Self-consistent Green Function Research Articles

Cross-shell states in 15C: A test for p-sd interactions

The low-lying structure of 15C has been investigated via the neutron-removal 16C(d,t) reaction. Along with the known bound neutron sd-shell states, unbound p-shell hole states have been observed. The excitation energies and the deduced spectroscopic factors of the cross-shell states are an important measure of the [(p)−1(sd)2] neutron configurations in 15C. Our results show a very good agreement with shell-model calculations using the SFO-tls interaction for 15C. However, this same interaction predicted energies that were too low for the corresponding hole states in the N=9 isotone 17O and adjustment of the p-sd and sd-sd monopole terms was required to match the 17O energies. In addition, the excitation energies and spectroscopic factors have been compared to the first calculations of 15C with the ab initio self-consistent Green's function method employing the NNLOsat interaction. The results show the sensitivity to the size of the N=8 shell gap and highlight the need to go beyond the current truncation scheme.

A Fully Coupled Scheme for a Self-Consistent Poisson-NEGF Solver

This work presents a fully coupled scheme for a self-consistent Poisson-nonequilibrium Green function (NEGF) solver. In this solver, responses of the Green functions to the potential perturbation are rigorously calculated. As a result, the detailed dependence of the electron density on the electrostatic potential can be accurately considered. When applied to the steady-state (DC) simulation, the convergence behavior is much improved compared with the conventional Gummel-type approach. As a numerical example, real-space NEGF results are shown for a highly scaled nanosheet MOSFET under the ballistic transport approximation.

Semiconducting SWCNT Photo Detector for High Speed Switching Through Single Halo Doping

The method opted for accuracy, and no existing studies are based on this method. A design and characteristic survey of a new small band gap semiconducting Single Wall Carbon Nano Tube (SWCNT) Field Effect Transistor as a photodetector is carried out. In the proposed device, better performance is achieved by increasing the diameter and introducing a new single halo (SH) doping in the channel length of the CNTFET device. This paper is a study and analysis of the performance of a Carbon Nano Tube Field Effect Transistor (CNTFET) as a photodetector using the self-consistent Poisson and Green function method. The 2D self-consistent Poisson and Green’s function method for various optical intensities and wavelength simulate this proposed photodetector. The performance study is based on the simulation of drain current, transconductance, sub-threshold swing, cut-off frequency, gain, directivity, and quantum efficiency under dark and illuminated conditions. These quantum simulation results show that cut-off frequency increases while there is an increase in diameter. The proposed SH-CNTFET provides better performance in terms of higher gain and directivity than conventional CNTFET (C-CNTFET). This device will be helpful in optoelectronic integrated circuits (OEIC) receivers due to its superior performance.

Green's function method for the two-dimensional frustrated spin- 12 Heisenberg magnetic lattice

The magnon Hedin's equations are derived via the Schwinger functional derivative technique, and the resulting self-consistent Green's function method is used to calculate ground state spin patterns and magnetic structure factors for 2-dimensional magnetic systems with frustrated spin-1/2 Heisenberg exchange coupling. Compared to random-phase approximation treatments, the inclusion of a self-energy correction improves the accuracy in the case of scalar product interactions, as shown by comparisons between our method and exact benchmarks in homogeneous and inhomogeneous finite systems. We also find that for cross-product interactions (e.g. antisymmetric exchange), the method does not perform equally well, and an inclusion of higher corrections is in order. Aside from indications for future work, our results clearly indicate that the Green's function method in the form proposed here already shows potential advantages in the description of systems with a large number of atoms as well as long-range interactions.

