We consider a family of Schrodinger Hamiltonians consisting of a bulk Honeycomb potential and a perturbing edge potential. The edge potential interpolates between two different periodic Structures via a domain wall. We begin by reviewing our recent bifurcation theory of edge states for continuous two-dimensional Honeycomb Structures. The topologically protected bifurcation of edge states is seeded by the zero-energy eigenstate of a one-dimensional Dirac operator. We contrast these protected bifurcations with (more common) non-protected bifurcations from spectral band edges, which are induced by bound states of an effective Schrodinger operator. Numerical simulations for Honeycomb Structures of varying contrasts and "rational edges" (zigzag, armchair and others), support the following scenario: (a) For low contrast, under a sign condition on a distinguished Fourier coefficient of the bulk Honeycomb potential, there exist topologically protected edge states localized transverse to zigzag edges. Otherwise, and for general edges, we expect long lived {\it edge quasi-modes} which slowly leak energy into the bulk. (b) For an arbitrary rational edge, there is a threshold in the medium-contrast (depending on the choice of edge) above which there exist topologically protected edge states. In the special case of the armchair edge, there are two families of protected edge states; for each parallel quasimomentum (the quantum number associated with translation invariance) there are edge states which propagate in opposite directions along the armchair edge.
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edge states in Honeycomb Structures
arXiv: Mathematical Physics, 2015Co-Authors: Charles Fefferman, James P Leethorp, Michael I WeinsteinAbstract:An edge state is a time-harmonic solution of a conservative wave system, e.g. Schroedinger, Maxwell, which is propagating (plane-wave-like) parallel to, and localized transverse to, a line-defect or "edge". Topologically protected edge states are edge states which are stable against spatially localized (even strong) deformations of the edge. First studied in the context of the quantum Hall effect, protected edge states have attracted huge interest due to their role in the field of topological insulators. Theoretical understanding of topological protection has mainly come from discrete (tight-binding) models and direct numerical simulation. In this paper we consider a rich family of continuum PDE models for which we rigorously study regimes where topologically protected edge states exist. Our model is a class of Schroedinger operators on $\mathbb{R}^2$ with a background 2D Honeycomb potential perturbed by an "edge-potential". The edge potential is a domain-wall interpolation, transverse to a prescribed "rational" edge, between two distinct periodic Structures. General conditions are given for the bifurcation of a branch of topologically protected edge states from Dirac points of the background Honeycomb structure. The bifurcation is seeded by the zero mode of a 1D effective Dirac operator. A key condition is a spectral no-fold condition for the prescribed edge. We then use this result to prove the existence of topologically protected edge states along zigzag edges of certain Honeycomb Structures. Our results are consistent with the physics literature and appear to be the first rigorous results on the existence of topologically protected edge states for continuum 2D PDE systems describing waves in a non-trivial periodic medium. We also show that the family of Hamiltonians we study contains cases where zigzag edge states exist, but which are not topologically protected.
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wave packets in Honeycomb Structures and two dimensional dirac equations
Communications in Mathematical Physics, 2014Co-Authors: Charles Fefferman, Michael I WeinsteinAbstract:In a recent article (Fefferman and Weinstein, in J Am Math Soc 25:1169–1220, 2012), the authors proved that the non-relativistic Schrodinger operator with a generic Honeycomb lattice potential has conical (Dirac) points in its dispersion surfaces. These conical points occur for quasi-momenta, which are located at the vertices of the Brillouin zone, a regular hexagon. In this paper, we study the time-evolution of wave-packets, which are spectrally concentrated near such conical points. We prove that the large, but finite, time dynamics is governed by the two-dimensional Dirac equations.
Seymur Cahangirov - One of the best experts on this subject based on the ideXlab platform.
