Atomic-scale Systems Research Articles

Towards optimal control: the probabilistic route in quantum systems

There is a fundamental limit to what is knowable about atomic and molecular scale systems. This fuzziness is not always due to the act of measurement. Other contributing factors include system parameter uncertainty, functional uncertainty that originates from input functions, and sensors noises to mention a few. This indeterminism has led to major challenges in the development of accurate control methods for atomic scale systems. To address the probabilistic and uncertain nature of these systems, this work proposes a novel control framework that considers the representation of the quantum system states and the quantification of its physical properties following a probabilistic approach. Our framework is fully probabilistic. It uses the Shannon relative entropy from information theory to design optimal randomised controllers that can achieve a desired outcome of an atomic scale system. Two experiments are carried out to illustrate the applicability and effectiveness of the proposed approach.

Third-order exceptional line in a nitrogen-vacancy spin system.

Exceptional points (EPs) are singularities in non-Hermitian systems, where k (k ≥ 2) eigenvalues and eigenstates coalesce. High-order EPs exhibit richer topological characteristics and better sensing performance than second-order EPs. Theory predicts even richer non-Hermitian topological phases for high-order EP geometries, such as lines or rings formed entirely by high-order EPs. However, experimental exploration of high-order EP geometries has hitherto proved difficult due to the demand for more degrees of freedom in the Hamiltonian's parameter space or a higher level of symmetries. Here we observe a third-order exceptional line in an atomic-scale system. To this end, we use a nitrogen-vacancy spin in diamond and introduce multiple symmetries in the non-Hermitian Hamiltonian realized with the system. Furthermore, we show that the symmetries play an essential role in the occurrence of high-order EP geometries. Our approach can in future be further applied to explore high-order EP-related topological physics at the atomic scale and, potentially, for applications of high-order EPs in quantum technologies.

Controlled Switching of Bistable Nanophase Domains on a Silicon Surface.

Switching the crystalline phase of a material via electrostatic control is a proven strategy for developing memory devices such as memristors that are based on nonvolatile resistance switching phenomena. However, phase switching in atomic-scale systems is often difficult to control and poorly understood. Here, we explore nonvolatile switching of long 2.3 nm wide bistable nanophase domains in a Sn double-layer structure grown on Si(111), using a scanning tunneling microscope. We identified two mechanisms for this phase switching phenomenon. First, the electrical field across the tunnel gap continuously tunes the relative stability of the two phases and favors one over the other depending on the tunneling polarity. The second mechanism involves carrier injection into empty Sn orbitals. The coupling between these relatively long-lived hot electrons and surface phonons induces a lattice instability at sufficiently large tunneling current and provides access to a hidden metastable state of matter. This hidden state is nonvolatile but can be erased by choosing the appropriate tunneling conditions or raising the temperature. Similar mechanisms could possibly be exploited in phase-change memristor and field effect devices.

Quantum transport via dot devices with arbitrarily strong interactions

The paper develops a theory of tunneling electron transport through atomic-scale systems (or briefly quantum dots) with arbitrarily strong interaction. The theory is based on a diagram technique for nonequilibrium Green’s functions defined on Hubbard operators. The use of Hubbard operators, describing many-body states of an entire quantum dot, makes it possible to represent the Hamiltonian of the quantum dot in a universal diagonal form and consider its coupling with two leads within the perturbation theory. It is shown that in the case when all Hubbard operators are defined for the same site, some rules of the diagram technique for Hubbard operators, initially developed for lattice models, have to be modified. As an example of the application of the modified theory, the current-voltage characteristics of the single-impurity Anderson model with infinitely large Coulomb repulsion are calculated. It is shown that taking into account the multiple electron tunneling processes with spin flips results in the dip in the center of the Lorentz distribution peak, describing the density of states of the one level Anderson impurity coupled with two leads. The emergence of this dip in the density of states leads to a peculiar feature in the bias voltage dependence of the differential conductivity, which can be detected experimentally.

