We investigate the response of the Rashba spin-orbit system to a time-periodic scalar potential, in order to determine whether an induced magnetization exists. We approach this by employing the Floquet Green's function method within the Keldysh formalism, computing the nonequilibrium steady state of the system. We find that, even in the absence of an external magnetic field, the system evolves into a state with an oscillating magnetization density that is remarkably rich in structure. We provide a detailed physical interpretation of the results by performing a Fourier decomposition in nonlocal momentum space, which helps uncover the physical origin of the induced magnetic field in terms of Fermi surface spin polarization and the system's dynamical character.

We present INTW, a modular software environment designed for advanced electronic structure calculations. Developed in Fortran95, INTW is capable of reading self-consistent field (SCF) results, such as electron energies, wave functions, and potentials, generated by the Quantum ESPRESSO and SIESTA codes. Using these SCF results as input, INTW provides a suite of specialized subroutines and functions for the computation of various electron-and phonon-related physical properties, facilitating detailed analysis of material properties at the quantum level. INTW particularly stands out in its treatment of symmetry, fully exploiting it even when dealing with electron spinor wave functions. Furthermore, it can efficiently work with both localized basis set codes, such as SIESTA, and plane-wave codes like Quantum ESPRESSO. These capabilities make INTW unique, offering a versatile approach that effectively combines the use of symmetry with both localized basis sets and plane-wave methods. Program summary Program Title: INTW CPC Library link to program files: (to be added by Technical Editor) Developer's repository link: https://github.com/eiguren/intw Code Ocean capsule: (to be added by Technical Editor) Licensing provisions: GPL-3.0-or-later Programming language: Fortran95 Nature of problem: Accessing advanced electronic structure problems, such as the anisotropic electron-phonon interaction on the Fermi surface, requires efficient treatment of the data generated by general-purpose codes such as Quantum ESPRESSO and SIESTA. Moreover, fully exploiting symmetry operations is challenging but offers significant efficiency gains and qualitative benefits. The problem is to provide a modular framework that enables such calculations in a flexible, symmetry-aware, and computationally efficient environment set of tools. Solution method: Electron and phonon states are calculated only in the irreducible Brillouin zone provided by Quantum ESPRESSO and SIESTA. INTW interfaces with these codes to generate electron (spinor) states and phonon induced (spinor) potentials at arbitrary momenta using symmetry operations. INTW efficiently calculates the nearest-neighbor overlap matrices for Wannier functions by exploiting symmetry. In SIESTA, phonons are calculated using the supercell method, although INTW computes only the irreducible atomic displacements needed to construct the force-constant matrix. The electron-phonon matrix elements are computed either (1) by Fourier interpolation of the phonon potential or (2) using the Wannier interpolation technique for matrix elements. The Fermi surface is treated with a symmetrized triangulated mesh for calculating electron-phonon-related properties. Additional comments including restrictions and unusual features: The INTW package is more an environment with a modular structure designed to facilitate access to complex problems in electronic structure theory, rather than being focused on calculating specific material properties.The utilities for calculating electron-phonon matrix elements, phonon interpolation, Wannier functions, and Fermi surface properties are presented as examples of general-purpose use within this environment, which the users can take as templates for implementing new utilities. INTW operates with both the SIESTA code, which uses localized atomic basis sets, and Quantum ESPRESSO, which is implemented as a plane-wave code.

Exploiting symmetries in the numerical renormalization group (NRG) method significantly enhances performance by improving the accuracy, increasing the computational speed, and optimizing the memory efficiency. Published codes focus on continuous rotations and unitary groups, which generally are not applicable to systems with strong crystal-field effects. The PointGroupNRG code implements symmetries related to discrete rotation groups, which are defined by the user in terms of Clebsch-Gordan coefficients, together with particle conservation and spin rotation symmetries. In this paper we present a new version of the code that extends the available finite groups, previously limited to simply reducible point groups, in a way that all point and double groups become accessible. It also includes the full spin-orbital rotation group. Moreover, to improve the code's flexibility for impurities with complex interactions, this new version allows to choose between a standard Anderson Hamiltonian for the impurity or, as another novel feature, an ionic model that requires only the spectrum and the impurity Lehmann amplitudes.

