Linear scaling calculation of band edge states and doped semiconductors

Linear scaling methods provide total energy, but no energy levels and canonical wavefuctions. From the density matrix computed through the density matrix purification methods, we propose an order-N (O(N)) method for calculating both the energies and wavefuctions of band edge states, which are important for optical properties and chemical reactions. In addition, we also develop an O(N) algorithm to deal with doped semiconductors based on the O(N) method for band edge states calculation. We illustrate the O(N) behavior of the new method by applying it to boron nitride (BN) nanotubes and BN nanotubes with an adsorbed hydrogen atom. The band gap of various BN nanotubes are investigated systematicly and the acceptor levels of BN nanotubes with an isolated adsorbed H atom are computed. Our methods are simple, robust, and especially suited for the application in self-consistent field electronic structure theory

Imaging and manipulating electrons in a 1D quantum dot with Coulomb blockade microscopy

Motivated by the recent experiments by the Westervelt group using a mobile tip to probe the electronic state of quantum dots formed on a segmented nanowire, we study the shifts in Coulomb blockade peak positions as a function of the spatial variation of the tip potential, which can be termed "Coulomb blockade microscopy". We show that if the tip can be brought sufficiently close to the nanowire, one can distinguish a high density electronic liquid state from a Wigner crystal state by microscopy with a weak tip potential. In the opposite limit of a strongly negative tip potential, the potential depletes the electronic density under it and divides the quantum wire into two partitions. There the tip can push individual electrons from one partition to the other, and the Coulomb blockade micrograph can clearly track such transitions. We show that this phenomenon can be used to qualitatively estimate the relative importance of the electron interaction compared to one particle potential and kinetic energies. Finally, we propose that a weak tip Coulomb blockade micrograph focusing on the transition between electron number N=0 and N=1 states may be used to experimentally map the one-particle potential landscape produced by impurities and inhomogeneities.Comment: 4 pages 7 figure

Ordered and periodic chaos of the bounded one dimensinal multibarrier potential

Numerical analysis indicates that there exists an unexpected new ordered chaos for the bounded one-dimensional multibarrier potential. For certain values of the number of barriers, repeated identical forms (periods) of the wavepackets result upon passing through the multibarrier potential.Comment: 16 pages, 9 figures, 1 Table. Some former text removed and other introduce

Local electronic nematicity in the one-band Hubbard model

Nematicity is a well known property of liquid crystals and has been recently discussed in the context of strongly interacting electrons. An electronic nematic phase has been seen by many experiments in certain strongly correlated materials, in particular, in the pseudogap phase generic to many hole-doped cuprate superconductors. Recent measurements in high $T_c$ superconductors has shown even if the lattice is perfectly rotationally symmetric, the ground state can still have strongly nematic local properties. Our study of the two-dimensional Hubbard model provides strong support of the recent experimental results on local rotational $C_4$ symmetry breaking. The variational cluster approach is used here to show the possibility of an electronic nematic state and the proximity of the underlying symmetry-breaking ground state within the Hubbard model. We identify this nematic phase in the overdoped region and show that the local nematicity decreases with increasing electron filling. Our results also indicate that strong Coulomb interaction may drive the nematic phase into a phase similar to the stripe structure. The calculated spin (magnetic) correlation function in momentum space shows the effects resulting from real-space nematicity

The Optimal Inhomogeneity for Superconductivity: Finite Size Studies

We report the results of exact diagonalization studies of Hubbard models on a $4\times 4$ square lattice with periodic boundary conditions and various degrees and patterns of inhomogeneity, which are represented by inequivalent hopping integrals $t$ and $t^{\prime}$. We focus primarily on two patterns, the checkerboard and the striped cases, for a large range of values of the on-site repulsion $U$ and doped hole concentration, $x$. We present evidence that superconductivity is strongest for $U$ of order the bandwidth, and intermediate inhomogeneity, $0 <t^\prime< t$. The maximum value of the ``pair-binding energy'' we have found with purely repulsive interactions is $\Delta_{pb} = 0.32t$ for the checkerboard Hubbard model with $U=8t$ and $t^\prime = 0.5t$. Moreover, for near optimal values, our results are insensitive to changes in boundary conditions, suggesting that the correlation length is sufficiently short that finite size effects are already unimportant.Comment: 8 pages, 9 figures; minor revisions; more references adde

Theory of momentum resolved tunneling into a short quantum wire

Motivated by recent tunneling experiments in the parallel wire geometry, we calculate results for momentum resolved tunneling into a short one-dimensional wire, containing a small number of electrons. We derive some general theorems about the momentum dependence, and we carry out exact calculations for up to N=4 electrons in the final state, for a system with screened Coulomb interactions that models the situation of the experiments. We also investigate the limit of large $N$ using a Luttinger-liquid type analysis. We consider the low-density regime, where the system is close to the Wigner crystal limit, and where the energy scale for spin excitations can be much lower than for charge excitations, and we consider temperatures intermediate between the relevant spin energies and charge excitations, as well as temperatures below both energy scales.Comment: 19 pages, 13 figures, clarified text in a few points, added 1 figure, updated reference