Gorkov algebraic diagrammatic construction formalism at third order

Background: The Gorkov approach to self-consistent Green's function theory has been formulated by Som\`a, Duguet, and Barbieri in [Phys. Rev. C 84, 064317 (2011)]. Over the past decade, it has become a method of reference for first-principles computations of semimagic nuclear isotopes. The currently available implementation is limited to a second-order self-energy and neglects particle-number nonconserving terms arising from contracting three-particle forces with anomalous propagators. For nuclear physics applications, this is sufficient to address first-order energy differences (i.e., two neutron separation energies, excitation energies of states dominating the one-nucleon spectral function), ground-state radii and moments on an accurate enough basis. However, addressing absolute binding energies, fine spectroscopic details of $N\ifmmode\pm\else\textpm\fi{}1$ particle systems or delicate quantities such as second-order energy differences associated with pairing gaps, requires going to higher truncation orders.Purpose: The formalism is extended to third order in the algebraic diagrammatic construction (ADC) expansion with two-body Hamiltonians.Methods: The expansion of Gorkov propagators in Feynman diagrams is combined with the algebraic diagrammatic construction up to the third order as an organization scheme to generate the Gorkov self-energy.Results: Algebraic expressions for the static and dynamic contributions to the self-energy, along with equations for the matrix elements of the Gorkov eigenvalue problem, are derived. It is first done for a general basis before specifying the set of equations to the case of spherical systems displaying rotational symmetry. Workable approximations to the full self-consistency problem are also elaborated on. The formalism at third order it thus complete for a general two-body Hamiltonian.Conclusions: Working equations for the full Gorkov-ADC(3) are now available for numerical implementation.

Examination of the sensitivity of quasifree reactions to details of the bound-state overlap functions

It is often stated that heavy-ion nucleon knockout reactions are mostly sensitive to the tails of the bound-state wavefunctions. In contrast, (p,2p) and (p,pn) reactions are known to access information on the full overlap functions within the nucleus. We analyze the oxygen isotopic chain and explore the differences between single-particle wave functions generated with potential models, used in the experimental analysis of knockout reactions, and ab initio computations from self-consistent Green's function theory. Contrary to the common belief, we find that not only the tail of the overlap functions, but also their internal part are assessed in both reaction mechanisms, which are crucial to yield accurately determined spectroscopic information.

Importance truncation in non-perturbative many-body techniques

Expansion many-body methods correspond to solving complex tensor networks. The (iterative) solving of the network and the (repeated) storage of the unknown tensors requires a computing power growing polynomially with the size of basis of the one-body Hilbert space one is working with. Thanks to current computer capabilities, ab initio calculations of nuclei up to mass $A\sim100$ delivering a few percent accuracy are routinely feasible today. However, the runtime and memory costs become quickly prohibitive as one attempts (possibly at the same time) (i) to reach out to heavier nuclei, (ii) to employ symmetry-breaking reference states to access open-shell nuclei and (iii) to aim for yet a greater accuracy. The challenge is particularly exacerbated for non-perturbative methods involving the repeated storage of (high-rank) tensors obtained via iterative solutions of non-linear equations. The present work addresses the formal and numerical implementations of so-called importance truncation (IT) techniques within the frame of one particular non-perturbative expansion method, i.e., Gorkov Self-Consistent Green's Function (GSCGF) theory, with the goal to eventually overcome above-mentioned limitations. By a priori truncating irrelevant tensor entries, IT techniques are shown to reduce the storage to less than 1% of its original cost in realistic GSCGF calculations performed at the ADC(2) level while maintaining a 1% accuracy on the correlation energy. The future steps will be to extend the present development to the next, e.g., ADC(3), truncation level and to SCGF calculations applicable to doubly open-shell nuclei.

