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We study the motion (translational, vibrational, and rotational) of a diatomic impurity immersed in an electron liquid and exposed to electronic current. An approach based on the linear response time-dependent density functional theory combined with the Ehrenfest dynamics leads to a system of linear algebraic equations, which account for the competing and counteracting effects of the current-induced force (electron wind) and the electronic friction. These forces, by means of the dynamic exchange-correlation kernel $f_{xc}({\bf r},{\bf r}',\omega)$, include the electronic viscosity contribution. Starting from the ground state at the equilibrium inter-nuclear distance and applying a current pulse, we observe three phases of the motion: (I) acceleration due to the prevalence of the current-induced force, (II) stabilization upon balancing of the two forces, and (III) deceleration due to the friction after the end of the pulse. The viscous contribution to the force largely increases the acceleration (deceleration) at the first (third) phase of the process. For the aluminium HEG electron density, we find this correction to amount to up to 70% of the total electron wind and friction effects., Comment: 11 pages, 5 figures

DFT calculations yield useful ground-state energies and densities, while Green's function techniques (such as $GW$) are mostly used to produce spectral functions. From the Galitskii-Migdal formula, we extract the exchange-correlation of DFT directly from a Green's function. This spectral representation provides an alternative to the fluctuation-dissipation theorem of DFT, identifying distinct single-particle and many-particle contributions. Results are illustrated on the uniform electron gas and the two-site Hubbard model.

Factoring a wave function into marginal and conditional factors partitions the subsystem kinetic energy into two terms. The first depends solely on the marginal wave function, through its gauge-covariant derivative, while the second depends on the quantum metric of the conditional wave function over the manifold of marginal variables. We derive an identity for the rate of change of the second term.

The exact factorization of the time-dependent electron-nuclear wavefunction has been employed successfully in the field of quantum molecular dynamics simulations for interpreting and simulating light-induced ultrafast processes. In this work, we summarize the major developments leading to the formulation of a trajectory-based approach, derived from the exact factorization equations, capable of dealing with nonadiabatic electronic processes, and including spin-orbit coupling and the non-perturbative effect of an external time-dependent field. This trajectory-based quantum-classical approach has been dubbed coupled-trajectory mixed quantum-classical (CT-MQC) algorithm, whose performance is tested here to study the photo-dissociation dynamics of IBr.

We present a method which enables solid-state density functional theory calculations to be applied to systems of almost unlimited size. Computations of physical effects up to the micron length scale but which nevertheless depend on the microscopic details of the electronic structure, are made possible. Our approach is based on a generalization of the Bloch state which involves an additional sum over a finer grid in reciprocal space around each ${\bf k}$-point. We show that this allows for modulations in the density and magnetization of arbitrary length on top of a lattice-periodic solution. Based on this, we derive a set of ultra long-range Kohn-Sham equations. We demonstrate our method with a sample calculation of bulk LiF subjected to an arbitrary external potential containing nearly 3500 atoms. We also confirm the accuracy of the method by comparing the spin density wave state of bcc Cr against a direct supercell calculation starting from a random magnetization density. Furthermore, the spin spiral state of $\gamma$-Fe is correctly reproduced and the screening by the density of a saw-tooth potential over 20 unit cells of silicon is verified.

Accurately describing excited states within Kohn-Sham (KS) density functional theory (DFT), particularly those which induce ionization and charge transfer, remains a great challenge. Common exchange-correlation (xc) approximations are unreliable for excited states owing, in part, to the absence of a derivative discontinuity in the xc energy ($\Delta$), which relates a many-electron energy difference to the corresponding KS energy difference. We demonstrate, analytically and numerically, how the relationship between KS and many-electron energies leads to the step structures observed in the exact xc potential, in four scenarios: electron addition, molecular dissociation, excitation of a finite system, and charge transfer. We further show that steps in the potential can be obtained also with common xc approximations, as simple as the LDA, when addressed from the ensemble perspective. The article therefore highlights how capturing the relationship between KS and many-electron energies with advanced xc approximations is crucial for accurately calculating excitations, as well as the ground-state density and energy of systems which consist of distinct subsystems., Comment: EK and MJPH contributed equally to this work

We extend the two leading methods for the \emph{ab initio} computational descrip tion of phonon-mediated superconductors, namely Eliashberg theory and density fu nctional theory for superconductors (SCDFT), to include plasmonic effects. Furth ermore, we introduce a hybrid formalism in which the Eliashberg approximation fo r the electron-phonon coupling is combined with the SCDFT treatment of the dynam ically screened Coulomb interaction. The methods have been tested on a set of we ll-known conventional superconductors by studying how the plasmon contribution a ffects the phononic mechanism in determining the critical temperature (\tc). Our simulations show that plasmonic SCDFT leads to a good agreement between predict ed and measured \tc's, whereas Eliashberg theory considerably overestimates the plasmon-mediated pairing and, therefore, \tc. The hybrid approach, on the other hand, gives results close to SCDFT and overall in excellent agreement with exper iments.

