Ground State Configuration Research Articles

Inner-shell excitation in the YbF molecule and its impact on laser cooling

The YbF molecule is a sensitive system for measuring the electron’s electric dipole moment. The precision of this measurement can be improved by direct laser cooling of the molecules to ultracold temperature. However, low-lying electronic states arising from excitation of a 4f electron may hinder laser cooling. One set of these “4f hole” states lies below the A2Π1/2 excited state used for laser cooling, and radiative decay to these intermediate levels, even with branching ratios as small as 10−5, can be a hindrance. Other 4f hole states lie very close to the A2Π1/2 state, and a perturbation results in states of mixed character that are involved in the laser cooling cycle. This perturbation may enhance the loss of molecules to states outside of the laser cooling cycle. We model the perturbation of the A2Π1/2 state to determine the strength of the coupling between the states, the de-perturbed potential energy curves, and the radiative branching ratios to various vibrational levels of the ground state, X2Σ+. We use electronic structure calculations to characterize the 4f hole states and the strengths of transitions between these states and the A2Π1/2 and X2Σ+ states. We identify a leak out of the cooling cycle with a branching ratio of roughly 5×10−4, dominated by the contribution of the ground state configuration in a 4f hole state. Finally, we assess the impact of these results for laser cooling of YbF and molecules with similar structure.

Strong correlation between structure and magnetic ordering in tetragonally distorted off-stoichiometric spinels Mn1.15Co1.85O4 and Mn1.17Co1.60Cu0.23O4

We report a systematic study on the structural and magnetic properties of off-stoichiometric polycrystalline bulk spinels ${\mathrm{Mn}}_{1.15}{\mathrm{Co}}_{1.85}{\mathrm{O}}_{4}$ and ${\mathrm{Mn}}_{1.17}{\mathrm{Co}}_{1.60}{\mathrm{Cu}}_{0.23}{\mathrm{O}}_{4}$ using neutron and x-ray diffraction, ferromagnetic resonance, and magnetic measurements. Both compounds show a weak tetragonal distortion with $c/a<1$, where the crystal structure could be refined in the tetragonal space group $I{4}_{1}/amd$. Both ${\mathrm{Co}}^{2+}$ and ${\mathrm{Cu}}^{2+}$ ions are located at the tetrahedral $A$ site, and ${\mathrm{Mn}}^{3+}$ and ${\mathrm{Co}}^{3+}$ at the octahedral $B$ site. Ferrimagnetic (FI) ordering of ${\mathrm{Mn}}_{1.15}{\mathrm{Co}}_{1.85}{\mathrm{O}}_{4}$ and ${\mathrm{Mn}}_{1.17}{\mathrm{Co}}_{1.60}{\mathrm{Cu}}_{0.23}{\mathrm{O}}_{4}$ sets in below 184 and 164 K, respectively. Magnetic structure analysis revealed that the ferrimagnetically coupled ${A}^{2+}$- and ${B}^{3+}$-site moments are aligned parallel to the tetragonal $c$ axis. Additionally, a noncollinear antiferromagnetic order appears in the $ab$ plane, where the moments point along [110] and $[1\overline{1}0]$. The net magnetic moment [$2{\ensuremath{\mu}}_{\mathrm{FI}}({\mathrm{Mn}}_{B}$/${\mathrm{Co}}_{B})\ensuremath{-}{\ensuremath{\mu}}_{\mathrm{FI}}({\mathrm{Co}}_{A}$)] of ${\mathrm{Mn}}_{1.15}{\mathrm{Co}}_{1.85}{\mathrm{O}}_{4}$ obtained from neutron data varies between 0.88--1.08 ${\ensuremath{\mu}}_{B}$ which is in good agreement with $M=0.89\text{--}1.13$ ${\ensuremath{\mu}}_{B}$ as determined from magnetization measurements. However, for the Cu-containing compound a larger discrepancy in the magnetic moment was observed between the neutron data (1.89--1.92 ${\ensuremath{\mu}}_{B}$) and low-temperature ($T=1.9$ K) field-dependent ($H=90$ kOe) magnetization data ($0.97\text{--}1.21$ ${\ensuremath{\mu}}_{B}$). From the three-sublattice model we obtained canting angles ${28}^{\ensuremath{\circ}}$ and ${25}^{\ensuremath{\circ}}$ for ${\mathrm{Mn}}_{1.15}{\mathrm{Co}}_{1.85}{\mathrm{O}}_{4}$ and ${\mathrm{Mn}}_{1.17}{\mathrm{Co}}_{1.60}{\mathrm{Cu}}_{0.23}{\mathrm{O}}_{4}$, respectively. Both the bulk systems exhibit high magnetocrystalline anisotropy (${K}_{\text{U}}\ensuremath{\sim}9\ifmmode\times\else\texttimes\fi{}{10}^{5}$ and $7.5\ifmmode\times\else\texttimes\fi{}{10}^{5}$ erg/${\mathrm{cm}}^{3}$) and a field-induced transition (${H}_{\text{D}}$) across 4.0 kOe due to the domain reorientation. Temperature ($1.9\text{--}350$ K) and field ($\ifmmode\pm\else\textpm\fi{}90$ kOe) dependence of magnetization data confirms the high-spin ($S=\frac{3}{2}$ and $S=2$) ground-state configuration for both the divalent Co and trivalent Mn.

