The origin of incipient ferroelectricity in lead telluride.

The interactions between electrons and lattice vibrations are fundamental to materials behaviour. In the case of group IV-VI, V and related materials, these interactions are strong, and the materials exist near electronic and structural phase transitions. The prototypical example is PbTe whose incipient ferroelectric behaviour has been recently associated with large phonon anharmonicity and thermoelectricity. Here we show that it is primarily electron-phonon coupling involving electron states near the band edges that leads to the ferroelectric instability in PbTe. Using a combination of nonequilibrium lattice dynamics measurements and first principles calculations, we find that photoexcitation reduces the Peierls-like electronic instability and reinforces the paraelectric state. This weakens the long-range forces along the cubic direction tied to resonant bonding and low lattice thermal conductivity. Our results demonstrate how free-electron-laser-based ultrafast X-ray scattering can be utilized to shed light on the microscopic mechanisms that determine materials properties.

Bayesian variable selection in structured high-dimensional covariate spaces with applications in genomics

We consider the problem of variable selection in regression modeling in high-dimensional spaces where there is known structure among the covariates. This is an unconventional variable selection problem for two reasons: (1) The dimension of the covariate space is comparable, and often much larger, than the number of subjects in the study, and (2) the covariate space is highly structured, and in some cases it is desirable to incorporate this structural information in to the model building process. We approach this problem through the Bayesian variable selection framework, where we assume that the covariates lie on an undirected graph and formulate an Ising prior on the model space for incorporating structural information. Certain computational and statistical problems arise that are unique to such high-dimensional, structured settings, the most interesting being the phenomenon of phase transitions. We propose theoretical and computational schemes to mitigate these problems. We illustrate our methods on two different graph structures: the linear chain and the regular graph of degree k. Finally, we use our methods to study a specific application in genomics: the modeling of transcription factor binding sites in DNA sequences. © 2010 American Statistical Association.

Physics of Hexagonal Limit-Periodic Phases: Thermodynamics, Formation and Vibrational Modes

Limit-periodic (LP) structures exhibit a type of nonperiodic order yet to be found in a natural material. A recent result in tiling theory, however, has shown that LP order can spontaneously emerge in a two-dimensional (2D) lattice model with nearest-and next-nearest-neighbor interactions. In this dissertation, we explore the question of what types of interactions can lead to a LP state and address the issue of whether the formation of a LP structure in experiments is possible. We study emergence of LP order in three-dimensional (3D) tiling models and bring the subject into the physical realm by investigating systems with realistic Hamiltonians and low energy LP states. Finally, we present studies of the vibrational modes of a simple LP ball and spring model whose results indicate that LP materials would exhibit novel physical properties.

A 2D lattice model defined on a triangular lattice with nearest- and next-nearest-neighbor interactions based on the Taylor-Socolar (TS) monotile is known to have a LP ground state. The system reaches that state during a slow quench through an infinite sequence of phase transitions. Surprisingly, even when the strength of the next-nearest-neighbor interactions is zero, in which case there is a large degenerate class of both crystalline and LP ground states, a slow quench yields the LP state. The first study in this dissertation introduces 3D models closely related to the 2D models that exhibit LP phases. The particular 3D models were designed such that next-nearest-neighbor interactions of the TS type are implemented using only nearest-neighbor interactions. For one of the 3D models, we show that the phase transitions are first order, with equilibrium structures that can be more complex than in the 2D case.

In the second study, we investigate systems with physical Hamiltonians based on one of the 2D tiling models with the goal of stimulating attempts to create a LP structure in experiments. We explore physically realizable particle designs while being mindful of particular features that may make the assembly of a LP structure in an experimental system difficult. Through Monte Carlo (MC) simulations, we have found that one particle design in particular is a promising template for a physical particle; a 2D system of identical disks with embedded dipoles is observed to undergo the series of phase transitions which leads to the LP state.