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armchair nanoribbons of silicon and germanium Honeycomb Structures
Physical Review B, 2010Co-Authors: Seymur Cahangirov, Mehmet Topsakal, S CiraciAbstract:We present a first-principles study of bare and hydrogen passivated armchair nanoribbons of the puckered single layer Honeycomb Structures of silicon and germanium. Our study includes optimization of atomic structure, stability analysis based on the calculation of phonon dispersions, electronic structure and the variation of band gap with the width of the ribbon. The band gaps of silicon and germanium nanoribbons exhibit family behavior similar to those of graphene nanoribbons. The edges of bare nanoribbons are sharply reconstructed, which can be eliminated by the hydrogen termination of dangling bonds at the edges. Periodic modulation of the nanoribbon width results in a superlattice structure which can act as a multiple quantum wells. Specific electronic states are confined in these wells. Confinement trends are qualitatively explained by including the effects of the interface. In order to investigate wide and long superlattice Structures we also performed empirical tight binding calculations with parameters determined from \textit{ab initio} calculations.
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first principles study of defects and adatoms in silicon carbide Honeycomb Structures
Physical Review B, 2010Co-Authors: E. Bekaroglu, Seymur Cahangirov, Mehmet Topsakal, S CiraciAbstract:We present a study of mechanical, electronic and magnetic properties of two-dimensional (2D), monolayer of silicon carbide (SiC) in Honeycomb structure and its quasi-one-dimensional (quasi-1D) armchair nanoribbons using first-principles plane-wave method. In order to reveal dimensionality effects, a brief study of three-dimensional (3D) bulk and 1D atomic chain of SiC are also included. Calculated bond-lengths, cohesive energies, charge transfers and band gaps display a clear dimensionality effect. The stability analysis based on the calculation of phonon frequencies indicates that 2D SiC monolayer is stable in planar geometry. We found that 2D SiC monolayer in Honeycomb structure and its bare and hydrogen passivated nanoribbons are ionic, nonmagnetic, wide band gap semiconductors. The band gap is further increased upon self-energy corrections. The mechanical properties are investigated using the strain energy calculations. The effect of various vacancy defects, adatoms, and substitutional impurities on electronic and magnetic properties in 2D SiC monolayer and in its armchair nanoribbons is also investigated. Some of these vacancy defects and impurities, which are found to influence physical properties and attain magnetic moments, can be used to functionalize SiC Honeycomb Structures.
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first principles study of zinc oxide Honeycomb Structures
Physical Review B, 2009Co-Authors: Mehmet Topsakal, Seymur Cahangirov, E. Bekaroglu, S CiraciAbstract:We present a first-principles study of the atomic, electronic, and magnetic properties of two-dimensional (2D), single and bilayer ZnO in Honeycomb structure and its armchair and zigzag nanoribbons. In order to reveal the dimensionality effects, our study includes also bulk ZnO in wurtzite, zincblende, and hexagonal Structures. The stability of 2D ZnO, its nanoribbons and flakes are analyzed by phonon frequency, as well as by finite temperature ab initio molecular-dynamics calculations. 2D ZnO in Honeycomb structure and its armchair nanoribbons are nonmagnetic semiconductors but acquire net magnetic moment upon the creation of zinc-vacancy defect. Zigzag ZnO nanoribbons are ferromagnetic metals with spins localized at the oxygen atoms at the edges and have high spin polarization at the Fermi level. However, they change to nonmagnetic metal upon termination of their edges with hydrogen atoms. From the phonon calculations, the fourth acoustical mode specified as twisting mode is also revealed for armchair nanoribbon. Under tensile stress the nanoribbons are deformed elastically maintaining Honeycomblike structure but yield at high strains. Beyond yielding point Honeycomblike structure undergo a structural change and deform plastically by forming large polygons. The variation in the electronic and magnetic properties of these nanoribbons have been examined under strain. It appears that plastically deformed nanoribbons may offer a new class of materials with diverse properties.
