arXiv subjects

Eran Rabani

Publications and source records attributed to Eran Rabani.

At least 73 records · Page 4Linked to original sources

arXiv2019

Nonmonotonic band gap evolution in bent phosphorene nanosheets

Nonmonotonic bending-induced changes of fundamental band gaps and quasiparticle energies are observed for realistic nanoscale phosphorene nanosheets. Calculations using stochastic many-body perturbation theory (sGW) show that even slight curvature causes significant changes in the electronic properties. For small bending radii (< 4 nm) the band-gap changes from direct to indirect. The response of phosphorene to deformation is strongly anisotropic (different for zig-zag vs. armchair bending) due to an interplay of exchange and correlation effects. Overall, our results show that fundamental band gaps of phosphorene sheets can be manipulated by as much as 0.7 eV depending on the bending direction.

cond-mat.mtrl-sci↗

arXiv2018

Stochastic density functional theory

Linear-scaling implementations of density functional theory (DFT) reach their intended efficiency regime only when applied to systems having a physical size larger than the range of their Kohn-Sham density matrix (DM). This causes a problem since many types of large systems of interest have a rather broad DM range and are therefore not amenable to analysis using DFT methods. For this reason, the recently proposed stochastic DFT (sDFT), avoiding exhaustive DM evaluations, is emerging as an attractive alternative linear-scaling approach. This review develops a general formulation of sDFT in terms of a (non)orthogonal basis representation and offers an analysis of the statistical errors (SEs) involved in the calculation. Using a new Gaussian-type basis-set implementation of sDFT, applied to water clusters and silicon nanocrystals, it demonstrates and explains how the standard deviation and the bias depend on the sampling rate and the system size in various types of calculations. We also develop basis-set embedded-fragments theory, demonstrating its utility for reducing the SEs for energy, density of states and nuclear force calculations. Finally, we discuss the algorithmic complexity of sDFT, showing it has CPU wall-time linear-scaling. The method parallelizes well over distributed processors with good scalability and therefore may find use in the upcoming exascale computing architectures.

physics.chem-ph↗

arXiv2018

Overlapped Embedded Fragment Stochastic Density Functional Theory for Covalently Bonded Materials

The stochastic density functional theory (DFT) [Phys. Rev. Lett. 111, 106402 (2013)] is a valuable linear scaling approach to Kohn-Sham DFT that does not rely on the sparsity of the density matrix. Linear (and often sub-linear) scaling is achieved by introducing a controlled statistical error in the density, energy and forces. The statistical error (noise) is proportional to the inverse square root of the number of stochastic orbitals and thus decreases slowly, however, by dividing the system to fragments that are embedded stochastically, the statistical error can be reduced significantly. This has been shown to provide remarkable results for non-covalently bonded systems, however, the application to covalently bonded systems had limited success, particularly for delocalized electrons. Here, we show that the statistical error in the density correlates with both the density and the density matrix of the system and propose a new fragmentation scheme that elegantly interpolates between overlapped fragments. We assess the performance of the approach for bulk silicon of varying supercell sizes (up to $N_{e}=16384$ electrons) and show that overlapped fragments reduce significantly the statistical noise even for systems with a delocalized density matrix.

physics.chem-ph↗

arXiv2018

Electron-hole correlations govern Auger recombination in nanostructures

The fast nonradiative decay of multiexcitonic states via Auger recombination is a fundamental process affecting a variety of applications based on semiconductor nanostructures. From a theoretical perspective, the description of Auger recombination in confined semiconductor nanostructures is a challenging task due to the large number of valance electrons and exponentially growing number of excited excitonic and biexcitonic states that are coupled by the Coulomb interaction. These challenges have restricted the treatment of Auger recombination to simple, noninteracting electron-hole models. Herein we present a novel approach for calculating Auger recombination lifetimes in confined nanostructures having thousands to tens of thousands of electrons, explicitly including electron-hole interactions. We demonstrate that the inclusion of electron-hole correlations are imperative to capture the correct scaling of the Auger recombination lifetime with the size and shape of the nanostructure. In addition, correlation effects are required to obtain quantitatively accurate lifetimes even for systems smaller than the exciton Bohr radius. Neglecting such correlations can result in lifetimes that are 2 orders of magnitude too long. We establish the utility of the new approach for CdSe quantum dots of varying sizes and for CdSe nanorods of varying diameters and lengths. Our new approach is the first theoretical method to postdict the experimentally known universal volume scaling law for quantum dots and makes novel predictions for the scaling of the Auger recombination lifetimes in nanorods.