Dynamical quantum phase transitions in a mesoscopic superconducting system

We inspect signatures of dynamical quantum phase transitions driven by two types of quenches acting on a correlated quantum dot embedded between superconducting and metallic reservoirs. Under stationary conditions the proximity induced on-dot pairing combined with the strong Coulomb repulsion prefers the quantum dot to be either in the singly occupied (spinful) or BCS-type (spinless) ground state configuration. We study the time evolution upon traversing such a phase boundary due to quantum quenches by means of the time-dependent numerical renormalization group approach, revealing non-analytic features in the low-energy return rate. Quench protocols can be realized in a controllable manner and we are confident that detection of this dynamical singlet-doublet phase transition would be feasible by the charge tunnelling spectroscopy.

First-order phase transition in a two dimensional BM3 model.

The phase behavior of a Biroli-Mézard model on the two dimensional square lattice in which hard-core particles can have at most three nearest neighboring occupied sites is investigated by means of grand-canonical Monte Carlo simulations. Finite-size scaling analysis of relevant thermodynamic quantities obtained via the histogram reweighting technique reveals that at high-density, the model undergoes a first-order phase transition with preferential sublattice occupation to a crystal phase with enantiomorph ground state configurations, in close analogy to the hard-core lattice gas with the exclusion range extended up to the third shell of nearest neighbors.

Common defects in diamond lattices as instances of the general T ⊗ (e+t2) Jahn-Teller effect

Finding the ground-state configuration of point defects in semiconductors is in general a high-dimensional optimization problem. However, their adiabatic potential energy surfaces (APES) can be described with few effective coordinates by exploiting symmetry arguments within the Jahn-Teller (JT) theoretical framework. In this paper, we propose a general framework, that combines group theory and ab initio calculations, to build a full picture of common defects in diamond lattices (vacancies and substitutional impurities) as instances of the general T $\ensuremath{\bigotimes}\phantom{\rule{4pt}{0ex}}(e+{t}_{2})$ APES. Starting from the original tetrahedral symmetry, we consider all possible JT symmetries and we numerically investigate the shape of the APES by targeting the minimum energy path between equivalent JT distortions taking as examples the vacancy (V) and the metallic impurities Pd, Pt, and Au in crystalline silicon.

Exact solution of the magnetic properties for ternary ferrimagnetic mixed-spin Ising nanoislands

ABSTRACT The ferrimagnetic mixed-spin ternary nanoisland models with two and three layer structures were set up by the Ising model with spin quantum numbers 1, 3/2 and 1/2. Using the transfer matrix method, we got the magnetization, magnetic susceptibility and ground-state diagram exactly. The results show that the magnetic susceptibility of nanoisland with two-layer structure shows antiferromagnetic behavior, while that of nanoisland with three-layer structure shows antiferromagnetic or ferromagnetic behavior in different parameter areas. The antiferromagnetic behavior shows that the net spin of the ground-state system is zero. The ferromagnetic behavior shows that the magnetic susceptibility diverges at zero temperature, the Curie constant is proportional to the square of the net spin in the ground-state configuration of spins. The magnetization of the three-layer structure in an external magnetic field shows superparamagnetic behavior with many magnetization plateaus. It can be inferred that there should be similar results for finite Ising nanosystems.

