@article{nardelli_fattebert_bernholc_2001, title={O(N) real-space method for ab initio quantum transport calculations: Application to carbon nanotube-metal contacts}, volume={64}, ISSN={["2469-9969"]}, DOI={10.1103/physrevb.64.245423}, abstractNote={We present an ab initio O(N) method that combines an accurate optimized-orbital solution of the electronic structure problem with an efficient Green's function technique for evaluating the quantum conductance. As an important illustrative example, we investigate carbon nanotube-metal contacts and explain the anomalously large contact resistance observed in nanotube devices as due to the spatial separation of their conductance eigenchannels. The results for various contact geometries and strategies for improving device performance are discussed. The study of the electrical properties of nanostructures has seen intense activity in the last decade, due to the prom- ise of novel technological applications for nanoscale quan- tum electronic devices. The theoretical study of quantum conductance in such structures has thus become of primary interest and has been addressed by a variety of techniques. 1 Due to the complexity of describing an ''open'' system of a nanoscale device in contact with effectively infinite leads, most of the current approaches rely on phenomenological tight binding models, which for many systems may not pro- vide a sufficiently reliable and accurate description. There are only few examples of ab initio calculations of quantum conductance and the field is still in a critical phase of development. The existing methods are based on the so- lution of the quantum scattering problem for the electronic wave functions through the conductor using a number of related techniques: Lippman-Schwinger and perturbative Green's function methods have been used to study conduc- tance in metallic nanowires and recently in small molecular nanocontacts; 2,3 conduction in nanowires, junctions, and nanotube systems has been addressed using local 4 or nonlocal 5,6 pseudopotential methods and through the solution of the coupled-channel equations in a scattering-theoretic approach. 7-9 These methods are based on a plane wave rep- resentation of the electronic wave functions, which imposes severe restrictions on the size of the system because of the large number of basis functions necessary for an accurate description of the electron transmission process. Therefore, structureless jellium leads, which do not provide a micro- scopic description of the conductor-metal contact, had to be assumed in most cases for computational reasons. Only re- cently have real-space approaches been considered for a more efficient solution of the electronic transport problem. They are based on the use of linear combination of atomic orbitals 10 ~LCAO! or Gaussian 11 orbital bases. These are combined with either a scattering state solution for the transmission 10 or Green's function-based techniques. 11 In this paper we present an approach based on a real- space optimized-orbital solution of the electronic structure problem, combined with an efficient Green's function-based technique for the evaluation of the electron transmission probability. Both the ab initio and the transport algorithms scale essentially linearly with the size of the system, thus extending greatly the range of applicability of our method. This method has been already successfully applied to de- scribe quantum conductance in ideal and defective carbon nanotubes. 12 Following a brief overview of the methodology, we address the problem of contacts in a metal-carbon nano- tube assembly, which is very important in the design of effi- cient nanotube-based devices. Contact resistances of the or- der of MV are typically observed in most of the prototypical nanotube-based devices realized so far, 13-16 whereas from simple band structure arguments one would expect resis- tances of the order of a few tenths of kV, 17 because the fundamental resistance of a single ballistic channel is 12.9 kV. The results of our calculations provide an explanation for this pathologically high contact resistance and suggest strategies to improve the performance of nanotube-metal contacts. It is important to stress that this problem requires self-consistent ab initio methodology, in order to accurately describe the highly inhomogeneous environment of a nanowire-metal junction and to account for the charge trans- fer occurring at the interface between the two dissimilar ma- terials.}, number={24}, journal={PHYSICAL REVIEW B}, author={Nardelli, MB and Fattebert, JL and Bernholc, J}, year={2001}, month={Dec} }
 @article{bernholc_briggs_bungaro_nardelli_fattebert_rapcewicz_roland_schmidt_zhao_2000, title={Large-scale applications of real-space multigrid methods to surfaces, nanotubes, and quantum transport}, volume={217}, ISSN={["1521-3951"]}, DOI={10.1002/(sici)1521-3951(200001)217:1<685::aid-pssb685>3.0.co;2-3}, abstractNote={The development and applications of real-space multigrid methods are discussed. Multigrid techniques provide preconditioning and convergence acceleration at all length scales, and therefore lead to particularly efficient algorithms. When using localization regions and optimized, non-orthogonal orbitals, calculations involving over 1000 atoms become practical on massively parallel computers. The applications discussed in this chapter include: (i) dopant incorporation and ordering effects during surface incorporation of boron, which lead to the formation of ordered domains at half-monolayer coverage; (ii) incorporation of Mg into GaN during growth, and in particular the conditions that would lead to maximum p-type doping; (iii) optical fingerprints of surface structures for use in real-time feedback control of growth: and (iv) mechanisms of stress release and quantum transport properties of carbon nanotubes.}, number={1}, journal={PHYSICA STATUS SOLIDI B-BASIC SOLID STATE PHYSICS}, author={Bernholc, J and Briggs, EL and Bungaro, C and Nardelli, MB and Fattebert, JL and Rapcewicz, K and Roland, C and Schmidt, WG and Zhao, Q}, year={2000}, month={Jan}, pages={685–701} }