Nuclear energy density functionals grounded in ab initio calculations

We discuss the construction of a nuclear Energy Density Functional (EDF) from ab initio calculations, and we advocate the need of a methodical approach that is free from ad hoc assumptions. The equations of state (EoS) of symmetric nuclear and pure neutron matter are computed using the chiral NNLO$_{\rm sat}$ and the phenomenological AV4$^\prime$+UIX$_{c}$ Hamiltonians as inputs in the Self-consistent Green's Function (SCGF) and Auxiliary Field Diffusion Monte Carlo (AFDMC) methods, respectively. We propose a convenient parametrization of the EoS as a function of the Fermi momentum and fit it on the SCGF and AFDMC calculations. We apply the ab initio-based EDF to carry out an analysis of the binding energies and charge radii of different nuclei in the local density approximation. The NNLO$_{\rm sat}$-based EDF produces encouraging results, whereas the AV4$^\prime$+UIX$_{c}$-based one is farther from experiment. Possible explanations of these different behaviors are suggested, and the importance of gradient and spin-orbit terms is analyzed. Our work paves the way for a practical and systematic way to merge ab initio nuclear theory and DFT, while at the same time it sheds light on some of the critical aspects of this procedure.

Moving away from singly-magic nuclei with Gorkov Green’s function theory

Ab initio calculations of bulk nuclear properties (ground-state energies, root mean square charge radii and charge density distributions) are presented for seven complete isotopic chains around calcium, from argon to chromium. Calculations are performed within the Gorkov self-consistent Green's function approach at second order and make use of two state-of-the-art two- plus three-nucleon Hamiltonians, $NN$+$3N\text{(lnl)}$ and NNLO$_{\text{sat}}$. An overall good agreement with available experimental data is found, in particular for differential energies (charge radii) when the former (latter) interaction is employed. Remarkably, neutron magic numbers $N=28,32,34$ emerge and evolve following experimental trends. In contrast, pairing gaps are systematically underestimated. General features of the isotopic dependence of charge radii are also reproduced, as well as charge density distributions. A deterioration of the theoretical description is observed for certain nuclei and ascribed to the inefficient account of (static) quadrupole correlation in the present many-body truncation scheme. In order to resolve these limitations, we advocate the extension of the formalism towards incorporating breaking of rotational symmetry or, alternatively, performing a stochastic sampling of the self-energy.

Reexamining the relation between the binding energy of finite nuclei and the equation of state of infinite nuclear matter

The energy density is calculated in coordinate space for $^{12}$C, $^{40}$Ca, $^{48}$Ca, and $^{208}$Pb using a dispersive optical model constrained by all relevant data including the corresponding energy of the ground state. The energy density of $^{8}$Be is also calculated using the Green's function Monte-Carlo method employing the Argonne/Urbana two and three-body interactions. The nuclear interior minimally contributes to the total binding energy due to the 4$\pi r^2$ phase space factor. Thus, the volume contribution to the energy in the interior is not well constrained. The dispersive-optical-model energy densities are in good agreement with \textit{ab initio} self-consistent Green's function calculations of infinite nuclear matter restricted to treat only short-range and tensor correlations. These results call into question the degree to which the equation of state for nuclear matter is constrained by the empirical mass formula. In particular, the results in this paper indicate that saturated nuclear matter does not require the canonical value of 16 MeV binding per particle but only about 13-14 MeV when the interior of $^{208}$Pb is considered.

Green's Function Techniques for Infinite Nuclear Systems

I review the application of self-consistent Green's functions methods to study the properties of infinite nuclear systems. Improvements over the last decade, including the consistent treatment of three-nucleon forces and the development of extrapolation methods from finite to zero temperature, have allowed for realistic predictions of the equation of state of infinite symmetric, asymmetric and neutron matter based on chiral interactions. Microscopic properties, like momentum distributions or spectral functions, are also accessible. Using an indicative set of results based on a subset of chiral interactions, I summarise here the first-principles description of infinite nuclear system provided by Green's functions techniques, in the context of several issues of relevance for nuclear theory including, but not limited to, the role of short-range correlations in nuclear systems, nuclear phase transitions and the isospin dependence of nuclear observables.