Cumulative geometric frustration and superextensive energy scaling in a nonlinear classical XY -spin model

Geometric frustration results from a discrepancy between the locally favored arrangement of the constituents of a system and the geometry of the embedding space. Geometric frustration can be either noncumulative, which implies an extensive energy growth, or cumulative, which implies superextensive energy scaling and highly cooperative ground-state configurations which may depend on the dimensions of the system. Cumulative geometric frustration was identified in a variety of continuous systems including liquid crystals, filament bundles, and molecular crystals. However, a spin-lattice model which clearly demonstrates cumulative geometric frustration was lacking. In this paper we describe a nonlinear variation of the XY-spin model on a triangular lattice that displays cumulative geometric frustration. The model is studied numerically and analyzed in three distinct parameter regimes, which are associated with different energy minimizing configurations. We show that, despite the difference in the ground-state structure in the different regimes, in all cases the superextensive power-law growth of the frustration energy for small domains grows with the same universal exponent that is predicted from the structure of the underlying compatibility condition.

Zentropy Theory for Positive and Negative Thermal Expansion

It has been observed in both natural and man-made materials that volume sometimes decreases with increasing temperature. Though mechanistic understanding has been gained for some individual materials, a general answer to the question “Why does volume sometimes decrease with the increase of temperature?” remains lacking. Based on the thermodynamic relation that the derivative of volume with respect to temperature, i.e., thermal expansion, is equal to the negative derivative of entropy with respect to pressure, we developed a general theory in terms of multiscale entropy to understand and predict the change of volume as a function of temperature, which is termed as zentropy theory in the present work. It is shown that a phase at high temperatures is a statistical representation of the ground-state stable and multiple nonground-state metastable configurations. It is demonstrated that when the volumes of the nonground-state configurations with high probabilities are smaller than that of the ground-state configuration, the volume of the phase may decrease with the increase of temperature in certain ranges of temperature-pressure combinations, depicting the negative divergency of thermal expansion at the critical point. As examples, positive and negative divergencies of thermal expansion are predicted at the critical points of Ce and Fe3Pt, respectively, along with the temperature and pressure ranges for abnormally positive and negative thermal expansions. The authors believe that the zentropy theory is applicable to predict anomalies of other physical properties of phases because the change of entropy drives the responses of a system to external stimuli.

Exploring the halo character and dipole response in the dripline nucleus F31

Lying at the lower edge of the `island of inversion', neutron-rich Fluorine isotopes ($^{29-31}$F) provide a curious case to study the configuration mixing in this part of the nuclear landscape. Recent studies have suggested that a prospective two-neutron halo in the dripline nucleus $^{31}$F could be linked to the occupancy of the $pf$ intruder configurations. Focusing on configuration mixing, matter radii and neutron-neutron ($nn$) correlations in the ground-state of $^{31}$F, we explore various scenarios to analyze its possible halo nature as well as the low-lying electric dipole ($E$1) response within a three-body approach. We use an analytical, transformed harmonic oscillator basis under the aegis of a hyperspherical formalism to construct the ground state three-body wave function of $^{31}$F. The $^{31}$F ground-state configuration mixing and its matter radius are computed for different choices of the $^{30}$F structure coupled to the valence neutron. The admixture of {$p_{3/2}$, $d_{3/2}$, and $f_{7/2}$} components is found to play an important role, favouring the dominance of inverted configurations with dineutron spreads for two-neutron halo formation. The increase in matter radius with respect to the core radius, $\Delta r \geqslant$ 0.30 fm and the dipole distributions along with the integrated $B(E1)$ strengths of $\geqslant$ 2.6 $e^2$fm$^2$ are large enough to be compatible with other two-neutron halo nuclei. Three-body results for $^{31}$F indicate a large spatial extension in its ground state due to the inversion of the energy levels of the normal shell model scheme. The increase is augmented by and is proportional to the extent of the $p_{3/2}$ component in the wave function. Additionally, the enhanced dipole distributions and large $B(E1)$ strengths all point to the two-neutron halo character of $^{31}$F.