The numerical renormalization group (NRG) has been widely used as a magnetic impurity solver since the pioneering works by Wilson. Over the past decades, a significant attention has been focused on the application of symmetries in order to reduce the computational cost of the calculations and to improve their accuracy. In particular, a notable progress has been made in implementing continuous symmetries such as SO(3), useful for studying impurities in an isotropic medium, or SU(N), which is applicable to a wide range of systems. In this work, we focus on the application of discrete point group symmetries, which are particularly relevant for impurity systems in metals where crystal field effects are important. With this aim, we have developed an original NRG code written in the Julia language, PointGroupNRG, where we have implemented crystal point-group symmetries for the Anderson impurity model, as well as the continuous spin and charge symmetries. Among other results, we demonstrate the advantage of our procedure by applying the code to a two-impurity model with RKKY interaction and an impurity system with two orbitals of Eg symmetry and two channels. We also provide benchmarks to show the performance improvements obtained by exploiting the orbital symmetries.

The mechanism of Kondo screening in strongly correlated molecules with several unpaired electrons on a metal surface is still under debate. Here, we provide a theoretical framework that rationalizes the emergence of Kondo screening involving several extended molecular orbitals with unpaired electrons. We introduce a perturbative model, which provides simple rules to identify the presence of antiferromagnetic spin-flip channels involving charged molecular multiplets responsible for Kondo screening. The Kondo regime is confirmed by numerical renormalization group calculations. In addition, we introduce the concept of Kondo orbitals as molecular orbitals associated with the Kondo screening process, which provide a direct interpretation of experimental dI/dV I / d V maps of Kondo resonances. We demonstrate that this theoretical framework can be applied to different strongly correlated open-shell molecules on metal surfaces, obtaining good agreement with previously published experimental data.

Understanding the spin-relaxation mechanism of single adatoms is an essential step towards creating atomic magnetic memory bits or even qubits. Here we present an essentially parameter-free theory by combining \textit{ab-initio} electronic and vibrational properties with the many-body nature of atomic states. Our calculations account for the millisecond spin lifetime measured recently on Fe adatoms on MgO/Ag(100) and reproduce the dependence on the number of decoupling layers and the external magnetic field. We show how the atomic interaction with the environment should be tuned in order to enhance the magnetic stability, and propose a clear fingerprint for experimentally detecting a localized spin-phonon excitation.

We discuss coexistence of Kondo and spin excitation signals in tunneling spectroscopy in strongly correlated polyradical $π$-magnetic nanographenes on a metal surface. The Kondo signal is rationalized by a multi-orbital Kondo screening of the unpaired electrons. The fundamental processes are spin-flips of antiferromagnetic (AFM) order involving charged molecular multiplets. We introduce a~perturbative model, which provides simple rules to identify the presence of AFM channels responsible for Kondo screening. The Kondo regime is confirmed by numerical renormalization group calculations. This framework can be applied to similar strongly correlated open-shell systems.

This corrects the article DOI: 10.1103/PhysRevLett.129.076402.

We present a theoretical framework to describe polarons from first principles within a many-body Green's function formalism. Starting from a general electron-phonon Hamiltonian, we derive a self-consistent Dyson equation in which the phonon-mediated self-energy is composed by two distinct terms. One term is the Fan-Migdal self-energy and describes dynamic electron-phonon processes, the other term is a new contribution to the self-energy originating from the static displacements of the atomic nuclei in the polaronic ground state. The lowest-order approximation to the present theory yields the standard many-body perturbation theory approach to electron-phonon interactions in the limit of large polarons, and the ab initio polaron equations introduced in [Sio et al., Phys. Rev. B 99, 235139 (2019); Phys. Rev. Lett. 122, 246403 (2019)] in the limit of small polarons. A practical recipe to implement the present unifying formalism in first-principles calculations is outlined. We apply our method to the Fr\"ohlich model, and obtain remarkably accurate polaron energies at all couplings, in line with Feynman's polaron theory and diagrammatic Monte Carlo calculations. We also recover the well-known results of Fr\"ohlich and Pekar at weak and strong coupling, respectively. The present approach enables predictive many-body calculations of polarons in real materials at all couplings.