cond-mat.mes-hall↗

arXiv2018

Note: On the memory kernel and the reduced system propagator

We relate the memory kernel in the Nakajima-Zwanzig-Mori time-convolution approach to the reduced system propagator which is often used to obtain the kernel in the Tokuyama-Mori time-convolutionless approach. The connection provides a robust and simple formalism to compute the memory kernel for a generalized system-bath model circumventing the need to compute high order system-bath observables. We illustrate this for a model system with electron-electron and electron-phonon couplings, driven away from equilibrium.

cond-mat.other↗

arXiv2018

Swift $GW$ beyond $10,000$ electrons using fractured stochastic orbitals

We introduce the concept of fractured stochastic orbitals (FSOs), short vectors that sample a small number of space points and enable an efficient stochastic sampling of any general function. As a first demonstration, FSOs are applied in conjunction with simple direct-projection to accelerate our recent stochastic $GW$ technique; the new developments enable accurate prediction of $G_{0}W_{0}$ quasiparticle energies and gaps for systems with up to $N_{e}>10,000$ electrons, with small statistical errors of $\pm0.05\,{\rm eV}$ and using less than 2000 core CPU hours. Overall, stochastic $GW$ scales now linearly (and often sub-linearly) with $N_{e}.$

physics.comp-ph↗

arXiv2018

First principles absorption spectra of Au nanoparticles: from quantum to classical

Absorption cross-section spectra for gold nanoparticles were calculated using fully quantum Stochastic Density Functional Theory and a classical Finite-Difference Time Domain (FDTD) Maxwell solver. Spectral shifts were monitored as a function of size (1.3-3.1 nm) and shape (octahedron, cubeoctahedron, and truncated cube). Even though the classical approach is forced to fit the quantum TDDFT at 3.1nm, at smaller sizes there is a significant deviation as the classical theory is unable to account for peak splitting and spectral blue shifts even after quantum spectral corrections. We attribute the failure of classical methods at predicting these features to quantum effects and low density of states in small nanoparticles. Classically, plasmon resonances are modeled as collective conduction electron excitations, but at small nanoparticle size these excitations transition to few or even individual conductive electron excitations, as indicated by our results.

physics.atm-clus↗

arXiv2018

Simple eigenvalue-self-consistent $\barΔGW_{0}$

We derive a general form of eigenvalue self-consistency for $GW_{0}$ in the time domain and use it to obtain a simplified postprocessing eigenvalue self-consistency, which we label $\barΔGW_{0}$. The method costs the same as a one-shot $G_{0}W_{0}$ when the latter gives the full frequency-domain (or time-domain) matrix element of the self-energy. The accuracy of $\barΔGW_{0}$ increases with system size, as demonstrated here by comparison to other $GW$ self-consistency results and to CCSD(T) predictions. When combined with the large-scale stochastic $G_{0}W_{0}$ formulation $\barΔGW_{0}$ is applicable to very large systems, as exemplified by periodic supercells of semiconductors and insulators with 2048 valence electrons. For molecules the error of our eventual partially self-consistent approach starts at about 0.2eV for small molecules and decreases to 0.05eV for large ones, while for the periodic solids studied here the mean-absolute-error is only 0.03eV.

physics.chem-ph↗

arXiv2018

Stochastic Density Functional Theory at Finite Temperatures

Simulations in the warm dense matter regime using finite temperature Kohn-Sham density functional theory (FT-KS-DFT), while frequently used, are computationally expensive due to the partial occupation of a very large number of high-energy KS eigenstates which are obtained from subspace diagonalization. We have developed a stochastic method for applying FT-KS-DFT, that overcomes the bottleneck of calculating the occupied KS orbitals by directly obtaining the density from the KS Hamiltonian. The proposed algorithm, scales as $O\left(NT^{-1}\right)$ and is compared with the high-temperature limit scaling $O\left(N^{3}T^{3}\right)$ of the deterministic approach, where $N$ is the system size (number of electrons, volume etc.) and $T$ is the temperature. The method has been implemented in a plane-waves code within the local density approximation (LDA); we demonstrate its efficiency, statistical errors and bias in the estimation of the free energy per electron for a diamond structure silicon. The bias is small compared to the fluctuations, and is independent of system size. In addition to calculating the free energy itself, one can also use the method to calculate its derivatives and obtain the equations of state.

