Orthogonal orientation control of carbon nanotube growth.

Carbon nanotubes (CNTs) have attracted attention for their remarkable electrical properties and have being explored as one of the best building blocks in nano-electronics. A key challenge to realize such potential is the control of the nanotube growth directions. Even though both vertical growth and controlled horizontal growth of carbon nanotubes have been realized before, the growth of complex nanotube structures with both vertical and horizontal orientation control on the same substrate has never been achieved. Here, we report a method to grow three-dimensional (3D) complex nanotube structures made of vertical nanotube forests and horizontal nanotube arrays on a single substrate and from the same catalyst pattern by an orthogonally directed nanotube growth method using chemical vapor deposition (CVD). More importantly, such a capability represents a major advance in controlled growth of carbon nanotubes. It enables researchers to control the growth directions of nanotubes by simply changing the reaction conditions. The high degree of control represented in these experiments will surely make the fabrication of complex nanotube devices a possibility.

Reformulating time-dependent density functional theory with non-orthogonal localized molecular orbitals.

Time-dependent density functional theory (TDDFT) has broad application in the study of electronic response, excitation and transport. To extend such application to large and complex systems, we develop a reformulation of TDDFT equations in terms of non-orthogonal localized molecular orbitals (NOLMOs). NOLMO is the most localized representation of electronic degrees of freedom and has been used in ground state calculations. In atomic orbital (AO) representation, the sparsity of NOLMO is transferred to the coefficient matrix of molecular orbitals (MOs). Its novel use in TDDFT here leads to a very simple form of time propagation equations which can be solved with linear-scaling effort. We have tested the method for several long-chain saturated and conjugated molecular systems within the self-consistent charge density-functional tight-binding method (SCC-DFTB) and demonstrated its accuracy. This opens up pathways for TDDFT applications to large bio- and nano-systems.

Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O(2) sigma model

In the presence of a chemical potential, the physics of level crossings leads to singularities at zero temperature, even when the spatial volume is finite. These singularities are smoothed out at a finite temperature but leave behind nontrivial finite size effects which must be understood in order to extract thermodynamic quantities using Monte Carlo methods, particularly close to critical points. We illustrate some of these issues using the classical nonlinear O(2) sigma model with a coupling β and chemical potential μ on a 2+1-dimensional Euclidean lattice. In the conventional formulation this model suffers from a sign problem at nonzero chemical potential and hence cannot be studied with the Wolff cluster algorithm. However, when formulated in terms of the worldline of particles, the sign problem is absent, and the model can be studied efficiently with the "worm algorithm." Using this method we study the finite size effects that arise due to the chemical potential and develop an effective quantum mechanical approach to capture the effects. As a side result we obtain energy levels of up to four particles as a function of the box size and uncover a part of the phase diagram in the (β,μ) plane. © 2010 The American Physical Society.