Structural evolution and shape transition in even-even Hf-isotopes within the relativistic mean-field approach

In this theoretical study, we calculate the ground state parameters like binding energy, charge radii, neutron skin-thickness, chemical potentials, quadrupole deformation parameter, neutron separation energy, and single-particle energy for Hf isotopes of mass 170 ⩽ A ⩽ 220. The potential energy surface in parallel with the Fermi energy as a function of the quadrupole deformation parameter is estimated to determine the ground state configuration. The Relativistic Hartree-Bogoliubov approach with density-dependent DD-ME2 and the relativistic mean-field formalism with the popular NL3 and NL3⁎ parameter sets are used for the present analysis. The study involves a constant gap BCS approach within NL3, & NL3⁎ and Bogoliubov transformation within DD-ME2 parameter sets to examine the effect of pairing correlations. The calculated bulk quantities are reasonably good agreement with available experimental data, the finite range droplet model predictions, and the Weizsäcker-Skyrme mass formula. We find the signature of shell/sub-shell closure at N = 126 for all the parameter sets, which indicates the stability of 198Hf in the neutron drip-line region of the Hf-isotopes.

Phonon eigenfunctions of inhomogeneous lattices: Can you hear the shape of a cone?

We study the phonon modes of interacting particles on the surface of a truncated cone resting on a plane subject to gravity, inspired by recent colloidal experiments. We derive the ground-state configuration of the particles under gravitational pressure in the small-cone-angle limit and find an inhomogeneous triangular lattice with spatially varying density but robust local order. The inhomogeneity has striking effects on the normal modes such that an important feature of the cone geometry, namely its apex angle, can be extracted from the lattice excitations. The shape of the cone leads to energy crossings at long wavelengths and frequency-dependent quasilocalization at short wavelengths. We analytically derive the localization domain boundaries of the phonons in the limit of small cone angle and check our results with numerical results for eigenfunctions.

High-resolution spectroscopy of neutral Yb atoms in a solid Ne matrix

We present an experimental and theoretical study of the absorption and emission spectra of Yb atoms in a solid Ne matrix at a resolution of 0.025 nm. Five absorption bands were identified as due to transitions from the $4{f}^{14}5{d}^{0}6{s}^{2}{\phantom{\rule{4pt}{0ex}}}^{1}{S}_{0}$ ground-state configuration to $4{f}^{14}5{d}^{0}6s6p$ and $4{f}^{13}5{d}^{1}6{s}^{2}$ configurations. The two lowest-energy bands were assigned to outer-shell transitions to $6s6p{\phantom{\rule{4pt}{0ex}}}^{3}{P}_{1}$ and ${}^{1}{P}_{1}$ atomic states and displayed the structure of a broad doublet and an asymmetric triplet, respectively. The remaining three higher-frequency bands were assigned to inner-shell transitions to distinct $J=1$ states arising from the $4{f}^{13}5{d}^{1}6{s}^{2}$ configuration and were highly structured with narrow linewidths. A classical simulation was performed to identify the stability and symmetry of possible trapping sites in the Ne crystal. It showed that the overarching $1+2$ structure of the high-frequency bands could be predominantly ascribed to crystal-field splitting in the axial field of a 10-atom vacancy of ${C}_{4v}$ symmetry. Their prominent substructures were shown to be manifestations of phonon sidebands associated with the zero-phonon lines on each crystal-field state. Unprecedented for a metal--rare-gas system, resolution of individual phonon states on an allowed electronic transition was possible under excitation spectroscopy which reflects the semiquantum nature of solid Ne. In contrast to the absorption spectra, emission spectra produced by steady-state excitation into the ${}^{1}{P}_{1}$ absorption band consisted of simple, unstructured fluorescence bands.