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Monolayer Honeycomb Structures of group-IV elements and III-V binary compounds: First-principles calculations
Physical Review B, 2009Co-Authors: H Sahin, Seymur Cahangirov, Mehmet Topsakal, E. Bekaroglu, Ethem Aktürk, R. T. Senger, Salim CiraciAbstract:Using first-principles plane wave calculations, we investigate two dimensional Honeycomb structure of Group IV elements and their binary compounds, as well as the compounds of Group III-V elements. Based on structure optimization and phonon mode calculations, we determine that 22 different Honeycomb materials are stable and correspond to local minima on the Born-Oppenheimer surface. We also find that all the binary compounds containing one of the first row elements, B, C or N have planar stable Structures. On the other hand, in the Honeycomb Structures of Si, Ge and other binary compounds the alternating atoms of hexagons are buckled, since the stability is maintained by puckering. For those Honeycomb materials which were found stable, we calculated optimized Structures, cohesive energies, phonon modes, electronic band Structures, effective cation and anion charges, and some elastic constants. The band gaps calculated within Density Functional Theory using Local Density Approximation are corrected by GW0 method. Si and Ge in Honeycomb structure are semimetal and have linear band crossing at the Fermi level which attributes massless Fermion character to charge carriers as in graphene. However, all binary compounds are found to be semiconductor with band gaps depending on the constituent atoms. We present a method to reveal elastic constants of 2D Honeycomb Structures from the strain energy and calculate the Poisson’s ratio as well as in-plane stiffness values. Preliminary results show that the nearly lattice matched heteroStructures of these compounds can offer new alternatives for nanoscale electronic devices. Similar to those of the three-dimensional Group IV and Group III-V compound semiconductors, one deduces interesting correlations among the calculated properties of present Honeycomb Structures. PACS numbers: 73.22.-f, 61.48.De, 63.22.-m, 62.23.Kn
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two and one dimensional Honeycomb Structures of silicon and germanium
Physical Review Letters, 2009Co-Authors: Seymur Cahangirov, Mehmet Topsakal, E Akturk, H Sahin, S CiraciAbstract:First-principles calculations of structure optimization, phonon modes, and finite temperature molecular dynamics predict that silicon and germanium can have stable, two-dimensional, low-buckled, Honeycomb Structures. Similar to graphene, these puckered Structures are ambipolar and their charge carriers can behave like a massless Dirac fermion due to their pi and pi(*) bands which are crossed linearly at the Fermi level. In addition to these fundamental properties, bare and hydrogen passivated nanoribbons of Si and Ge show remarkable electronic and magnetic properties, which are size and orientation dependent. These properties offer interesting alternatives for the engineering of diverse nanodevices.
Charles Fefferman - One of the best experts on this subject based on the ideXlab platform.
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bifurcations of edge states topologically protected and non protected in continuous 2d Honeycomb Structures
2D Materials, 2016Co-Authors: Charles Fefferman, James P Leethorp, Michael I WeinsteinAbstract:Edge states are time-harmonic solutions to energy-conserving wave equations, which are propagating parallel to a line-defect or 'edge' and are localized transverse to it. This paper summarizes and extends the authors' work on the bifurcation of topologically protected edge states in continuous two-dimensional (2D) Honeycomb Structures. We consider a family of Schrodinger Hamiltonians consisting of a bulk Honeycomb potential and a perturbing edge potential. The edge potential interpolates between two different periodic Structures via a domain wall. We begin by reviewing our recent bifurcation theory of edge states for continuous 2D Honeycomb Structures (http://arxiv.org/abs/1506.06111). The topologically protected edge state bifurcation is seeded by the zero-energy eigenstate of a one-dimensional Dirac operator. We contrast these protected bifurcations with (more common) non-protected bifurcations from spectral band edges, which are induced by bound states of an effective Schrodinger operator. Numerical simulations for Honeycomb Structures of varying contrasts and 'rational edges' (zigzag, armchair and others), support the following scenario: (a) for low contrast, under a sign condition on a distinguished Fourier coefficient of the bulk Honeycomb potential, there exist topologically protected edge states localized transverse to zigzag edges. Otherwise, and for general edges, we expect long lived edge quasi-modes which slowly leak energy into the bulk. (b) For an arbitrary rational edge, there is a threshold in the medium-contrast (depending on the choice of edge) above which there exist topologically protected edge states. In the special case of the armchair edge, there are two families of protected edge states; for each parallel quasimomentum (the quantum number associated with translation invariance) there are edge states which propagate in opposite directions along the armchair edge.