Self-Consistent Green's Function Theory for Atomic Nuclei

Nuclear structure theory has recently gone through a major renewal with the development of ab initio techniques that can be applied to a large number of atomic nuclei, well beyond the light sector that had been traditionally targeted in the past. Self-consistent Green's function theory is one among these techniques. The present work aims to give an overview of the self-consistent Green's function approach for atomic nuclei, including examples of recent applications and a discussion on the perspectives for extending the method to nuclear reactions, doubly open-shell systems and heavy nuclei.

(Invited) Ferroelectric-HfO2 Devices: Physics and Applications

1. Introduction Ferroelectric-HfO2 (FE-HfO2) is a key technology enabler for energy-efficient memory devices because of its high scalability and CMOS-compatibility [1]. FE memory device is low-power, high-speed and high reliability by field-driven operation. FE memory device can be implemented in the form of capacitor, resistor, and transistor, which provides us design flexibility of memory system. Thanks to the material break-through and the device architecture innovation, FE memory device opens up new opportunities in memory market. In this talk, I will overview our recent research progress on FE-HfO2 memory devices and discuss future perspectives. 2. Capacitor memory - NVSRAM The most mature device structure is capacitor type. It is natural to replace conventional FE-material by scalable FE-HfO2. We can take an advantage of low power operation of FE-HfO2 for smart power management in IoT application. IoT sensor node devices are expected to operate in an intermittent mode. The active rate of a transistor is much lower than clock frequency in IoT device. In order to suppress standby leakage power, especially in SRAM, it is important to bring the transistors in sleep mode as much as possible. Normally-off computing is the idea that stores the current state data in NV memory, turns the power off, and restore the data after power-on without much latency and power overhead. NV-SRAM [2] has been revisited by using FE-HfO2 which realizes good scalability as well as cost effective process. NV-SRAM has been designed, fabricated by integrating FE-HfO2 capacitor [3] in back-end process as shown in Fig. 1. Store, power-off, and recall operation are successfully demonstrated. 3. Resistive memory - FTJ Ferroelectric Tunnel Junction (FTJ) memory is an emerging memory for high capacity memory. A ferroelectric thin film is sandwiched by two electrodes, which works as resistive change memory, as shown in Fig. 2. FTJ was proposed back in 1970s [4] and current state-of-the-art nanoscale ferroelectric thin film technologies are to finally realize it. FTJ utilizes polarization switching to change on-sate and off-state tunneling electroresistance (TER). Design guideline and high TER as much as >30 has been recently demonstrated by FE-HfO2 (Fig. 2) [5]. FTJ also shows multi-level cell operation and high resistance, which are useful for hardware AI application. Moreover, scalability has been thoroughly investigated by self-consistent potential and non-equilibrium Green function method to compete with other high capacity memories (Fig. 3) [6]. 4. Transistor memory - FeFET Ferroelectric FET (FeFET) memory is a transistor which has a thin FE layer as gate insulator. This is another type of device structure for high capacity memory. Recently, 3D stacked FeFET has been proposed [7], which can possibly compete with NAND flash memory in terms of memory capacity.There are several challenges to realize such 3D stacked FeFET using conventional poly-Si channel. Poly-Si channel has low mobility and forms a low-k interfacial layer which causes voltage loss and reliability degradation by charge trapping. In this work, we propose to use amorphous oxide semiconductor, IGZO [8], as an alternative channel material. IGZO channel provides high mobility as a deposited channel and prevent low-k interfacial layer formation. We have demonstrated ferro- electricity in the combination of FE-HfO2 and IGZO (Fig. 4), and large memory window with nearly ideal subthreshold swing and high endurance operations [9]. 5. Conclusions FE-HfO2 is a key technology enabler for energy-efficient computing because of its high scalability and CMOS-compatibility. NVSRAM serves for smart power management in IoT applications. FTJ and FeFET have a potential for low power and high capacity memory as well as machine learning accelerator. Acknowledgment The author acknowledges Nozomu Ueyama, Yusaku Tagawa, Fei Mo, Kiyoshi Takeuchi, Takuya Saraya and Toshiro Hiramoto for technical discussion and help. This work is partly supported by JST CREST 16815651, JST PRESTO 15656058, MEXT KAKENHI 16K18085 and 18H01489.

