Generalized Foldy-Wouthuysen transformation for relativistic two-component methods: Systematic analysis of two-component Hamiltonians.

The generalized Foldy-Wouthuysen (GFW) transformation was proposed as a generic form that unifies four types of transformations in relativistic two-component methods: unnormalized GFW(UN), and normalized form 1, form 2, and form 3 (GFW(N1), GFW(N2), and GFW(N3)). The GFW transformation covers a wide range of transformations beyond the simple unitary transformation of the Dirac Hamiltonian, allowing for the systematic classification of all existing two-component methods. New two-component methods were also systematically derived based on the GFW transformation. These various two-component methods were applied to hydrogen-like and helium-like ions. Numerical errors in energy were evaluated and classified into four types: the one-electron Hamiltonian approximation, the two-electron operator approximation, the newly defined "picture difference error (PDE)," and the error in determining the transformation, and errors in multi-electron systems were discussed based on this classification.

Theoretical examination of QED Hamiltonian in relativistic molecular orbital theory.

Theoretical discussions are given on issues in relativistic molecular orbital theory to which the quantum electrodynamics (QED) Hamiltonian is applied. First, several QED Hamiltonians previously proposed are sifted by the orbital rotation invariance, the charge conjugation and time reversal invariance, and the nonrelativistic limit. The discussion on orbital rotation invariance shows that orbitals giving a stationary point of total energy should be adopted for QED Hamiltonians that are not orbital rotation invariant. A new total energy expression is then proposed, in which a counter term corresponding to the energy of the polarized vacuum is subtracted from the total energy. This expression prevents the possibility of total energy divergence due to electron correlations, stemming from the fact that the QED Hamiltonian does not conserve the number of particles. Finally, based on the Hamiltonian and energy expression, the Dirac-Hartree-Fock (DHF) and electron correlation methods are reintroduced. The QED-based DHF equation is shown to give information on positrons from negative-energy orbitals while having the same form as the conventional DHF equation. Three electron correlation methods are derived: the QED-based configuration interactions and single- and multireference perturbation methods. Numerical calculations show that the total energy of the QED Hamiltonian indeed diverged and that the counter term is effective in avoiding the divergence. The relativistic molecular orbital theory presented in this article also provides a methodology for dealing with systems containing positrons based on the QED Hamiltonian.

Analytical quadrature method using recurrence formulas for two-electron integrals of frequency-dependent Breit interaction.

A recursive scheme was proposed to calculate two-electron integrals of frequency-dependent Breit interactions in electronic structure calculations using Gaussian basis functions. As shown in a previous study [R. Ahlrichs, Phys. Chem. Chem. Phys. 8 (2006) 3072-3077], the vertical recurrence relation for the two-electron integrals of the general two-body potential is valid. In addition, the authors have shown that the horizontal case is also valid. Explicit expressions for generalized molecular incomplete gamma function corresponding to the frequency-dependent Gaunt and gauge potentials were then derived, along with their asymptotic formulas. In addition, an implementation for computing the generalized molecular incomplete gamma function was proposed. Through numerical calculations, the shape of the curves of the generalized molecular incomplete gamma functions were found to vary significantly from that of the zero-energy case with the increase in the energy variable.

Douglas-Kroll and infinite order two-component transformations of Dirac-Fock operator.

We extended the conventional Douglas-Kroll (DK) and infinite order two-component (IOTC) methods to a technique applicable to Fock matrices, called extended DK (EDK) and extended IOTC (EIOTC), respectively. First, we defined a strategy to divide the Dirac-Fock operator into zero- and first-order terms. We then demonstrated that the first-order extended DK transformation, which is the Foldy-Wouthuysen transformation for the zero-order term, as well as the second- and third-order EDK and EIOTC, could be well defined. The EDK- and EIOTC-transformed Fock matrix, kinetic energy operator, nuclear attraction operator, and density matrix were derived. These equations were numerically evaluated, and it was found that these methods were accurate. In particular, EIOTC was consistent with the four-component approach. Four-component and extended two-component calculations are more expensive than non-relativistic calculations due to small-component-type two-electron integrals. We developed a new approximation formula, RIS-V, for small-component-type two-electron integrals, including the spin-orbit interaction between electrons. These results suggest that the RIS-V formula effectively accelerates the four-component and extended two-component methods.