Ab initio calculations of the phonon-induced band structure renormalization are currently based on the perturbative Allen-Heine theory and its many-body generalizations. These approaches are unsuitable to describe materials where electrons form localized polarons. Here, we develop a self-consistent, many-body Green's function theory of band structure renormalization that incorporates localization and self-trapping. We show that the present approach reduces to the Allen-Heine theory in the weak-coupling limit, and to total energy calculations of self-trapped polarons in the strong-coupling limit. To demonstrate this methodology, we reproduce the path-integral results of Feynman and diagrammatic Monte Carlo calculations for the Fröhlich model at all couplings, and we calculate the zero point renormalization of the band gap of an ionic insulator including polaronic effects.

We study the strength of the electron-phonon interaction on Fe single adatoms on MgO/Ag(100) based on many-body ab initio spin collinear calculations. In particular, we analyze the relative importance of the substrate and, among other results, we conclude that the interface electron state of Ag(100) plays a prominent role in determining the electron-phonon coupling of localized Fe electron states. The analysis of the hybridization of the adatom with the substrate reveals qualitative differences for even or odd coverages of MgO, affecting significantly the spectral structure and strength of the electron-phonon coupling. Our calculations indicate that the electron-phonon interaction is very strong for <= 1 layers of MgO, while it is sharply suppressed for larger coverages, a trend that is consistent with recent experimental findings.

We outline a numerical procedure to incorporate the crystal symmetries in the Helmholtz Fermi Surface Harmonics basis set, which are the solutions of the Helmholtz equation defined on the Fermi surface. This improvement allows for an optimal representation of anisotropic quantities defined on the Fermi surface in terms of a few symmetric elements of the set. We demonstrate the general validity of our approach by identifying the fully symmetric Helmholtz Fermi Surface Harmonics subset for several representative systems with different crystal structures, namely, FCC-Cu, HEX-MgB2, and BCC-YH6. Furthermore, we illustrate the potential of the method applied to the electron-phonon problem, showing that the anisotropic electron-phonon mass-enhancement parameter lambda(k) can be represented to high accuracy by a handful of coefficients. This works as an effective filter, paving the way for a reduction of several orders of magnitude in the computation of superconductivity, impurity problems, or any other Fermi-surface-dependent property of metals from first principles.

We present an alternative representation for the anisotropic Eliashberg equations of superconductivity, whose numerical solution yields an efficiency gain of several orders of magnitude with respect to the conventional representation in momentum space. Our method is a practical realization of a long-sought approach, whose essence is a linear transformation from regular k space to a set of orthonormal functions defined as the solutions of the Helmholtz equation on the Fermi surface. In this way, all the anisotropy of the problem can be described by a handful of coefficients with built-in symmetry. We perform benchmark calculations on the gap anisotropy of MgB2, and reproduce previous results at a remarkably reduced computational cost. Furthermore, we apply our methodology to efficiently determine the transition temperature of the compressed YH6 hydride, obtaining very good agreement with recent experimental measurements. The simplification introduced by our method enables the high-throughput exploration of superconducting materials without having to resort to the isotropic approximation, and opens up possibilities towards first-principles calculations of more advanced theories of superconductivity.

We present a comprehensive first-principles analysis of the non-adiabatic effects due to the electron-phonon interaction on the vibrational spectrum of the electron-doped monolayer MoS$_{2}$. Deep changes in the Fermi surface upon doping cause the linewidth broadening of the normal modes governing the spin-conserving inter-valley electronic scattering, which become unstable with the population of all the spin-split conduction valleys. We find that the non-adiabatic spectral effects modify dramatically the adiabatic dispersion of the long-wavelength optical phonon modes, responsible for intra-valley scattering, as soon as inequivalent valleys get populated. These results are illustrated by means of a simple analytical model. Finally, we explain the emergence of an intricate dynamical structure for the strongly interacting out-of-plane polarized A 0 1 optical vibrational mode spectrum by means of a multiple-phonon quasi-particle picture defined in the full complex frequency plane, showing that this intriguing spectral structure originates from the splitting of the original adiabatic branch induced by the electron-phonon coupling.