Hyperchaos in a Bose-Hubbard Chain with Rydberg-Dressed Interactions

We study the chaos and hyperchaos of Rydberg-dressed Bose–Einstein condensates (BECs) in a one-dimensional optical lattice. Due to the long-range, soft-core interaction between the dressed atoms, the dynamics of the BECs are described by the extended Bose-Hubbard model. In the mean-field regime, we analyze the dynamical stability of the BEC by focusing on the ground state and localized state configurations. Lyapunov exponents of the two configurations are calculated by varying the soft-core interaction strength, potential bias, and length of the lattice. Both configurations can have multiple positive Lyapunov exponents, exhibiting hyperchaotic dynamics. We show the dependence of the number of the positive Lyapunov exponents and the largest Lyapunov exponent on the length of the optical lattice. The largest Lyapunov exponent is directly proportional to areas of phase space encompassed by the associated Poincaré sections. We demonstrate that linear and hysteresis quenches of the lattice potential and the dressed interaction lead to distinct dynamics due to the chaos and hyperchaos. Our work is relevant to current research on chaos as well as collective and emergent nonlinear dynamics of BECs with long-range interactions.

Investigation of Electronic Structure and Electrochemical Properties of Na2MnSiO4 as a Cathode Material for Na Ion Batteries

The polyanionic compound Na2MnSiO4 is regarded as one of the promising cathode materials for Na-ion batteries due to good specific capacity with its attractive prospect of utilization of two electrons in the redox processes. So, in this study, we have performed the thermodynamic and electronic structure analysis of Na2MnSiO4 using first principles density functional theory calculations. The intermediate ground state configurations for Na2MnSiO4of Na de-intercalation were found using the cluster expansion method and are used to obtain the 0 K voltage profile as a function of Na concentration. This material shows an average voltage of 4.2 V and the finite temperature analysis at 300 K using Monte Carlo simulations indicates that this material undergoes two phase mixing when desodiate beyond 1.5 Na/f.u. The chemical bonding interactions between the constituents are analyzed using the density of states, crystal orbital Hamilton population, charge density, charge transfer and electron localization function analyses. From these analyses we found that the interaction between Mn and O is iono-covalent and that between Si-O is mainly covalent in nature. The involvement of oxygen in the redox reaction apart from the transition metal is identified using the Bader charge analysis. Relevant Na diffusion pathways and their corresponding calculated energy barriers are compared with the partially Fe substituted Na2MnSiO4 to understand the effect of Mn-site substitution on the process of Na migration through this material.

3D Atomic Structure of Supported Metallic Nanoparticles Estimated from 2D ADF STEM Images: A Combination of Atom-Counting and a Local Minima Search Algorithm.

Determining the 3D atomic structure of nanoparticles (NPs) is critical to understand their structure-dependent properties. It is hereby important to perform such analyses under conditions relevant for the envisioned application. Here, the 3D structure of supported Au NPs at high temperature, which is of importance to understand their behavior during catalytic reactions, is investigated. To overcome limitations related to conventional high-resolution electron tomography at high temperature, 3D characterization of NPs with atomic resolution has been performed by applying atom-counting using atomic resolution annular dark-field scanning transmission electron microscopy (ADF STEM) images followed by structural relaxation. However, at high temperatures, thermal displacements, which affect the ADF STEM intensities, should be taken into account. Moreover, it is very likely that the structure of an NP investigated at elevated temperature deviates from a ground state configuration, which is difficult to determine using purely computational energy minimization approaches. In this paper, an optimized approach is therefore proposed using an iterative local minima search algorithm followed by molecular dynamics structural relaxation of candidate structures associated with each local minimum. In this manner, it becomes possible to investigate the 3D atomic structure of supported NPs, which may deviate from their ground stateconfiguration.

Forecasting Election Polls with Spin Systems

We show that the problem of political forecasting, i.e, predicting the result of elections and referendums, can be mapped to finding the ground state configuration of a classical spin system. Depending on the required prediction, this spin system can be a combination of XY, Ising and vector Potts models, always with two-spin interactions, magnetic fields, and on arbitrary graphs. By reduction to the Ising model our result shows that political forecasting is formally an NP-Hard problem. Moreover, we show that the ground state search can be recasted as Higher-order and Quadratic Unconstrained Binary Optimization (HUBO / QUBO) Problems, which are the standard input of classical and quantum combinatorial optimization techniques. We prove the validity of our approach by performing a numerical experiment based on data gathered from Twitter for a network of 10 people, finding good agreement between results from a poll and those predicted by our model. In general terms, our method can also be understood as a trend detection algorithm, particularly useful in the contexts of sentiment analysis and identification of fake news.