Examining the N=28 shell closure through high-precision mass measurements of Ar46–48

The strength of the $N$ = 28 magic number in neutron-rich argon isotopes is examined through high-precision mass measurements of $^{46-48}$Ar, performed with the ISOLTRAP mass spectrometer at ISOLDE/CERN. The new mass values are up to 90 times more precise than previous measurements. While they suggest the persistence of the $N$ = 28 shell closure for argon, we show that this conclusion has to be nuanced in light of the wealth of spectroscopic data and theoretical investigations performed with the \emph{SDPF-U} phenomenological shell model interaction. Our results are also compared with \emph{ab initio} calculations using the Valence Space In-Medium Similarity Renormalization Group and the Self-Consistent Green's Function approaches. Both calculations provide a very good account of mass systematics at and around $Z$ = 18 and, generally, a consistent description of the physics in this region. This combined analysis indicates that $^{46}$Ar is the transition between the closed-shell $^{48}$Ca and collective $^{44}$S.

Novel chiral Hamiltonian and observables in light and medium-mass nuclei

A novel parameterisation of a Hamiltonian based on chiral effective field theory is introduced. Specifically, three-nucleon operators at next-to-next-to-leading order are combined with an existing (and successful) two-body interaction containing terms up to next-to-next-to-next-to-leading order. The resulting potential is labelled $N\!N\!$+$3N\text{(lnl)}$. The objective of the present work is to investigate the performance of this new Hamiltonian across light and medium-mass nuclei. Binding energies, nuclear radii and excitation spectra are computed using no-core shell model and self-consistent Green's function approaches. Calculations with $N\!N\!$+$3N\text{(lnl)}$ are compared to two other representative Hamiltonians currently in use, namely NNLO$_{\text{sat}}$ and the older $N\!N\!$+$3N(400)$. Overall, the performance of the novel interaction is very encouraging. In light nuclei, total energies are generally in good agreement with experimental data. Known spectra are also well reproduced with a few notable exceptions. The good description of ground-state energies carries on to heavier nuclei, all the way from oxygen to nickel isotopes. Except for those involving excitation processes across the $N=20$ gap, which is overestimated by the new interaction, spectra are of very good quality, in general superior to those obtained with NNLO$_{\text{sat}}$. Although largely improving on $N\!N\!$+$3N(400)$ results, charge radii calculated with $N\!N\!$+$3N\text{(lnl)}$ still underestimate experimental values, as opposed to the ones computed with NNLO$_{\text{sat}}$ that successfully reproduce available data on nickel. On the whole, the new two- plus three-nucleon Hamiltonian introduced in the present work represents a promising alternative to existing nuclear interactions.

Lepton scattering from Ar40 and Ti48 in the quasielastic peak region

Neutron and proton spectral functions of $^{40}$Ar, $^{40}$Ca, and $^{48}$Ti isotopes are computed using the ab initio self-consistent Green's function approach. The resulting radii and charge distributions are in good agreement with available experimental data. The spectral functions of Ar and Ti are then utilized to calculate inclusive ($e$,$e$') cross sections within a factorization scheme and are found to correctly reproduce the recent Jefferson Lab measurements. Based on these successful agreements, the weak charged and neutral current double-differential cross sections for neutrino-$^{40}$Ar scattering are predicted in the quasielastic region. Results obtained by replacing the (experimentally inaccessible) neutron spectral distribution of $^{40}$Ar with the (experimentally accessible) proton distribution of $^{48}$Ti are compared and the accuracy of this approximation is assessed.

AbInitio Optical Potentials and Nucleon Scattering on Medium Mass Nuclei.

