ChiYung Yam

Time-dependent Density Functional Theory For Open Systems

With our proof of the holographic electron density theorem for time-dependent systems, a first-principles method for any open electronic system is established. By introducing the self-energy density functionals for the dissipative interactions between the reduced system and its environment, we develop a time-dependent densityfunctional 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 dissipative interactions, 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.

Theoretical prediction of topological insulators in thallium-based III-V-VI2 ternary chalcogenides

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 ? 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.

A tribological study of double-walled and triple-walled carbon nanotube oscillators

We reported in a previous study (Zhao et al 2003 Phys. Rev. Lett. 91 175504) 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 micro-canonical 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 off-axial instabilities, leading to strong frictional effects.

Time-dependent density functional theory for quantum transport

Based on our earlier works [X. Zheng et al., Phys. Rev. B 75, 195127 (2007); J. S. Jin et al., J. Chem. Phys. 128, 234703 (2008)], we propose a rigorous and numerically convenient approach to simulate time-dependent quantum transport from first-principles. The proposed approach combines time-dependent density functional theory with quantum dissipation theory, and results in a useful tool for studying transient dynamics of electronic systems. Within the proposed exact theoretical framework, we construct a number of practical schemes for simulating realistic systems such as nanoscopic electronic devices. Computational cost of each scheme is analyzed, with the expected level of accuracy discussed. As a demonstration, a simulation based on the adiabatic wide-band limit approximation scheme is carried out to characterize the transient current response of a carbon nanotube based electronic device under time-dependent external voltages.

Dynamic admittance of carbon nanotube-based molecular electronic devices and their equivalent electric circuit

We use first-principles quantum mechanics to simulate the transient electrical response through carbon nanotube-based conductors under time-dependent bias voltages. The dynamic admittance and time-dependent charge distribution are reported and analyzed. We find that the electrical response of these two-terminal molecular devices can be mapped onto an equivalent classical electric circuit and that the switching time of these end-on carbon nanotube devices is only a few femtoseconds. This result is confirmed by studying the electric response of a simple two-site model device and is thus generalized to other two-terminal molecular electronic devices.

Localized-density-matrix implementation of time-dependent density-functional theory

A linear-scaling first-principles quantum mechanical method is developed to evaluate the optical responses of large molecular systems. Instead of a many-body wave function, the equation of motion is solved for the reduced single-electron density matrix in the time domain. The locality of the reduced single-electron density matrix is utilized to ensure that computational time scales linearly with system size. The two-electron Coulomb integrals are evaluated with the fast multipole method, and the calculation of exchange-correlation quadratures utilizes the locality of an exchange-correlation functional and the integral prescreening technique. As an illustration, the resulting time-dependent density-functional theory is used to calculate the absorption spectra of polyacetylene oligomers and linear alkanes. The linear-scaling of computational time versus the system size is clearly demonstrated.

Density matrix based time-dependent density functional theory and the solution of its linear response in real time domain

A density matrix based time-dependent density functional theory is extended in the present work. Chebyshev expansion is introduced to propagate the linear response of the reduced single-electron density matrix upon the application of a time-domain delta-type external potential. The Chebyshev expansion method is more efficient and accurate than the previous fourth-order Runge-Kutta method and removes a numerical divergence problem. The discrete Fourier transformation and filter diagonalization of the first-order dipole moment are implemented to determine the excited state energies. It is found that the filter diagonalization leads to highly accurate values for the excited state energies. Finally, the density matrix based time-dependent density functional is generalized to calculate the energies of singlet-triplet excitations.

Time-dependent versus static quantum transport simulations beyond linear response

To explore whether the density-functional theory–nonequilibrium Green’s function formalism (DFT-NEGF) provides a rigorous framework for quantum transport, we carried out time-dependent density-functional-theory (TDDFT) calculations of the transient current through two realistic molecular devices, a carbon chain and a benzenediol molecule between two aluminum electrodes. The TDDFT simulations for the steady-state current exactly reproduce the results of fully self-consistent DFT-NEGF calculations even beyond linear response. In contrast, sizable differences are found with respect to an equilibrium, non-self-consistent treatment, which are related here to differences in the Kohn-Sham and fully interacting susceptibilities of the device region. Moreover, earlier analytical conjectures on the equivalence of static and time-dependent approaches in the low-bias regime are confirmed with high numerical precision.

Time-dependent quantum transport: An efficient method based on Liouville-von-Neumann equation for single-electron density matrix

Basing on our hierarchical equations of motion for time-dependent quantum transport [X. Zheng, G. H. Chen, Y. Mo, S. K. Koo, H. Tian, C. Y. Yam, and Y. J. Yan, J. Chem. Phys. 133, 114101 (2010)], we develop an efficient and accurate numerical algorithm to solve the Liouville-von-Neumann equation. We solve the real-time evolution of the reduced single-electron density matrix at the tight-binding level. Calculations are carried out to simulate the transient current through a linear chain of atoms, with each represented by a single orbital. The self-energy matrix is expanded in terms of multiple Lorentzian functions, and the Fermi distribution function is evaluated via the Padè spectrum decomposition. This Lorentzian-Padè decomposition scheme is employed to simulate the transient current. With sufficient Lorentzian functions used to fit the self-energy matrices, we show that the lead spectral function and the dynamics response can be treated accurately. Compared to the conventional master equation approaches, our method is much more efficient as the computational time scales cubically with the system size and linearly with the simulation time. As a result, the simulations of the transient currents through systems containing up to one hundred of atoms have been carried out. As density functional theory is also an effective one-particle theory, the Lorentzian-Padè decomposition scheme developed here can be generalized for first-principles simulation of realistic systems.

Interference and Molecular Transport - A Dynamical View: Time-Dependent Analysis of Disubstituted Benzenes

The primary issue in molecular electronics is measuring and understanding how electrons travel through a single molecule strung between two electrodes. A key area involves electronic interference that occurs when electrons can follow more than one pathway through the molecular entity. When the phases developed along parallel pathways are inequivalent, interference effects can substantially reduce overall conductance. This fundamentally interesting issue can be understood using classical rules of physical organic chemistry, and the subject has been examined broadly. However, there has been little dynamical study of such interference effects. Here, we use the simplest electronic structure model to examine the coherent time-dependent transport through meta- and para-linked benzene circuits, and the effects of decoherence. We find that the phase-caused coherence/decoherence behavior is established very quickly (femtoseconds), that the localized dephasing at any site reduces the destructive interference of the meta-linked species (raising the conductance), and that thermal effects are essentially ineffectual for removing coherence effects.