Realistic nuclear charge distribution model function for analytic nuclear attraction integrals in Gaussian basis functions.

In electronic structure theory, the charge distribution of a nucleus is usually approximated by point charge, Gaussian function, or homogeneously charged sphere, because they have an analytical nuclear attraction integral (NAI) formula. However, these functions do not always provide good approximations for nuclei with large mass number. The two-parameter Fermi (2pF) distribution and more realistic distributions describe well even nuclei with large mass number but do not have analytical NAI formulas. We propose a new function model called augmented Gaussian 12 (AG12), which has sufficient number of parameters and analytical NAI formulas. With the proposed fitting scheme, the AG12 charge distribution model optimally reproduces 2pF and the more realistic charge distributions. Moreover, AG12 fitted to 2pF model reproduces the energy difference of hydrogen-like ions well between the Gaussian distribution and 2pF models. Calculations using AG12 also suggested necessity to use more realistic nuclear charge distributions than 2pF.

Probing embedded topological modes in bulk-like GeTe-Sb2Te3 heterostructures.

The interface between topological and normal insulators hosts metallic states that appear due to the change in band topology. While topological states at a surface, i.e., a topological insulator-air/vacuum interface, have been studied intensely, topological states at a solid-solid interface have been less explored. Here we combine experiment and theory to study such embedded topological states (ETSs) in heterostructures of GeTe (normal insulator) and [Formula: see text] [Formula: see text] (topological insulator). We analyse their dependence on the interface and their confinement characteristics. First, to characterise the heterostructures, we evaluate the GeTe-Sb[Formula: see text]Te[Formula: see text] band offset using X-ray photoemission spectroscopy, and chart the elemental composition using atom probe tomography. We then use first-principles to independently calculate the band offset and also parametrise the band structure within a four-band continuum model. Our analysis reveals, strikingly, that under realistic conditions, the interfacial topological modes are delocalised over many lattice spacings. In addition, the first-principles calculations indicate that the ETSs are relatively robust to disorder and this may have practical ramifications. Our study provides insights into how to manipulate topological modes in heterostructures and also provides a basis for recent experimental findings [Nguyen et al. Sci. Rep. 6, 27716 (2016)] where ETSs were seen to couple over thick layers.

Structural transition pathway and bipolar switching of the GeTe-Sb2Te3 superlattice as interfacial phase-change memory.

We investigated the resistive switching mechanism between the high-resistance state (HRS) and the low-resistance state (LRS) of the GeTe-Sb2Te3 (GST) superlattice. First-principles calculations were performed to identify the structural transition pathway and to evaluate the current-voltage (I-V) characteristics of the GST device cell. After determining the atomistic structures of the stable structural phases of the GST superlattice, we found the structural transition pathways and the transition states of possible elementary processes in the device, which consisted of a thin film of GST superlattice and semi-infinite electrodes. The calculations of the I-V characteristics were examined to identify the HRS and the LRS, and the results reasonably agreed with those of our previous study (H. Nakamura, et al., Nanoscale, 2017, 9, 9286). The calculated HRS/LRS and analysis of the transition states of the pathways suggest that a bipolar switching mode dominated by the electric-field effect is possible.

Resistive switching mechanism of GeTe-Sb2Te3 interfacial phase change memory and topological properties of embedded two-dimensional states.

A theoretical study of an interfacial phase change memory made of a GeTe-Sb2Te3 superlattice with W electrodes is presented to identify the high and low resistance states and the switching mechanism. The ferro structure of the GeTe layer block in the Te-Ge-Te-Ge sequence can be in the low resistance state only if the SET/RESET mode consists of a two step dynamical process, corresponding to a vertical flip of the Ge layer with respect to the Te layer, followed by lateral motion driven by thermal relaxation. The importance of spin-orbit coupling at the GeTe/Sb2Te3 interface to the "bias polarity-dependent" SET/RESET operation is shown, and an analysis of the two-dimensional states confined at the GeTe/Sb2Te3 interface inside the resistive switching layer is presented. Our results allow us to propose a phase diagram for the transition from a topologically nontrivial to a trivial gap state of these two-dimensional compounds.