We derive abinitio optical potentials from self-consistent Green's function theory and compute the elastic scattering of neutrons off oxygen and calcium isotopes. The comparison with scattering data is satisfactory at low scattering energies. The method is benchmarked against the no-core shell model with continuum calculations, showing that virtual excitations of the target are crucial to predict proper fragmentation and absorption at higher energies. This is a significant step toward deriving optical potentials for medium mass nuclei and complex many-body systems in general.

Ab initio constraints on thermal effects of the nuclear equation of state

We exploit the many-body self-consistent Green's function method to analyze finite-temperature properties of infinite nuclear matter and to explore the behavior of the thermal index used to simulate thermal effects in equations of state for astrophysical applications. We show how the thermal index is both density and temperature dependent, unlike often considered, and we provide an error estimate based on our ${\it ab~initio}$ calculations. The inclusion of many-body forces is found to be critical for the density dependence of the thermal index. We also compare our results to a parametrization in terms of the density dependence of the nucleon effective mass. Our study questions the validity of predictions made for the gravitational-wave signal from neutron-star merger simulations with a constant thermal index.

Nuclear matter properties at finite temperatures from effective interactions

We study if commonly used nucleon-nucleon effective interactions, obtained from fitting the properties of cold nuclear matter and of finite nuclei, can properly describe the hot dense nuclear matter produced in intermediate-energy heavy-ion collisions. We use two representative effective interactions, i.e., an improved isospin- and momentum-dependent interaction with its isovector part calibrated by the results from the \emph{ab initio} non-perturbative self-consistent Green's function (SCGF) approach with chiral forces, and a Skyme-type interaction fitted to the equation of state of cold nuclear matter from chiral effective many-body perturbation theory and the binding energy of finite nuclei. In the mean-field approximation, we evaluate the equation of state and the single-nucleon potential for nuclear matter at finite temperatures and compare them to those from the SCGF approach. We find that the improved isospin- and momentum-dependent interaction reproduces reasonably well the SCGF results due to its weaker momentum dependence of the mean-field potential than in the Skyrme-type interaction. Our study thus indicates that effective interactions with the correct momentum dependence of the mean-filed potential can properly describe the properties of hot dense nuclear matter and are thus suitable for use in transport models to study heavy-ion collisions at intermediate energies.

Core-polarization effects and effective charges in O and Ni isotopes from chiral interactions

Most nuclear structure calculations, even for full configuration interaction approaches, are performed within truncated model spaces. These require consistent transformations of the Hamiltonian and operators to account for the missing physics beyond the active space, so that several recent efforts have been devoted to find compatible derivations of the effective operators. The effective charges employed in the shell-model calculations, and fitted to reproduce experimental data, can be seen as the phenomenological counterpart of such renormalization for electromagnetic operators. Here, we make a first step to lay the bases for their microscopic derivation in the context of the Self-Consistent Green's Function approach. We compute electric quadrupole (E2) effective charges from microscopic theory by coupling the single-nucleon propagators to core-polarization phonons, derived consistently from a realistic nuclear interaction. The polarization effects are included by evaluating the Feynman diagrams that couple the internal multi-nucleon configurations to the single-particle transitions induced by the electromagnetic operator. The effective charges for E2 static moments and transitions are computed for selected isotopes in the Oxygen ($^{14}\text{O}$, $^{16}$O, $^{22}$O and $^{24}$O) and Nickel ($^{48}$Ni, $^{56}$Ni, $^{68}$Ni and $^{78}$Ni) chains. The values found are orbital dependent especially for the neutron effective charges, which show also a characteristic decreasing trend along each isotopic chain. In general, the values are compatible with the phenomenological ones commonly used for shell-model studies in the $0p\, 1s\, 0d$ and $1p\,0f\,0g_{\frac{9}{2}}$ valence spaces.The phenomenological shell-model effective charges can be explained through \textit{ab initio} approaches, where the sole experimental input comes from the fitting of the realistic nuclear interaction.