A many-body wave function can be factorized in Fock space into a marginal amplitude describing a set of strongly correlated orbitals and a conditional amplitude for the remaining weakly correlated part. The marginal amplitude is the solution of a Schr\"odinger equation with an effective Hamiltonian that can be viewed as embedding the marginal wave function in the environment of weakly correlated electrons. Here, the complementary equation for the conditional amplitude is replaced by a generalized Kohn-Sham equation, for which an orbital-dependent functional approximation is shown to reproduce the topological phase diagram of a multiband Hubbard model as a function of crystal field and Hubbard parameters. The roles of band filling and interband fluctuations are elucidated., Comment: 5 pages, 4 figures

The dissociation dynamics of diatomic molecules interacting with (near) optical laser pulses of different duration is investigated by an elaborate discussion of the electric field of the laser and by a direct solution of the time-dependent molecular Schr\"odinger equation. The systematic variation of the pulse duration from the electronic time scale (attoseconds) to the nuclear time scale (femtoseconds) shows that the employed few-cycle laser pulses lead to well-known but quite different dissociation mechanisms. A comparative calculation with a model pulse and an experimentally realized attosecond pulse emphasizes that, and to what extent, a realistic modeling of the electric field is of central importance in the attosecond regime.

The recently developed exact factorization approach condenses all electronic effects on the nuclear subsystem into scalar and vector potentials that appear in an effective time dependent Schr\"{o}dinger equation. Starting from this equation, we derive subsystem Ehrenfest identities characterizing the energy, momentum and angular momentum transfer between electrons and nuclei. An effective electromagnetic force operator induced by the electromagnetic field corresponding to the effective scalar and vector potentials appears in all three identities. The effective magnetic field has two components that can be identified with the Berry curvature calculated with (a) different cartesian coordinates of the same nucleus and (b) arbitrary cartesian coordinates of two different nuclei. (a) has a classical interpretation as the induced magnetic field felt by the nucleus, while (b) has no classical analog. Subsystem Ehrenfest identities are ideally suited for quantifying energy transfer in electron-phonon systems. With two explicit examples we demonstrate the usefulness of the new identities.

The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here resolves the problems arising from the translational and rotational invariance of this Hamiltonian that afflict the existing many-body Green's function theories. We derive a coupled set of exact equations for the electronic and nuclear Green's functions and provide a systematic way to approximately compute the properties of arbitrary many-body systems of electrons and nuclei beyond the Born-Oppenheimer approximation. The case of crystalline solids is discussed in detail., Comment: 21 pages, 1 figure

Capturing the non-collinear magnetic ground state of the spinel vanadates AV$_2$O$_4$ (A= Mn, Fe and Co) remains an outstanding challenge for state-of-the-art ab-initio methods. We demonstrate that both the non-collinear spin texture, as well as the magnitude of local moments, are captured by a single value of the on-site Hubbard $U$ of 2.7~eV in conjunction with the local spin density approximation (LSDA+$U$), provided the source term (i.e., magnetic monopole term) is removed from the exchange-correlation magnetic field ${\bf B}_{XC}$. We further demonstrate that the magnetic monopole structure in ${\bf B}_{XC}$ is highly sensitive to the value of $U$, to the extent that the interplay between on-site localization and local moment magnitude is qualitatively different depending on whether the source term is removed or not. This suggests that in treating strongly correlated magnetic materials within the LSDA+$U$ formalism, subtraction of the unphysical magnetic monopole term from the exchange-correlation magnetic field is essential to correctly treat the magnetic ground state., Comment: 4 pages, 3 figures

Density functional theory is generalized to incorporate electron-phonon coupling. A Kohn-Sham equation yielding the electronic density $n_U(\mathbf{r})$, a conditional probability density depending parametrically on the phonon normal mode amplitudes $U=\{U_{\mathbf{q}\lambda}\}$, is coupled to the nuclear Schr\"odinger equation of the exact factorization method. The phonon modes are defined from the harmonic expansion of the nuclear Schr\"odinger equation. A nonzero Berry curvature on nuclear configuration space affects the phonon modes, showing that the potential energy surface alone is generally not sufficient to define the phonons. An orbital-dependent functional approximation for the non\-adiabatic exchange-correlation energy reproduces the leading-order nonadiabatic electron-phonon-induced band structure renormalization in the Fr\"ohlich model.