What's the evidence that NICE guidance has been implemented? Results from a national evaluation using time series analysis, audit of patients' notes, and interviews

OBJECTIVES: To assess the extent and pattern of implementation of guidance issued by the National Institute for Clinical Excellence (NICE). DESIGN: Interrupted time series analysis, review of case notes, survey, and interviews. SETTING: Acute and primary care trusts in England and Wales. PARTICIPANTS: All primary care prescribing, hospital pharmacies; a random sample of 20 acute trusts, 17 mental health trusts, and 21 primary care trusts; and senior clinicians and managers from five acute trusts. MAIN OUTCOME MEASURES: Rates of prescribing and use of procedures and medical devices relative to evidence based guidance. RESULTS: 6308 usable patient audit forms were returned. Implementation of NICE guidance varied by trust and by topic. Prescribing of some taxanes for cancer (P <0.002) and orlistat for obesity (P <0.001) significantly increased in line with guidance. Prescribing of drugs for Alzheimer’s disease and prophylactic extraction of wisdom teeth showed trends consistent with, but not obviously a consequence of, the guidance. Prescribing practice often did not accord with the details of the guidance. No change was apparent in the use of hearing aids, hip prostheses, implantable cardioverter defibrillators, laparoscopic hernia repair, and laparoscopic colorectal cancer surgery after NICE guidance had been issued. CONCLUSIONS: Implementation of NICE guidance has been variable. Guidance seems more likely to be adopted when there is strong professional support, a stable and convincing evidence base, and no increased or unfunded costs, in organisations that have established good systems for tracking guidance implementation and where the professionals involved are not isolated. Guidance needs to be clear and reflect the clinical context

Fluctuations of the correlation dimension at metal-insulator transitions

We investigate numerically the inverse participation ratio, $P_2$, of the 3D Anderson model and of the power-law random banded matrix (PRBM) model at criticality. We found that the variance of $\ln P_2$ scales with system size $L$ as $\sigma^2(L)=\sigma^2(\infty)-A L^{-D_2/2d}$, being $D_2$ the correlation dimension and $d$ the system dimension. Therefore the concept of a correlation dimension is well defined in the two models considered. The 3D Anderson transition and the PRBM transition for $b=0.3$ (see the text for the definition of $b$) are fairly similar with respect to all critical magnitudes studied.Comment: RevTex, 5 pages, 4 eps figures, to be published in Phys. Rev. Let

Interaction effects and quantum phase transitions in topological insulators

We study strong correlation effects in topological insulators via the Lanczos algorithm, which we utilize to calculate the exact many-particle ground-state wave function and its topological properties. We analyze the simple, noninteracting Haldane model on a honeycomb lattice with known topological properties and demonstrate that these properties are already evident in small clusters. Next, we consider interacting fermions by introducing repulsive nearest-neighbor interactions. A first-order quantum phase transition was discovered at finite interaction strength between the topological band insulator and a topologically trivial Mott insulating phase by use of the fidelity metric and the charge-density-wave structure factor. We construct the phase diagram at $T = 0$ as a function of the interaction strength and the complex phase for the next-nearest-neighbor hoppings. Finally, we consider the Haldane model with interacting hard-core bosons, where no evidence for a topological phase is observed. An important general conclusion of our work is that despite the intrinsic nonlocality of topological phases their key topological properties manifest themselves already in small systems and therefore can be studied numerically via exact diagonalization and observed experimentally, e.g., with trapped ions and cold atoms in optical lattices.Comment: 13 pages, 12 figures. Published versio

Polariton Lasing in a Multilevel Quantum Dot Strongly Coupled To a Single Photon Mode

We present an approximate analytic expression for the photoluminescence spectral function of a model polariton system, which describes a quantum dot, with a finite number of fermionic levels, strongly interacting with the lowest photon mode of a pillar microcavity. Energy eigenvalues and wavefunctions of the electron-hole-photon system are obtained by numerically diagonalizing the Hamiltonian. Pumping and photon losses through the cavity mirrors are described with a master equation, which is solved in order to determine the stationary density matrix. The photon first-order correlation function, from which the spectral function is found, is computed with the help of the Quantum Regression Theorem. The spectral function qualitatively describes the polariton lasing regime in the model, corresponding to pumping rates two orders of magnitude lower than those needed for ordinary (photon) lasing. The second-order coherence functions for the photon and the electron-hole subsystems are computed as functions of the pumping rate.Comment: version accepted in Phys. Rev.