An assessment of SPH simulations of sudden expansion/contraction 3-D channel flows

In this paper, we investigate the application of smoothed particle hydrodynamics (SPH) to the computation of 3-D flows in channels with sudden expansion or contraction. In the same context, we also discuss 2-D SPH computations applicable to channels characterized by cross-sections of large aspect ratios. The particle nature of SPH allows us to treat macro-systems similarly to atomic systems, transferring knowledge from molecular dynamics (MD) and dissipative particle dynamics (DPD) and suggesting a common framework for simulations at different scales. Computations are carried out by making use of tools previously used for atomic-scale systems (usually MD) and mesoscopic systems (usually DPD). The results obtained suggest that SPH captures the main flow characteristics and achieves good accuracy both in 2-D and 3-D, at least for Re values in the range 0.0177 to 55.4 investigated here. Minor numerical artifacts may be observed near the solid boundaries, especially at corner discontinuities. Such localized inaccuracies near points of geometric discontinuity are common in all numerical simulation methods.

Atomic-Scale Control of Coherent Thermal Radiation

Controlling the temporal coherence of thermal radiation plays an important role in energy harvesting and thermal management. Conventional approaches for thermal radiation control rely on resonances in bulk thermal emitters, which usually have a large footprint and display little tunability. In this work, we explore the possibility to control coherent thermal emission with atomically thin emitters. We show that, despite the atomic thickness, the peak emissivity of these emitters could be as high as the bulk emitters. We identify several linear scaling laws for the radiative properties of atomic-scale systems, providing a pathway for controlling thermal radiation with atomic precision.

A chirality-dependent peridynamic model for the fracture analysis of graphene sheets

Based on the bond-based peridynamic (BPD) method, a chirality-dependent peridynamic (CDPD) model is proposed for the fracture analysis of single layer graphene sheets (SLGS). The peridynamic (PD) parameters in the CDPD model are derived by analyzing the stress-strain relations of SLGS at atomic scale, and thus the CDPD model can provide a multiscale insight into the fracture analysis of SLGS with considering the effect of chirality. In order to increase the efficiency of CDPD simulations of large atomic-scale systems, a special coarse-grain (CG) technique is employed by considering the chiral structure of SLGS in the CDPD simulations. The effect of grid type, grid orientation and grid spacing on the numerical convergence is investigated. The proposed CDPD model is validated by comparing with the available molecular dynamics (MD) results, and the comparisons demonstrate the importance of considering the atomistic structure of SLGS when PD theory is applied in the fracture analysis because the chirality dominates the propagating directions of cracks. The crack propagations in SLGS with various chiralities are studied using the CDPD model. The numerical results indicate that the fracture of SLGS is significantly dependent on the chirality. Especially, examples of large-sized SLGS (750 nm × 750 nm) with about 20 million atoms in the corresponding fully atomistic systems demonstrate the applicability and effectiveness of the proposed CDPD model in the simulation of microscale structures of SLGS without loss of chiral features. To study such large systems is almost impractical for the fully atomistic simulation. This study also provides a significant insight for extending the PD model to the studies on chirality-related materials at microscale.

Precision Spectroscopy of Negative-Ion Resonances in Ultralong-Range Rydberg Molecules.

The level structure of negative ions near the electron detachment limit dictates the low-energy scattering of an electron with the parent neutral atom. We demonstrate that a single ultracold atom bound inside a Rydberg orbit forming an ultralong-range Rydberg molecule provides an atomic-scale system that is highly sensitive to electron-neutral scattering and thus allows for detailed insights into the underlying near-threshold anion states. Our measurements reveal the so-far unobserved fine structure of the ^{3}P_{J} triplet of Rb^{-} and allows us to extract parameters of the associated p-wave scattering resonances that deviate from previous theoretical estimates. Moreover, we observe a novel alignment mechanism for Rydberg molecules mediated by spin-orbit coupling in the negative ion.

Correlation-driven transport asymmetries through coupled spins in a tunnel junction

Spin–spin correlations can be the driving force that favours certain ground states and are key in numerous models that describe the behaviour of strongly correlated materials. While the sum of collective correlations usually lead to a macroscopically measurable change in properties, a direct quantification of correlations in atomic scale systems is difficult. Here we determine the correlations between a strongly hybridized spin impurity on the tip of a scanning tunnelling microscope and its electron bath by varying the coupling to a second spin impurity weakly hybridized to the sample surface. Electronic transport through these coupled spins reveals an asymmetry in the differential conductance reminiscent of spin-polarized transport in a magnetic field. We show that at zero field, this asymmetry can be controlled by the coupling strength and is related to either ferromagnetic or antiferromagnetic spin–spin correlations in the tip.