cond-mat.mtrl-sci↗

arXiv2017

Quasiparticle spectra from molecules to bulk

A stochastic cumulant GW method is presented, allowing us to map the evolution of photoemission spectra, quasiparticle energies, lifetimes and emergence of collective excitations from molecules to bulk-like systems with up to thousands of valence electrons, including Si nanocrystals and nanoplatelet. The quasiparticle energies rise due to their coupling with collective shake-up (plasmon) excitations, and this coupling leads to significant spectral weight loss (up to 50% for the low energy states), shortening the lifetimes and shifting the spectral features to lower energy by as much as 0.6 eV. Such features are common to all the systems studied irrespective of their size and shape. For small and low dimensional systems the surface plasmon resonances affect the frequency of the collective excitation and position of the satellites.

cond-mat.mes-hall↗

arXiv2017

Stochastic GW calculations for molecules

Quasiparticle (QP) excitations are extremely important for understanding and predicting charge transfer and transport in molecules, nanostructures and extended systems. Since density functional theory (DFT) within the Kohn-Sham (KS) formulation does not provide reliable QP energies, many-body perturbation techniques such as the GW approximation are essential. The main practical drawback of GW implementations is the high computational scaling with system size, prohibiting its use in extended, open boundary systems with many dozens of electrons or more. Recently, a stochastic formulation of GW (sGW) was presented [Phys. Rev. Lett. 113, 076402 (2014)] with a near-linear-scaling complexity, illustrated for a series of silicon nanocrystals reaching systems of more than 3000 electrons. This advance provides a route for many-body calculations on very larges systems that were impossible with previous approaches. While earlier we have shown the gentle scaling of sGW, its accuracy was not extensively demonstrated. Therefore, we show that this new sGW approach is very accurate by calculating the ionization energies of a group of sufficiently small molecules where a comparison to other GW codes is still possible. Using a set of 10 such molecules, we demonstrate that sGW provides reliable vertical ionization energies in close agreement with benchmark deterministic GW results [J. Chem. Theory Comput, 11, 5665 (2015)], with mean (absolute) deviation of 0.05 and 0.09eV. For completeness, we also provide a detailed review of the sGW theory and numerical implementation.

physics.chem-ph↗

arXiv2017

Equilibrium configurations of large nanostructures using the embedded saturated-fragments stochastic density functional theory

An \emph{ab initio} Langevin dynamics approach is developed based on stochastic density functional theory (sDFT) within a new \emph{embedded saturated } \emph{fragment }formalism, applicable to covalently bonded systems. The forces on the nuclei generated by sDFT contain a random component natural to Langevin dynamics and its standard deviation is used to estimate the friction term on each atom by satisfying the fluctuation\textendash dissipation relation. The overall approach scales linearly with system size even if the density matrix is not local and is thus applicable to ordered as well as disordered extended systems. We implement the approach for a series of silicon nanocrystals (NCs) of varying size with a diameter of up to $3$nm corresponding to $N_{e}=3000$ electrons and generate a set of configurations that are distributed canonically at a fixed temperature, ranging from cryogenic to room temperature. We also analyze the structure properties of the NCs and discuss the reconstruction of the surface geometry.

physics.chem-ph↗

arXiv2017

A Stochastic Formulation of the Resolution of Identity: Application to Second Order Møller-Plesset Perturbation Theory

A stochastic orbital approach to the resolution of identity (RI) approximation for 4-index 2-electron electron repulsion integrals (ERIs) is presented. The stochastic RI-ERIs are then applied to Møller-Plesset perturbation theory (MP2) utilizing a \textit{multiple stochastic orbital approach}. The introduction of multiple stochastic orbitals results in an $N^3$ scaling for both the stochastic RI-ERIs and stochastic RI-MP2. We demonstrate that this method exhibits a small prefactor and an observed scaling of $N^{2.4}$ for a range of water clusters, already outperforming MP2 for clusters with as few as 21 water molecules.

physics.chem-ph↗

arXiv2016

Spontaneous charge carrier localization in extended one-dimensional systems

Charge carrier localization in extended atomic systems has been described previously as being driven by disorder, point defects or distortions of the ionic lattice. Here we show for the first time by means of first-principles computations that charge carriers can spontaneously localize due to a purely electronic effect in otherwise perfectly ordered structures. Optimally-tuned range-separated density functional theory and many-body perturbation calculations within the GW approximation reveal that in trans-polyacetylene and polythiophene the hole density localizes on a length scale of several nanometers. This is due to exchange-induced translational symmetry breaking of the charge density. Ionization potentials, optical absorption peaks, excitonic binding energies and the optimally-tuned range parameter itself all become independent of polymer length as it exceeds the critical localization scale. Moreover, lattice disorder and the formation of a polaron result from the charge localization in contrast to the traditional view that lattice distortions precede charge localization. Our results can explain experimental findings that polarons in conjugated polymers form instantaneously after exposure to ultrafast light pulses.