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bifurcations of edge states topologically protected and non protected in continuous 2d Honeycomb Structures
arXiv: Mathematical Physics, 2015Co-Authors: Charles Fefferman, James P Leethorp, Michael I WeinsteinAbstract:This paper summarizes and extends the authors' work on the bifurcation of topologically protected edge states in continuous two-dimensional Honeycomb Structures. We consider a family of Schrodinger Hamiltonians consisting of a bulk Honeycomb potential and a perturbing edge potential. The edge potential interpolates between two different periodic Structures via a domain wall. We begin by reviewing our recent bifurcation theory of edge states for continuous two-dimensional Honeycomb Structures. The topologically protected bifurcation of edge states is seeded by the zero-energy eigenstate of a one-dimensional Dirac operator. We contrast these protected bifurcations with (more common) non-protected bifurcations from spectral band edges, which are induced by bound states of an effective Schrodinger operator. Numerical simulations for Honeycomb Structures of varying contrasts and "rational edges" (zigzag, armchair and others), support the following scenario: (a) For low contrast, under a sign condition on a distinguished Fourier coefficient of the bulk Honeycomb potential, there exist topologically protected edge states localized transverse to zigzag edges. Otherwise, and for general edges, we expect long lived {\it edge quasi-modes} which slowly leak energy into the bulk. (b) For an arbitrary rational edge, there is a threshold in the medium-contrast (depending on the choice of edge) above which there exist topologically protected edge states. In the special case of the armchair edge, there are two families of protected edge states; for each parallel quasimomentum (the quantum number associated with translation invariance) there are edge states which propagate in opposite directions along the armchair edge.
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edge states in Honeycomb Structures
arXiv: Mathematical Physics, 2015Co-Authors: Charles Fefferman, James P Leethorp, Michael I WeinsteinAbstract:An edge state is a time-harmonic solution of a conservative wave system, e.g. Schroedinger, Maxwell, which is propagating (plane-wave-like) parallel to, and localized transverse to, a line-defect or "edge". Topologically protected edge states are edge states which are stable against spatially localized (even strong) deformations of the edge. First studied in the context of the quantum Hall effect, protected edge states have attracted huge interest due to their role in the field of topological insulators. Theoretical understanding of topological protection has mainly come from discrete (tight-binding) models and direct numerical simulation. In this paper we consider a rich family of continuum PDE models for which we rigorously study regimes where topologically protected edge states exist. Our model is a class of Schroedinger operators on $\mathbb{R}^2$ with a background 2D Honeycomb potential perturbed by an "edge-potential". The edge potential is a domain-wall interpolation, transverse to a prescribed "rational" edge, between two distinct periodic Structures. General conditions are given for the bifurcation of a branch of topologically protected edge states from Dirac points of the background Honeycomb structure. The bifurcation is seeded by the zero mode of a 1D effective Dirac operator. A key condition is a spectral no-fold condition for the prescribed edge. We then use this result to prove the existence of topologically protected edge states along zigzag edges of certain Honeycomb Structures. Our results are consistent with the physics literature and appear to be the first rigorous results on the existence of topologically protected edge states for continuum 2D PDE systems describing waves in a non-trivial periodic medium. We also show that the family of Hamiltonians we study contains cases where zigzag edge states exist, but which are not topologically protected.
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wave packets in Honeycomb Structures and two dimensional dirac equations
Communications in Mathematical Physics, 2014Co-Authors: Charles Fefferman, Michael I WeinsteinAbstract:In a recent article (Fefferman and Weinstein, in J Am Math Soc 25:1169–1220, 2012), the authors proved that the non-relativistic Schrodinger operator with a generic Honeycomb lattice potential has conical (Dirac) points in its dispersion surfaces. These conical points occur for quasi-momenta, which are located at the vertices of the Brillouin zone, a regular hexagon. In this paper, we study the time-evolution of wave-packets, which are spectrally concentrated near such conical points. We prove that the large, but finite, time dynamics is governed by the two-dimensional Dirac equations.
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wave packets in Honeycomb Structures and two dimensional dirac equations
arXiv: Mathematical Physics, 2012Co-Authors: Charles Fefferman, Michael I WeinsteinAbstract:In a recent article [10], the authors proved that the non-relativistic Schrodinger operator with a generic Honeycomb lattice potential has conical (Dirac) points in its dispersion surfaces. These conical points occur for quasi-momenta, which are located at the vertices of the Brillouin zone, a regular hexagon. In this paper, we study the time-evolution of wave-packets, which are spectrally concentrated near such conical points. We prove that the large, but finite, time dynamics is governed by the two-dimensional Dirac equations.