Influence of Cholesterol on Phospholipid Bilayer Structure and Dynamics.

In this study, the influence of cholesterol on lipid bilayers is investigated by changing phospholipid headgroup, cholesterol concentration, chain saturation, and temperature. Molecular dynamics (MD) simulations were used to characterize bilayers containing phosphatidylcholine (PC) head groups with either fully saturated dimyristoyl (DM) or monounsaturated dioleoyl (DO) acyl chains and cholesterol concentrations ranging from 5 to 50%. To further explore the effects of cholesterol on bilayers with different head groups, we also performed MD simulations of bilayer systems having 15% cholesterol with phosphatidic acid (PA), phosphatidylethanolamine (PE), phosphatidylglycerol (PG), phosphatidylinositol (PI), and phosphatidylserine (PS), each having DM chains and at a temperature above the solid gel phase transition. Additionally, bilayers of DMPA, DMPE, and DMPS with 15% cholesterol were simulated at temperatures below the solid gel phase transition temperatures. Compared to membranes without cholesterol, cholesterol in the model bilayers increases chain order in bilayers with the highest order in the liquid ordered and solid gel phases. Head group properties and acyl chain saturation are also found to critically impact bilayer dynamics, largely through the formation of hydrogen bonds between membrane components. These results provide a better understanding of the basic characteristics on structure and dynamics of cholesterol-containing membranes by revealing molecular details of interactions between cholesterol and phospholipids as well as add to the library of simulation data necessary for the MD community to accurately represent relevant models of atomic-scale systems.

Approaching the quantum limit for plasmonics: linear atomic chains

Optical excitations in atomic-scale materials can be strongly mixed, with contributions from both single-particle transitions and collective response. This complicates the quantum description of these excitations, because there is no clear way to define their quantization. To develop a quantum theory for these optical excitations, they must first be characterized so that single-particle-like and collective excitations can be identified. Linear atomic chains, such as atom chains on surfaces, linear arrays of dopant atoms in semiconductors, or linear molecules, provide ideal testbeds for studying collective excitations in small atomic-scale systems. We use exact diagonalization to study the many-body excitations of finite (10 to 25) linear atomic chains described by a simplified model Hamiltonian. Exact diagonalization results can be very different from the density functional theory (DFT) results usually obtained. Highly correlated, multiexcitonic states, strongly dependent on the electron–electron interaction strength, dominate the exact spectral and optical response but are not present in DFT excitation spectra. The ubiquitous presence of excitonic many-body states in the spectra makes it hard to identify plasmonic excitations. A combination of criteria involving a many-body state’s transfer dipole moment, balance, transfer charge, dynamical response, and induced-charge distribution do strongly suggest which many-body states should be considered as plasmonic. This analysis can be used to reveal the few plasmonic many-body states hidden in the dense spectrum of low-energy single-particle-like states and many higher-energy excitonic-like states. These excitonic states are the predominant excitation because of the many possible ways to develop local correlations.

Global transition path search for dislocation formation in Ge on Si(001)

Global optimization of transition paths in complex atomic scale systems is addressed in the context of misfit dislocation formation in a strained Ge film on Si(001). Such paths contain multiple intermediate minima connected by minimum energy paths on the energy surface emerging from the atomic interactions in the system. The challenge is to find which intermediate states to include and to construct a path going through these intermediates in such a way that the overall activation energy for the transition is minimal. In the numerical approach presented here, intermediate minima are constructed by heredity transformations of known minimum energy structures and by identifying local minima in minimum energy paths calculated using a modified version of the nudged elastic band method. Several mechanisms for the formation of a 90° misfit dislocation at the Ge–Si interface are identified when this method is used to construct transition paths connecting a homogeneously strained Ge film and a film containing a misfit dislocation. One of these mechanisms which has not been reported in the literature is detailed. The activation energy for this path is calculated to be 26% smaller than the activation energy for half loop formation of a full, isolated 60° dislocation. An extension of the common neighbor analysis method involving characterization of the geometrical arrangement of second nearest neighbors is used to identify and visualize the dislocations and stacking faults.