cond-mat.mes-hall↗

arXiv2015

Stochastic Optimally-Tuned Ranged-Separated Hybrid Density Functional Theory

We develop a stochastic formulation of the optimally-tuned range-separated hybrid density functional theory which enables significant reduction of the computational effort and scaling of the non-local exchange operator at the price of introducing a controllable statistical error. Our method is based on stochastic representations of the Coulomb convolution integral and of the generalized Kohn-Sham density matrix. The computational cost of the approach is similar to that of usual Kohn-Sham density functional theory, yet it provides much more accurate description of the quasiparticle energies for the frontier orbitals. This is illustrated for a series of silicon nanocrystals up to sizes exceeding 3000 electrons. Comparison with the stochastic GW many-body perturbation technique indicates excellent agreement for the fundamental band gap energies, good agreement for the band-edge quasiparticle excitations, and very low statistical errors in the total energy for large systems. The present approach has a major advantage over one-shot GW by providing a self-consistent Hamiltonian which is central for additional post-processing, for example in the stochastic Bethe-Salpeter approach.

physics.chem-ph↗

arXiv2015

Exact Calculation of the Time Convolutionless Master Equation Generator: Application to the Nonequilibrium Resonant Level Model

The generalized quantum master equation provides a powerful tool to describe the dynamics in quantum impurity models driven away from equilibrium. Two complementary approaches, one based on Nakajima--Zwanzig--Mori time-convolution (TC) and the other on the Tokuyama--Mori time-convolutionless (TCL) formulations provide a starting point to describe the time-evolution of the reduced density matrix. A key in both approaches is to obtain the so called "memory kernel" or "generator", going beyond second or fourth order perturbation techniques. While numerically converged techniques are available for the TC memory kernel, the canonical approach to obtain the TCL generator is based on inverting a super-operator in the \emph{full} Hilbert space, which is difficult to perform and thus, all applications of the TCL approach rely on a perturbative scheme of some sort. Here, the TCL generator is expressed using a reduced system propagator which can be obtained from system observables alone and requires the calculation of super-operators and their inverse in the \emph{reduced }Hilbert space rather than the full one. This makes the formulation amenable to quantum impurity solvers or to diagrammatic techniques, such as the nonequilibrium Green's function. We implement the TCL approach for the resonant level model driven away from equilibrium and compare the time scales for the decay of the generator with that of the memory kernel in the TC approach. Furthermore, the effects of temperature, source-drain bias, and gate potential on the TCL/TC generators are discussed.

cond-mat.mes-hall↗

arXiv2015

Sub-Ohmic to super-Ohmic crossover behavior in nonequilibrium quantum systems with electron-phonon interactions

The transition from weakly damped coherent motion to localization in the context of the spin-boson model has been the subject of numerous studies with distinct behavior depending on the form of the phonon-bath spectral density, $J\left(ω\right)\proptoω^{s}$. Sub-Ohmic ($s<1$) and Ohmic ($s=1$) spectral densities show a clear localization transition at zero temperature and zero bias, while for super-Ohmic ($s>1$) spectral densities this transition disappears. In this work, we consider the influence of the phonon-bath spectral density on the \emph{nonequilibrium} dynamics of a quantum dot with electron-phonon interactions described by the extended Holstein model. Using the reduced density matrix formalism combined with the multi-layer multiconfiguration time-dependent Hartree approach, we investigate the dynamic response, the time scales for relaxation, as well as the existence of multiple long-lived solutions as the system-bath coupling changes from the sub- to the super-Ohmic cases. Bistability is shown to diminish for increasing powers of $s$ similar to the spin-boson case. However, the physical mechanism and the dependence on the model parameters such as the typical bath frequency $ω_{c}$ and the polaron shift $λ$ are rather distinct.

cond-mat.str-el↗

arXiv2015

Landauer Current and Mutual Information

We study quantum evolution of the entanglement of a quantum dot connected to left and right leads initially maintained at chemical potentials $μ_{L}$ and $μ_{R}$ respectively, within the non-interacting resonant-level model. The full nonequilirbium mixed state density matrix of the whole system is written down exactly, and entanglement is computed by recourse to the notion of mutual information. A strong and direct correlation is found between the Landauer current, and the entanglement at all times, the steady-state values in particular displaying a quadratic relationship at high temperatures. Strikingly, it is found that one can obtain a maximally entangled quantum dot by simply applying a sufficiently large `source-drain' voltage $V_{SD}$ even at high temperatures.

cond-mat.str-el↗