LP structures are well ordered but nonperiodic, and hence have nontrivial vibrational modes. In the third section of this dissertation, we study a ball and spring model with a LP pattern of spring stiffnesses and identify a set of extended modes with arbitrarily low participation ratios, a situation that appears to be unique to LP systems. The balls that oscillate with large amplitude in these modes live on periodic nets with arbitrarily large lattice constants. By studying periodic approximants to the LP structure, we present numerical evidence for the existence of such modes, and we give a heuristic explanation of their structure.

Ground and Electronic Excited States from Pairing Matrix Fluctuation and Particle-Particle Random Phase Approximation

The accurate description of ground and electronic excited states is an important and challenging topic in quantum chemistry. The pairing matrix fluctuation, as a counterpart of the density fluctuation, is applied to this topic. From the pairing matrix fluctuation, the exact electron correlation energy as well as two electron addition/removal energies can be extracted. Therefore, both ground state and excited states energies can be obtained and they are in principle exact with a complete knowledge of the pairing matrix fluctuation. In practice, considering the exact pairing matrix fluctuation is unknown, we adopt its simple approximation --- the particle-particle random phase approximation (pp-RPA) --- for ground and excited states calculations. The algorithms for accelerating the pp-RPA calculation, including spin separation, spin adaptation, as well as an iterative Davidson method, are developed. For ground states correlation descriptions, the results obtained from pp-RPA are usually comparable to and can be more accurate than those from traditional particle-hole random phase approximation (ph-RPA). For excited states, the pp-RPA is able to describe double, Rydberg, and charge transfer excitations, which are challenging for conventional time-dependent density functional theory (TDDFT). Although the pp-RPA intrinsically cannot describe those excitations excited from the orbitals below the highest occupied molecular orbital (HOMO), its performances on those single excitations that can be captured are comparable to TDDFT. The pp-RPA for excitation calculation is further applied to challenging diradical problems and is used to unveil the nature of the ground and electronic excited states of higher acenes. The pp-RPA and the corresponding Tamm-Dancoff approximation (pp-TDA) are also applied to conical intersections, an important concept in nonadiabatic dynamics. Their good description of the double-cone feature of conical intersections is in sharp contrast to the failure of TDDFT. All in all, the pairing matrix fluctuation opens up new channel of thinking for quantum chemistry, and the pp-RPA is a promising method in describing ground and electronic excited states.

Phase transfer catalysts drive diverse organic solvent solubility of single-walled carbon nanotubes helically wrapped by ionic, semiconducting polymers.

Use of phase transfer catalysts such as 18-crown-6 enables ionic, linear conjugated poly[2,6-{1,5-bis(3-propoxysulfonicacidsodiumsalt)}naphthylene]ethynylene (PNES) to efficiently disperse single-walled carbon nanotubes (SWNTs) in multiple organic solvents under standard ultrasonication methods. Steady-state electronic absorption spectroscopy, atomic force microscopy (AFM), and transmission electron microscopy (TEM) reveal that these SWNT suspensions are composed almost exclusively of individualized tubes. High-resolution TEM and AFM data show that the interaction of PNES with SWNTs in both protic and aprotic organic solvents provides a self-assembled superstructure in which a PNES monolayer helically wraps the nanotube surface with periodic and constant morphology (observed helical pitch length = 10 ± 2 nm); time-dependent examination of these suspensions indicates that these structures persist in solution over periods that span at least several months. Pump-probe transient absorption spectroscopy reveals that the excited state lifetimes and exciton binding energies of these well-defined nanotube-semiconducting polymer hybrid structures remain unchanged relative to analogous benchmark data acquired previously for standard sodium dodecylsulfate (SDS)-SWNT suspensions, regardless of solvent. These results demonstrate that the use of phase transfer catalysts with ionic semiconducting polymers that helically wrap SWNTs provide well-defined structures that solubulize SWNTs in a wide range of organic solvents while preserving critical nanotube semiconducting and conducting properties.