Impurity-Mediated Early Condensation of a Charge Density Wave in an Atomic Wire Array.

We directly show how impurity atoms induce the condensation of a representative electronic phase, the charge density wave (CDW) phase, in atomic scale with scanning tunneling microscopy. Oxygen impurity atoms on the self-assembled metallic atomic wire array on a silicon crystal condense the CDW locally above the pristine transition temperature. More interestingly, the CDW along the wires is induced not by a single atomic impurity but by the cooperation of multiple impurities. First-principles calculations disclose the mechanism of the cooperation as the coherent superposition of the local lattice strain induced by impurities, stressing the coupled electronic and lattice degrees of freedom for the CDW. This opens the possibility of the strain engineering over electronic phases of atomic-scale systems.

Hydrodynamical interpretation of angular momentum and energy transfer in atomic processes

Through the description of several simple atomic-scale systems for illustration, the hydrodynamical interpretation of results of solving the time-dependent Schr\odinger equation is used to elucidate the fundamental processes of angular momentum and energy transfer. Connections are made between the hydrodynamical interpretation and conventional views such as interference of superpositions of states. Along with previous theoretical and experimental demonstration of the existence of the hydrodynamical signatures born in atomic-scale interactions and remaining in the asymptotic observables, these illustrations show the complementarity of the hydrodynamical and conventional pictures as well as additional insight provided by the former.

Designing rules and probabilistic weighting for fast materials discovery in the Perovskite structure

High-throughput electronic-structure calculations are becoming increasingly popular in materials science and in the design of new compounds. Electronic-structure theory, for example, in the form of density-functional theory, can be used to calculate stabilities and electronic properties as bandgaps of new compounds. However, in practice, the methods are often limited to rather small atomic-scale systems or periodic crystals with only a limited number of atoms in the unit cell. It is therefore of interest to be able to derive generally useful information from simple systems to be applied in other, more complex, crystals. Here, we consider a large database of calculated stabilities and bandgaps of oxides and oxynitrides in the perovskite structure. We use the database as a testing ground for existing ideas about the behavior of these types of compounds and we derive some new simple chemical-based rules which combine structural information, like the ionic radii of the chemical elements, with electronic data, like the number of electrons and the valences of the pure elements. The rules extracted from the ABO3 cubic perovskite are then tested using the ABO2N and A2BO4 stoichiometry in the cubic and layered perovskite structure, respectively. These rules allow a saving in computer time of around 80%.

EON: software for long time simulations of atomic scale systems

The EON software is designed for simulations of the state-to-state evolution of atomic scale systems over timescales greatly exceeding that of direct classical dynamics. States are defined as collections of atomic configurations from which a minimization of the potential energy gives the same inherent structure. The time evolution is assumed to be governed by rare events, where transitions between states are uncorrelated and infrequent compared with the timescale of atomic vibrations. Several methods for calculating the state-to-state evolution have been implemented in EON, including parallel replica dynamics, hyperdynamics and adaptive kinetic Monte Carlo. Global optimization methods, including simulated annealing, basin hopping and minima hopping are also implemented. The software has a client/server architecture where the computationally intensive evaluations of the interatomic interactions are calculated on the client-side and the state-to-state evolution is managed by the server. The client supports optimization for different computer architectures to maximize computational efficiency. The server is written in Python so that developers have access to the high-level functionality without delving into the computationally intensive components. Communication between the server and clients is abstracted so that calculations can be deployed on a single machine, clusters using a queuing system, large parallel computers using a message passing interface, or within a distributed computing environment. A generic interface to the evaluation of the interatomic interactions is defined so that empirical potentials, such as in LAMMPS, and density functional theory as implemented in VASP and GPAW can be used interchangeably. Examples are given to demonstrate the range of systems that can be modeled, including surface diffusion and island ripening of adsorbed atoms on metal surfaces, molecular diffusion on the surface of ice and global structural optimization of nanoparticles.

