By introducing the self-energy density functionals for the dissipative interactions between the reduced system and its environment, we develop a time-dependent density-functional theory formalism based on an equation of motion for the Kohn-Sham reduced single-electron density matrix of the reduced system. Two approximate schemes are proposed for the self-energy density functionals, the complete second order approximation and the wide-band limit approximation. A numerical method based on the wide-band limit approximation is subsequently developed and implemented to simulate the steady and transient current through various realistic molecular devices. Simulation results are presented and discussed.

We predict a new class of three dimensional topological insulators in thallium-based III-V-VI2 ternary chalcogenides, including TlBiQ2 and TlSbQ2 (Q = Te, Se and S). These topological insulators have robust and simple surface states consisting of a single Dirac cone at the Γ point. The mechanism for topological insulating behavior is elucidated using both first principle calculations and effective field theory models. Remarkably, one topological insulator in this class, TlBiTe2 is also a superconductor when doped with p-type carriers. We discuss the possibility that this material could be a topological superconductor. Another material TlSbS2 is on the border between topological insulator and trivial insulator phases, in which a topological phase transition can be driven by pressure. PACS numbers:Topological insulators have attracted great attention in condensed matter physics 1 . Since the first theoretical prediction 2 and the subsequent experimental observation 3 in HgTe quantum wells, several other topological insulators in three dimensional (3D) bulk materials have been theoretically predicted and experimentally observed 4-8 . In particular, tetradymite semiconductors Bi 2 Te 3 , Bi 2 Se 3 , and Sb 2 Te 3 are predicted to be topological insulators with a large bulk band gap whose surface state consists of a single Dirac cone 6 . The mechanism for the topological insulating behavior in these 3D materials is the band inversion at the Γ point caused by large spin-orbit coupling, similar to the mechanism first discovered in HgTe quantum wells 2 . The tetradymite semiconductors have a layered structure consisting of stacking quintuple layers, making surface preparation particularly simple.In this work we predict a new class of 3D topological insulators in the thallium-based III-V-VI 2 ternary chalcogenides. These inversion symmetric topological insulators have a bulk energy gap and topologically protected surface states consisting of a single Dirac cone. Unlike the tetradymite semiconductors, these materials are intrinsically 3D, and do not have a weakly coupled layer structure. Nonetheless, effective field theory model describing the band electrons close to the Fermi energy takes the same form as the model proposed earlier for the tetradymite semiconductors 6 , and the mechanism for topological insulating behavior can be understood in a similar way.The discovery of topological insulators also inspired the intense search for topological superconductors 9-13 . Time reversal invariant topological superconductors have a full pairing gap in the bulk and topologically protected surface states consisting of Majorana fermions, see Fig 1 of Ref. 9 . Wheareas Dirac fermions have both particle and hole types, Majorana fermions are their own antiparticles. 14 In the simplest version, the surface state of a 3D topological superconductor consists of a single Majorana cone, thus containing half the degree of freedom of the Dirac surface states of a simple 3D topological insulator. This fractionalization of the degree of freedo...

We reported in a previous study (Zhao et al 2003 Phys. Rev. Lett. 91 75504) that energy transfer from the orderly intertube translational oscillation to intratube vibrational modes for an isolated system of two coaxial carbon nanotubes at low temperatures takes place primarily via two distinct types of collective motion of the carbon nanotubes, i.e., off-axial rocking motion of the inner tube and radial wavy motion of the outer tube, and that these types of motion may or may not occur for such a system, depending upon the amount of the initial extrusion of the inner tube out of the outer tube. Our present study, using microcanonical molecular dynamics (MD), indicates the existence of an energy threshold, largely independent of system sizes and configurations, for a double-walled nano-oscillator to deviate from the intertube translational oscillation and thus to encounter significant intertube friction. The frictional forces associated with several distinct dissipative mechanisms are all found to exhibit no proportional dependence upon the normal force between the two surfaces in relative sliding, contrary to the conventional understanding resulting from tribological studies of macroscopic systems. Furthermore, simulation has been performed at different initial temperatures, revealing a strong temperature dependence of friction in the early phase of oscillation. Finally, our studies of three-walled nano-oscillators show that an initial extrusion of the middle tube can cause inner-tube offaxial instabilities, leading to strong frictional effects.

Based on the corrected Hohenberg-Kohn-Sham total energy density functional [Y. A. Zhang and Y. A. Wang, J. Chem. Phys. 130, 144116 (2009)], we have developed two linear-expansion shooting techniques (LIST)- direct LIST (LISTd) and indirect LIST (LISTi), to accelerate the convergence of self-consistent field (SCF) calculations. Case studies show that overall LISTi is the most robust and efficient algorithm for accelerating SCF convergence, whereas LISTd is advantageous in the early stage of an SCF process. More importantly, LISTi outperforms Pulay's direct inversion in the iterative subspace (DIIS) [P. Pulay, J. Comput. Chem. 3, 556 (1982)] and its two recent improvements, energy-DIIS [K. N. Kudin, G. E. Scuseria, and E. Cancès, J. Chem. Phys. 116, 8255 (2002)] and augmented Roothaan-Hall energy-DIIS [X. Hu and W. Yang, J. Chem. Phys. 132, 054109 (2010)].