An interacting lattice model describing the subspace spanned by a set of strongly-correlated bands is rigorously coupled to density functional theory to enable ab initio calculations of geometric and topological material properties. The strongly-correlated subspace is identified from the occupation number band structure as opposed to a mean-field energy band structure. The self-consistent solution of the many-body model Hamiltonian and a generalized Kohn-Sham equation exactly incorporates momentum-dependent and crystal-symmetric correlations into electronic structure calculations in a way that does not rely on a separation of energy scales. Calculations for a multiorbital Hubbard model demonstrate that the theory accurately reproduces the many-body polarization., Comment: 19 pages, 11 figures

This work establishes the algebraic structure of the Kohn-Sham equations to be solved in a density formulation of electron and phonon dynamics, including the superconducting order parameter. A Bogoliubov transform is required to diagonalize both the fermionic and bosonic Kohn-Sham Hamiltonians since they both represent a non-interacting quantum field theory. The Bogoliubov transform for phonons is non-Hermitian in the general case, and the corresponding time-evolution is non-unitary. Several sufficient conditions for ensuring that the bosonic eigenvalues are real are provided and a practical method for solving the system is described. Finally, we produce a set of approximate mean-field potentials which are functionals of the electronic and phononic density matrices and depend on the electron-phonon vertex.

By combining interface-sensitive non-linear magneto-optical experiments with femtosecond time resolution and ab-initio time-dependent density functional theory, we show that optically excited spin dynamics at Co/Cu(001) interfaces proceeds via spin-dependent charge transfer and backtransfer between Co and Cu. This ultrafast spin transfer competes with dissipation of spin angular momentum mediated by spin-orbit coupling already on sub 100 fs timescales. We thereby identify the fundamental microscopic processes during laser-induced spin transfer at a model interface for technologically relevant ferromagnetic heterostructures., Comment: 5 pages, 4 figures

We perform model calculations for a stretched LiF molecule, demonstrating that nonadiabatic charge transfer effects can be accurately and seamlessly described within a density functional framework. In alkali halides like LiF, there is an abrupt change in the ground state electronic distribution due to an electron transfer at a critical bond length $R=R_c$, where a barely avoided crossing of the lowest adiabatic potential energy surfaces calls the validity of the Born-Oppenheimer approximation into doubt. Modeling the $R$-dependent electronic structure of LiF within a two-site Hubbard model, we find that nonadiabatic electron-nuclear coupling produces a sizable elongation of the critical $R_c$ by 0.5 Bohr. This effect is very accurately captured by a simple and rigorously-derived correction, with an $M^{-1}$ prefactor, to the exchange-correlation potential in density functional theory; $M=$ reduced nuclear mass. Since this nonadiabatic term depends on gradients of the nuclear wavefunction and conditional electronic density, $\nabla_R \chi(R)$ and $\nabla_R n(\mathbf{r},R)$, it couples the Kohn-Sham equations at neighboring $R$ points. Motivated by an observed localization of nonadiabatic effects in nuclear configuration space, we propose a local conditional density approximation -- an approximation that reduces the search for nonadiabatic density functionals to the search for a single function $y(n)$.

The effective Hamiltonian for the linear $E\otimes e$ Jahn-Teller model describes the coupling between two electronic states and two vibrational modes in molecules or bulk crystal impurities. While in the Born-Oppenheimer approximation the Berry curvature has a delta function singularity at the conical intersection of the potential energy surfaces, the exact Berry curvature is a smooth peaked function. Numerical calculations revealed that the characteristic width of the peak is $\hbar K^{1/2}/gM^{1/2}$, where $M$ is the mass associated with the relevant nuclear coordinates, $K$ is the effective internuclear spring constant and $g$ is the electronic-vibrational coupling. This result is confirmed here by an asymptotic analysis of the $M\rightarrow\infty$ limit, an interesting outcome of which is the emergence of a separation of length scales. Being based on the exact electron-nuclear factorization, our analysis does not make any reference to adiabatic potential energy surfaces or nonadiabatic couplings. It is also shown that the Ham reduction factors for the model can be derived from the exact geometric phase., Comment: 12 pages, 8 figures

The many-body Berry phase formula for the macroscopic polarization is approximated by a sum of natural orbital geometric phases with fractional occupation numbers accounting for the dominant correlation effects. This reduced formula accurately reproduces the exact polarization in the Rice-Mele-Hubbard model across the band insulator-Mott insulator transition. A similar formula based on a one-body reduced Berry curvature accurately predicts the interaction-induced quenching of Thouless topological charge pumping.