The Hidden Meaning of Planck’s Constant

A new cosmological paradigm based upon global discrete self-similarity proposes a radical revision in our understanding of atomic scale dynamics. The discrete fractal scaling of this paradigm predicts a very large and discrete scale-dependence for gravitational coupling constants. This alternative gravitational scaling leads to revised values for the Planck mass, Planck length and Planck time, which appear to be more unified and physically comprehensible than is the case with the conventional Planck scale values. The fundamental interrelationship of the revised Planck mass, the corrected gravitational constant for atomic scale systems, the reduced Planck's constant and the velocity of light suggests a hidden meaning for Planck's constant. Within the context of the discrete fractal cosmological paradigm, Planck's constant is revealed as the fundamental unit of gravitational action for atomic scale systems. Implications for atomic scale dynamics are briefly outlined.

A method for finding the ridge between saddle points applied to rare event rate estimates

A method is presented for finding the ridge between first order saddle points on a multidimensional surface. For atomic scale systems, such saddle points on the energy surface correspond to atomic rearrangement mechanisms. Information about the ridge can be used to test the validity of the harmonic approximation to transition state theory, in particular to verify that second order saddle points--maxima along the ridge--are high enough compared to the first order saddle points. New minima along the ridge can also be identified during the path optimisation, thereby revealing additional transition mechanisms. The method is based on a string of discretisation points along a path between the first order saddle points and using an iterative optimisation which requires only the force acting on the atoms. At each iteration during the optimisation, the force is inverted along an unstable eigenmode perpendicular to the path. The method is applied to Al adatom diffusion on the Al(100) surface to find the ridge between 2-, 3- and 4-atom concerted displacements and hop mechanisms. A correction to the harmonic approximation of transition state theory was estimated by direct evaluation of the configuration integral along the ridge.

Sideband cooling of micromechanical motion to the quantum ground state

The advent of laser cooling techniques revolutionized the study of many atomic-scale systems, fuelling progress towards quantum computing with trapped ions and generating new states of matter with Bose-Einstein condensates. Analogous cooling techniques can provide a general and flexible method of preparing macroscopic objects in their motional ground state. Cavity optomechanical or electromechanical systems achieve sideband cooling through the strong interaction between light and motion. However, entering the quantum regime--in which a system has less than a single quantum of motion--has been difficult because sideband cooling has not sufficiently overwhelmed the coupling of low-frequency mechanical systems to their hot environments. Here we demonstrate sideband cooling of an approximately 10-MHz micromechanical oscillator to the quantum ground state. This achievement required a large electromechanical interaction, which was obtained by embedding a micromechanical membrane into a superconducting microwave resonant circuit. To verify the cooling of the membrane motion to a phonon occupation of 0.34 ± 0.05 phonons, we perform a near-Heisenberg-limited position measurement within (5.1 ± 0.4)h/2π, where h is Planck's constant. Furthermore, our device exhibits strong coupling, allowing coherent exchange of microwave photons and mechanical phonons. Simultaneously achieving strong coupling, ground state preparation and efficient measurement sets the stage for rapid advances in the control and detection of non-classical states of motion, possibly even testing quantum theory itself in the unexplored region of larger size and mass. Because mechanical oscillators can couple to light of any frequency, they could also serve as a unique intermediary for transferring quantum information between microwave and optical domains.

Structural and Chemical Properties of Gold Rare Earth Disilicide Core−Shell Nanowires

Clear understanding of the relationship between electronic structure and chemical activity will aid in the rational design of nanocatalysts. Core-shell Au-coated dysprosium and yttrium disilicide nanowires provide a model atomic scale system to understand how charges that transfer across interfaces affect other electronic properties and in turn surface activities toward adsorbates. Scanning tunneling microscopy data demonstrate self-organized growth of Au-coated DySi₂ nanowires with a nanometer feature size on Si(001), and Kelvin probe force microscopy data measure a reduction of work function that is explained in terms of charge transfer. Density functional theory calculations predict the preferential adsorption site and segregation path of Au adatoms on Si(001) and YSi₂. The chemical properties of Au-YSi₂ nanowires are then discussed in light of charge density, density of states, and adsorption energy of CO molecules.