First-Principles Study of Order–Disorder Transitions in Pseudobinary Clathrates

It has been recently demonstrated that the pseudoternary Ba8AlxGayGe46–x–y clathrate undergoes an order–disorder transition with increasing temperature that can be observed via site occupation factors (SOFs) and manifests itself, e.g., in electrical transport properties. Here, we generalize this result and analyze the characteristics of this order–disorder transition in the pseudobinary clathrates Ba8GaxGe46–x, Ba8GaxSi46–x, Ba8AlxGe46–x, and Ba8AlxSi46–x. To this end, we employ atomistic simulations that combine alloy cluster expansions trained against density functional theory calculations with Wang–Landau and ensemble Monte Carlo simulations. The simulations show that all four systems studied here display order–disorder transitions for at least some composition range. Based on an extensive literature survey, we also provide evidence for signatures of the transition in earlier experimental studies that to the best of our knowledge have hitherto not been related to such transitions. The predicted transition temperatures are lower for Ba8GaxGe46–x and Ba8GaxSi46–x than for Ba8AlxGe46–x and Ba8AlxSi46–x, although it appears that the simulations underestimate the transition temperatures for Ga-containing systems compared to the experiment. This nonetheless provides a sensible explanation for why the experimentally determined Al SOFs agree better with the simulated high-temperature disordered configurations, while the Ga SOFs more closely agree with the simulated ground-state configurations. As a result of stronger interactions, the SOFs vary substantially, especially near the stoichiometric 16:30 composition, providing an indication of why it has proved difficult to synthesize Ba8AlxGe46–x and Ba8AlxSi46–x samples at this ratio. The present study thereby yields detailed atomic-scale insights into the ordering in inorganic clathrates that, given the connection to transport properties established earlier, are not only useful from a fundamental perspective but also relevant for applications.

Chern-Simons-matter theories at large baryon number

We study SU(2) Chern-Simons theories at level k coupled to a scalar on T2 × ℝ at large baryon number. We find a homogeneous but anisotropic ground state configuration for any values of k on the IR fixed-point of those models. This classical analysis is valid as long as we take the baryon number large. As a corollary, by comparing the symmetry breaking pattern at large chemical potential, we find that the theory does not reduce to the singlet sector of the O(4) Wilson-Fisher fixed-point at large-k, as expected from general grounds. This paper will be one primitive step towards quantitative analysis of Chern-Simons-matter dualities using the large charge expansion.

Inverted harmonic oscillator dynamics of the nonequilibrium phase transition in the Dicke model.

We show how the dynamics of the Dicke model after a quench from the ground-state configuration of the normal phase into the superradiant phase can be described for a limited time by a simple inverted harmonic oscillator model and that this limited time approaches infinity in the thermodynamic limit. Although we specifically discuss the Dicke model, the presented mechanism can also be used to describe dynamical quantum phase transitions in other systems and presents an opportunity for simulations of physical phenomena associated with an inverted harmonic oscillator.

New Two-Dimensional Wide Band Gap Hydrocarbon Insulator by Hydrogenation of a Biphenylene Sheet.

Based on first-principles calculations, the ground state configuration (Cmma-CH) of a hydrogenated biphenylene sheet ( Science 2021, 372, 852) is carefully identified from hundreds of possible candidates generated by RG2 code ( Phys. Rev. B. 2018, 97, 014104). Cmma-CH contains four inequivalent benzene molecules in its crystalline cell due to its Cmma symmetry. Hydrogen atoms bond to carbon atoms in each benzene with a boat-like (DDUDDU) up/down sequence and reversed boat-1 (UUDUUD) sequence in adjacent benzene rings. Cmma-CH is energetically less stable than the proposed allotropes of hydrogenated graphene, but the formation energy for hydrogenating a biphenylene sheet is remarkably lower than that for hydrogenating graphene to graphane. Our results of mechanical and dynamical stability also confirm that Cmma-CH is a stable 2D hydrocarbon, which is expected to be realized experimentally. Especially, biphenylene undergoes a transition from normal metal to a wide band gap insulator (4.645 eV) by hydrogenation to Cmma-CH, which has potential applications in nanodevices at elevated temperatures and high voltages.