 @article{nardelli_fattebert_orlikowski_roland_zhao_bernholc_2000, title={Mechanical properties, defects and electronic behavior of carbon nanotubes}, volume={38}, ISSN={["1873-3891"]}, DOI={10.1016/S0008-6223(99)00291-2}, abstractNote={Using state-of-the-art classical and quantum simulations, we have studied the mechanical and electronic response of carbon nanotubes to external deformations, such as strain and bending. In strained nanotubes the spontaneous formation of double pentagon–heptagon defect pairs is observed. Tubes containing these defects are energetically preferred to uniformly stretched tubes at strains greater than 5%. These defects act as nucleation centers for the formation of dislocations in the originally ideal graphitic network and constitute the onset of further deformations of the carbon nanotube. In particular, plastic or brittle behaviors can occur depending upon the external conditions and tube symmetry. We have also investigated the effects that the presence of addimers has on strained carbon nanotubes. The main result is the formation of a new class of defects that wrap themselves about the circumference of the nanotube. These defects are shown to modify the geometrical structure and to induce the formation of nanotube-based quantum dots. Finally, we computed transport properties for various ideal and mechanically deformed carbon nanotubes. High defect densities are shown to greatly affect transport in individual nanotubes, while small diameter bent armchair nanotubes mantam thier basic electrical properties even in presence of large deformations with no defects involved.}, number={11-12}, journal={CARBON}, author={Nardelli, MB and Fattebert, JL and Orlikowski, D and Roland, C and Zhao, Q and Bernholc, J}, year={2000}, pages={1703–1711} }
 @article{fattebert_bernholc_2000, title={Towards grid-based O(N) density-functional theory methods: Optimized nonorthogonal orbitals and multigrid acceleration}, volume={62}, ISSN={["2469-9969"]}, DOI={10.1103/physrevb.62.1713}, abstractNote={We have formulated and implemented a real-space ab initio method for electronic structure calculations in terms of nonorthogonal orbitals defined on a grid. A multigrid preconditioner is used to improve the steepest descent directions used in the iterative minimization of the energy functional. Unoccupied or partially occupied states are included using a density matrix formalism in the subspace spanned by the nonorthogonal orbitals. The freedom introduced by the nonorthogonal real-space description of the orbitals allows for localization constraints that linearize the cost of the most expensive parts of the calculations, while keeping a fast convergence rate for the iterative minimization with multigrid acceleration. Numerical tests for carbon nanotubes show that very accurate results can be obtained for localization regions with radii of 8 bohr. This approach, which substantially reduces the computational cost for very large systems, has been implemented on the massively parallel Cray T3E computer and tested on carbon nanotubes containing more than 1000 atoms.}, number={3}, journal={PHYSICAL REVIEW B}, author={Fattebert, JL and Bernholc, J}, year={2000}, month={Jul}, pages={1713–1722} }
 @article{fattebert_1999, title={Finite difference schemes and block Rayleigh quotient iteration for electronic structure calculations on composite grids}, volume={149}, ISSN={["0021-9991"]}, DOI={10.1006/jcph.1998.6138}, abstractNote={We present an original numerical method to discretize the Kohn?Sham equations by a finite difference scheme in real-space when computing the electronic structure of a molecule. The singular atomic potentials are replaced by pseudopotentials and the discretization of the 3D problem is done on a composite mesh refined in part of the domain. A “Mehrstellenverfahren” finite difference scheme is used to approximate the Laplacian on the regular parts of the grid. The nonlinearity of the potential operator in the Kohn?Sham equations is treated by a fixed point algorithm. At each step an iterative scheme is applied to determine the searched solutions of the eigenvalue problem for a given fixed potential. The eigensolver is a block generalization of the Rayleigh quotient iteration which uses Petrov?Galerkin approximations. The algorithm is adapted to a multigrid resolution of the linear systems obtained in the inverse iterations. Numerical tests of the different algorithms are presented on problems coming from the electronic structure calculation of some molecules.}, number={1}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Fattebert, JL}, year={1999}, month={Feb}, pages={75–94} }
 @article{schmidt_fattebert_bernholc_bechstedt_1999, title={Self-energy effects in the optical anisotropy of GaP(001)}, volume={6}, ISSN={["0218-625X"]}, DOI={10.1142/S0218625X99001281}, abstractNote={ We calculate the reflectance anisotropy for GaP(001)(2×4) surfaces using a real-space multigrid method and ab initio pseudopotentials. Our results obtained within DFT-LDA show good qualitative agreement with recent experiments. This holds in particular for the stoichiometric trends. A strong negative anisotropy at low photon energies is linked to the formation of Ga–Ga bonds along the [110] direction. There are discrepancies, however, with respect to the line shape and the energetic positions of characteristic peaks. Substantial improvement is achieved by using a numerically efficient GW approach with approximations for local-field effects and dynamical screening. We find that the spectral features related to transitions between surface perturbed bulk wave functions are more strongly affected by self-energy corrections than anisotropies directly linked to surface electronic states. }, number={6}, journal={SURFACE REVIEW AND LETTERS}, author={Schmidt, WG and Fattebert, JL and Bernholc, J and Bechstedt, F}, year={1999}, month={Dec}, pages={1159–1165} }
 @article{fattebert_1998, title={A Block Rayleigh Quotient iteration with local quadratic convergence}, volume={7}, number={1998}, journal={Electronic Transactions on Numerical Analysis (CD-ROM)}, author={Fattebert, J. L.}, year={1998}, pages={56–74} }