An unexpected finding two decades ago demonstrated that Shockley electron states in noble metal surfaces are spin-polarized, forming a circulating spin texture in reciprocal space. The fundamental role played by the spin degree of freedom was then revealed, even for a non-magnetic system, whenever the spin-orbit coupling was present with some strength. Here we demonstrate that similarly to electrons in the presence of spin-orbit coupling, the propagating vibrational modes are also accompanied by a well-defined magnetic oscillation even in non-magnetic materials. Although this effect is illustrated by considering a single layer of the WSe2 dichalogenide, the phenomenon is completely general and valid for any non-magnetic material with spin-orbit coupling. The emerging phonon-induced magnetic oscillation acts as an additional effective flipping mechanism for the electron spin and its implications in the transport and scattering properties of the material are evident and profound.

Carrier doping by the electric field effect has emerged as an ideal route for monitoring many-body physics in two-dimensional materials where the Fermi level is tuned so that the strength of the interactions can also be scanned. The possibility of systematic doping together with high resolution photoemission has allowed to uncover a genuinely many-body electron spectrum in single-layer MoS 2 transition metal dichalcogenide, resolving three clear quasi-particle states, where only one should be expected if the electron–phonon interaction vanished. Here, we combine first-principles and consistent complex plane analytic approaches and bring into light the physical origin of the two gaps and the three quasi-particle bands which are unambiguously present in the photoemission spectrum. One of these states, though being strongly interacting with the accompanying virtual phonon cloud, presents a notably long lifetime which is an appealing property when trying to understand and take advantage of many-body interactions to modulate transport properties.

Controlling the magnetic moment of individual atoms is a technologically important challenge,with applications as high density storage devices. Breakthrough experimental studies have recentlyshown that it is possible to create stable magnetic quantum states in individual adatoms [1–3]. [...]

We investigate the role played by the electron spin and the spin-orbit interaction on the exceptional electronphonon coupling at the Tl/Si(111) surface. Our first-principles calculations demonstrate that the particular spin pattern of this system dominates the whole low-energy electron-phonon physics, which is remarkably explained by forbidden spin-spin scattering channels. In particular, we show that the strength of the electron-phonon coupling appears drastically weakened for surface states close to the K and K' valleys, which is unambiguously attributed to the spin polarization through the associated modulation due to the spinor overlaps. However, close to the {\Gamma} point, the particular spin pattern in this area is less effective in damping the electron-phonon matrix elements, and the result is an exceptional strength of electron-phonon coupling parameter {\lambda} ~ 1.4. These results are rationalized by a simple model for the electron-phonon matrix elements including the spinor terms.

We present a comprehensive ab initio analysis of the spin-charge correlations at the Tl/Si(111) surface, where the spin-orbit interaction is so strong that a detailed treatment of the noncollinear electron spin appears decisive for the correct description of the response properties. The relativistic limit enforces a unified treatment of the spin and charge densities as a four-vector, and the response function acquires then a 4 x 4 tensor structure. Our all-electron implementation allows us to resolve the real-space structure of the possible collective modes, and demonstrates the emergence of a novel collective excitation combining transverse-spin and ordinary charge oscillations of a similar order of magnitude, whose spin character is strongly enhanced as we approach the q -> 0 momentum limit.

We investigate the role played by the electron spin and the spin-orbit interaction on the exceptional electronphonon coupling at the Tl/Si(111) surface. Our first-principles calculations demonstrate that the particular spin pattern of this system dominates the whole low-energy electron-phonon physics, which is remarkably explained by forbidden spin-spin scattering channels. In particular, we show that the strength of the electron-phonon coupling appears drastically weakened for surface states close to the K and K′ valleys, which is unambiguously attributed to the spin polarization through the associated modulation due to the spinor overlaps. However, close to the Γ point, the particular spin pattern in this area is less effective in damping the electron-phonon matrix elements, and the result is an exceptional strength of electron-phonon coupling parameter λ ∼ 1.4. These results are rationalized by a simple model for the electron-phonon matrix elements including the spinor terms.