Accelerating Atomic Orbital-based Electronic Structure Calculation via Pole Expansion and Selected Inversion

We describe how to apply the recently developed pole expansion and selected inversion (PEXSI) technique to Kohn-Sham density function theory (DFT) electronic structure calculations that are based on atomic orbital discretization. We give analytic expressions for evaluating the charge density, the total energy, the Helmholtz free energy and the atomic forces (including both the Hellman-Feynman force and the Pulay force) without using the eigenvalues and eigenvectors of the Kohn-Sham Hamiltonian. We also show how to update the chemical potential without using Kohn-Sham eigenvalues. The advantage of using PEXSI is that it has a much lower computational complexity than that associated with the matrix diagonalization procedure. We demonstrate the performance gain by comparing the timing of PEXSI with that of diagonalization on insulating and metallic nanotubes. For these quasi-1D systems, the complexity of PEXSI is linear with respect to the number of atoms. This linear scaling can be observed in our computational experiments when the number of atoms in a nanotube is larger than a few hundreds. Both the wall clock time and the memory requirement of PEXSI is modest. This makes it even possible to perform Kohn-Sham DFT calculations for 10,000-atom nanotubes with a sequential implementation of the selected inversion algorithm. We also perform an accurate geometry optimization calculation on a truncated (8,0) boron-nitride nanotube system containing 1024 atoms. Numerical results indicate that the use of PEXSI does not lead to loss of accuracy required in a practical DFT calculation

Lifshitz Transition in Underdoped Cuprates

Recent studies show that quantum oscillations thought to be associated with a density wave reconstructed Fermi surface disappear at a critical value of the doping for YBa2Cu3O6+y, and the cyclotron mass diverges as the critical value is approached from the high doping side. We argue that the phenomenon is due to a Lifshitz transition where the pockets giving rise to the quantum oscillations connect to form an open (quasi-1d) Fermi surface. The estimated critical doping is close to that found by experiment, and the theory predicts a logarithmic divergence of the cyclotron mass with a coefficient comparable to that observed in experiment.Comment: 4 pages, 4 figure

Tunneling and delocalization in hydrogen bonded systems: a study in position and momentum space

Novel experimental and computational studies have uncovered the proton momentum distribution in hydrogen bonded systems. In this work, we utilize recently developed open path integral Car-Parrinello molecular dynamics methodology in order to study the momentum distribution in phases of high pressure ice. Some of these phases exhibit symmetric hydrogen bonds and quantum tunneling. We find that the symmetric hydrogen bonded phase possesses a narrowed momentum distribution as compared with a covalently bonded phase, in agreement with recent experimental findings. The signatures of tunneling that we observe are a narrowed distribution in the low-to-intermediate momentum region, with a tail that extends to match the result of the covalently bonded state. The transition to tunneling behavior shows similarity to features observed in recent experiments performed on confined water. We corroborate our ice simulations with a study of a particle in a model one-dimensional double well potential that mimics some of the effects observed in bulk simulations. The temperature dependence of the momentum distribution in the one-dimensional model allows for the differentiation between ground state and mixed state tunneling effects.Comment: 14 pages, 13 figure

Polarization and ellipticity of high-order harmonics from aligned molecules generated by linearly polarized intense laser pulses

We present theoretical calculations for polarization and ellipticity of high-order harmonics from aligned N$_2$, CO$_2$, and O$_2$ molecules generated by linearly polarized lasers. Within the rescattering model, the two polarization amplitudes of the harmonics are determined by the photo-recombination amplitudes for photons emitted parallel and perpendicular to the direction of the {\em same} returning electron wave packet. Our results show clear species-dependent polarization states, in excellent agreement with experiments. We further note that the measured polarization ellipse of the harmonic furnishes the needed parameters for a "complete" experiment in molecules.Comment: 4 pages, 4 figure

Effect of temperature-dependent shape anisotropy on coercivity with aligned Stoner-Wohlfarth soft ferromagnets

The temperature variation effect of shape anisotropy on the coercivity, HC(T), for the aligned Stoner-Wohlfarth (SW) soft ferromagnets, such as fcc Ni, fcc Co and bcc Fe, are investigated within the framework of Neel-Brown (N-B) analysis. An extended N-B equation is thus proposed,by introducing a single dimensionless correction function, the reduced magnetization, m(\tao) = MS(T)/MS(0), in which \tao = T/TC is the reduced temperature, MS(T) is the saturation magnetization, and TC is the Curie temperature. The factor, m(\tao), accounts for the temperature-dependent effect of the shape anisotropy. The constants, H0 and E0, are for the switching field at zero temperature and the potential barrier at zero field, respectively. According to this newly derived equation, the blocking temperature above which the properties of superparamagnetism show up is described by the expression, TB = E0m^2(\tao)/[kBln(t/t0)], with the extra correction factor m^2(\tao). The possible effect on HC(T) and the blocking temperature, TB, attributed to the downshift of TC resulting from the finite size effect has been discussed also.Comment: 22 pages, 2 figures, 1 table, Accepted by Phys. Rev.

P-band in a rotating optical lattice

We investigate the effects of rotation on the excited bands of a tight binding lattice, focusing particulary on the first excited (p-) band. Both the on-site energies and the hopping between lattice sites are modified by the effective magnetic field created by rotation, causing a non-trivial splitting and magnetic fine structure of the p-band. We show that Peierls substitution can be modified to describe p-band under rotation, and use this method to derive an effective Hamiltonian. We compare the spectrum of the effective Hamiltonian with a first principles calculation of the magnetic band structure and find excellent agreement, confirming the validity of our approach. We also discuss the on-site interaction terms for bosons and argue that many-particle phenomena in a rotating p-band can be investigated starting from this effective Hamiltonian.Comment: 7 pages, 4 figures, new discussion of effective Hamiltonian, references adde

Probing molecular frame photoionization via laser generated high-order harmonics from aligned molecules

Present photoionization experiments cannot measure molecular frame photoelectron angular distributions (MFPAD) from the outermost valence electrons of molecules. We show that details of the MFPAD can be retrieved with high-order harmonics generated by infrared lasers from aligned molecules. Using accurately calculated photoionization transition dipole moments for fixed-in-space molecules, we show that the dependence of the magnitude and phase of the high-order harmonics on the alignment angle of the molecules observed in recent experiments can be quantitatively reproduced. This result provides the needed theoretical basis for ultrafast dynamic chemical imaging using infrared laser pulses.Comment: 5 pages, 4 figure