The reliability of density-functional calculations hinges on accurately approximating the unknown exchange-correlation (xc) potential. Common (semi-)local xc approximations lack the jump experienced by the exact xc potential as the number of electrons infinitesimally surpasses an integer, and the spatial steps that form in the potential as a result of the change in the decay rate of the density. These features are important for an accurate prediction of the fundamental gap and the distribution of charge in complex systems. Although well-known concepts, the exact relationship between them remained unclear. In this Letter, we establish the common fundamental origin of these two features of the exact xc potential via an analytical derivation. We support our result with an exact numerical solution of the many-electron Schroedinger equation for a single atom and a diatomic molecule in one dimension. Furthermore, we propose a way to extract the fundamental gap from the step structures in the potential., Comment: 6 pages, 3 figures, supplementary material included

Spatial and time scales of spin density fluctuations (SDF) were analyzed in 3d ferromagnets using ab initio linear response calculations of complete wavevector and energy dependence of the dynamic spin susceptibility tensor. We demonstrate that SDF are spread continuously over the entire Brillouin zone and while majority of them reside within the 3d bandwidth, a significant amount comes from much higher energies. A validity of the adiabatic approximation in spin dynamics is discussed. The SDF spectrum is shown to have two main constituents: a minor low-energy spin wave contribution and a much larger high-energy component from more localized excitations. Using the fluctuation-dissipation theorem (FDT), the on-site spin correlator (SC) and the related effective fluctuating moment were properly evaluated and their universal dependence on the 3d band population is further discussed.

Spin-dependent exchange-correlation energy functionals in use today depend on the charge density and the magnetization density: $E_{\rm xc}[\rho,{\bf m}]$. However, it is also correct to define the functional in terms of the curl of ${\bf m}$ for physical external fields: $E_{\rm xc}[\rho,\nabla\times{\bf m}]$. The exchange-correlation magnetic field, ${\bf B}_{\rm xc}$, then becomes source-free. We study this variation of the theory by uniquely removing the source term from local and generalized gradient approximations to the functional. By doing so, the total Kohn-Sham moments are improved for a wide range of materials for both functionals. Significantly, the moments for the pnictides are now in good agreement with experiment. We also predict dramatic differences in the spatial geometry of ${\bf B}_{\rm xc}$ for the pnictides. Our source-free method is simple to implement in all existing density functional theory codes., Comment: 5 pages 2 figures and 1 table

A joint theoretical and experimental investigation is performed to understand the underlying physics of laser-induced demagnetization in Ni and Co films. Experimentally dynamics of spins is studied by determining the time-dependent amplitude of the Voigt vector and theoretically ab-initio calculations are performed using time-dependent density functional theory. We demonstrate that overall spin-orbit induced spin-flips are the most significant contributors with super-diffusive spin transport playing very limited to no role. Our study highlights the material dependent nature of the demagnetization during the process of thermalization of non-equilibrium spins., Comment: 4 pages, 4 figures, submitted to Physical Review Letters

With a view to the design of hard magnets without rare earths we explore the possibility of large magnetocrystalline anisotropy energies in Heusler compounds that are unstable with respect to a tetragonal distortion. We consider the Heusler compounds Fe$_2$YZ with Y = (Ni, Co, Pt), and Co$_2$YZ with Y = (Ni, Fe, Pt) where, in both cases, Z = (Al, Ga, Ge, In, Sn). We find that for the Co$_2$NiZ, Co$_2$PtZ, and Fe$_2$PtZ families the cubic phase is always, at $T=0$, unstable with respect to a tetragonal distortion, while, in contrast, for the Fe$_2$NiZ and Fe$_2$CoZ families this is the case for only 2 compounds -- Fe$_2$CoGe and Fe$_2$CoSn. For all compounds in which a tetragonal distortion occurs we calculate the MAE finding remarkably large values for the Pt containing Heuslers, but also large values for a number of the other compounds (e.g. Co$_2$NiGa has an MAE of -2.11~MJ/m$^3$). The tendency to a tetragonal distortion we find to be strongly correlated with a high density of states at the Fermi level in the cubic phase. As a corollary to this fact we observe that upon doping compounds for which the cubic structure is stable such that the Fermi level enters a region of high DOS, a tetragonal distortion is induced and a correspondingly large value of the MAE is then observed., Comment: 8 pages, 5 figures

We present an exact single-electron picture that describes the correlated electron dynamics in strong laser fields. Our approach is based on the factorization of the electronic wavefunction as a product of a marginal and a conditional amplitude. The marginal amplitude, which depends only on one electronic coordinate and yields the exact one-electron density and current density, obeys a time-dependent Schr\"odinger equation with an effective time-dependent potential. The exact equations are used to derive an approximation that is a step towards a general and feasible ab-initio single-electron approximation for molecules. The derivation also challenges the usual interpretation of the single-active electron approximation. From the study of model systems, we find that the exact and approximate single-electron potentials for processes with negligible two-electron ionization lead to a qualitatively similar dynamics, but that the ionization barrier may be explicitly time-dependent.

We report on {\it ab-initio} simulations of the quantum dynamics of electronic charge and spin when subjected to intense laser pulses. By performing separate calculations for a Ni thin film and bulk Ni, we conclude that surface effects have a dramatic influence on amplifying the laser induced demagnetization. We show that the reason for this amplification is due to increased spin-currents on the surface of the thin film. This enhancement is a direct consequence of the broken symmetry originating from the surface formation. We find that the underlying physics of demagnetization, during the early femtoseconds, for both bulk and thin film is dominated by spin-flips induced by spin-orbit coupling. After the first $\sim 40$ fs this changes in that the dominant cause of demagnetization is the flow of spin-currents, which leads to stronger demagnetization in the film compared to that of the bulk., Comment: 12 pages, 3 figures

A theoretical justification of the empirical surface hopping method for the laser-driven molecular dynamics is given utilizing the formalism of the exact factorization of the molecular wavefunction [Abedi et al., PRL $\textbf{105}$, 123002 (2010)] in its quantum-classical limit. Employing an exactly solvable $\textrm H_2^{\;+}$-like model system, it is shown that the deterministic classical nuclear motion on a single time-dependent surface in this approach describes the same physics as stochastic (hopping-induced) motion on several surfaces, provided Floquet surfaces are applied. Both quantum-classical methods do describe reasonably well the exact nuclear wavepacket dynamics for extremely different dissociation scenarios. Hopping schemes using Born-Oppenheimer surfaces or instantaneous Born-Oppenheimer surfaces fail completely.

The ground state energy of a system of electrons and nuclei is proven to be a variational functional of the conditional electronic density $n_R(\mathbf{r})$, the nuclear wavefunction $\chi(R)$ and an induced vector potential $A_{\mu}(R)$ and quantum geometric tensor $\mathcal{T}_{\mu\nu}(R)$ derived from the conditional electronic wavefunction $\Phi_R(r)$ over nuclear configuration space, where $r=\mathbf{r}_1,\mathbf{r}_2,\ldots$ are electronic coordinates and $R=\mathbf{R}_1,\mathbf{R}_2,\ldots$ are nuclear coordinates. The ground state $(n_R,\chi,A_{\mu},\mathcal{T}_{\mu\nu})$ can be calculated by solving self-consistently (i) conditional Kohn-Sham equations containing an effective potential $v_{\rm s}(\mathbf{r})$ that depends parametrically on $R$, (ii) the Schr\"odinger equation for $\chi(R)$ and (iii) Euler-Lagrange equations that determine $\mathcal{T}_{\mu\nu}$. The theory is applied to the $E\otimes e$ Jahn-Teller model.

Describing the dynamics of nuclei in molecules requires a potential energy surface, which is traditionally provided by the Born-Oppenheimer or adiabatic approximation. However, we also need to assign masses to the nuclei. There, the Born-Oppenheimer picture does not account for the inertia of the electrons and only bare nuclear masses are considered. Nowadays, experimental accuracy challenges the theoretical predictions of rotational and vibrational spectra and requires to include the participation of electrons in the internal motion of the molecule. More than 80 years after the original work of Born and Oppenheimer, this issue still is not solved in general. Here, we present a theoretical and numerical framework to address this problem in a general and rigorous way. Starting from the exact factorization of the electron-nuclear wave function, we include electronic effects beyond the Born-Oppenheimer regime in a perturbative way via position-dependent corrections to the bare nuclear masses. This maintains an adiabatic-like point of view: the nuclear degrees of freedom feel the presence of the electrons via a single potential energy surface, whereas the inertia of electrons is accounted for and the total mass of the system is recovered. This constitutes a general framework for describing the mass acquired by slow degrees of freedom due to the inertia of light, bounded particles. We illustrate it with a model of proton transfer, where the light particle is the proton, and with corrections to the vibrational spectra of molecules. Inclusion of the light particle inertia allows to gain orders of magnitude in accuracy.

Nonadiabatic quantum interferences emerge whenever nuclear wavefunctions in different electronic states meet and interact in a nonadiabatic region. In this work, we analyze how nonadiabatic quantum interferences translate in the context of the exact factorization of the molecular wavefunction. In particular, we focus our attention on the shape of the time-dependent potential energy surface - the exact surface on which the nuclear dynamics takes place. We use a one-dimensional exactly-solvable model to reproduce different conditions for quantum interferences, whose characteristic features already appear in one-dimension. The time-dependent potential energy surface develops complex features when strong interferences are present, in clear contrast to the observed behavior in simple nonadiabatic crossing cases. Nevertheless, independent classical trajectories propagated on the exact time-dependent potential energy surface reasonably conserve a distribution in configuration space that mimics the one of the exact nuclear probability density., Comment: Accepted in J. Chem. Phys

With the goal of pushing Spintronic devices towards faster and faster timescales, we demonstrate, using ab-intio time-dependent density functional theory simulations of bulk Heusler compounds subject to ultrashort intense laser pulses, that the local magnetic moment can increase or decrease in a few femtoseconds. This speed is due to the all optical nature of the process, which transfers spin moment from one sublattice to another. This transfer depends on easily tunable laser parameters. By comparing the spin dynamics of a variety of Heusler (or half-Heusler) compounds, we demonstrate that the density of states explains the observed moment transfer; most the physics of inter sublattice moment transfer is due to the flow of spin current which is governed by availability of states above the Fermi level.

We present a novel ab-initio single-electron approach to correlated electron dynamics in strong laser fields. By writing the electronic wavefunction as a product of a marginal one-electron wavefunction and a conditional wavefunction, we show that the exact harmonic spectrum can be obtained from a single-electron Schr\"odinger equation. To obtain the one-electron potential in practice, we propose an adiabatic approximation, i.e. a potential is generated that depends only on the position of one electron. This potential, together with the laser interaction, is then used to obtain the dynamics of the system. For a model Helium atom in a laser field, we show that by using our approach, the high-order harmonic generation spectrum can be obtained to a good approximation.

Trajectory-based mixed quantum-classical approaches to coupled electron-nuclear dynamics suffer from well-studied problems such as the lack of (or incorrect account for) decoherence in the trajectory surface hopping method and the inability of reproducing the spatial splitting of a nuclear wave packet in Ehrenfest-like dynamics. In the context of electronic non-adiabatic processes, these problems can result in wrong predictions for quantum populations and in unphysical outcomes for the nuclear dynamics. In this paper we propose a solution to these issues by approximating the coupled electronic and nuclear equations within the framework of the exact factorization of the electron-nuclear wave function. We present a simple quantum-classical scheme based on coupled classical trajectories, and test it against the full quantum mechanical solution from wave packet dynamics for some model situations which represent particularly challenging problems for the above-mentioned traditional methods., Comment: 32 pages, 11 figures

Hydrogen-rich compounds have been extensively studied both theoretically and experimentally in the quest for novel high-temperature superconductors. Reports on sulfur-hydride attaining metallicity under pressure and exhibiting superconductivity at temperatures as high as 200 K have spurred an intense search for room-temperature superconductors in hydride materials. Recently, compressed phosphine was reported to metallize at pressures above 45 GPa, reaching a superconducting transition temperature (T$_{c}$) of 100 K at 200 GPa. However, neither the exact composition nor the crystal structure of the superconducting phase have been conclusively determined. In this work the phase diagram of PH$_n$ ($n=1,2,3,4,5,6$) was extensively explored by means of {\it ab initio} crystal structure predictions using the Minima Hopping Method (MHM). The results do not support the existence of thermodynamically stable PH$_n$ compounds, which exhibit a tendency for elemental decomposition at high pressure even when vibrational contributions to the free energies are taken into account. Although the lowest energy phases of PH$_{1,2,3}$ display T$_{c}$'s comparable to experiments, it remains uncertain if the measured values of T$_{c}$ can be fully attributed to a phase-pure compound of PH$_n$.

A fully first principles theory capable of treating strongly correlated solids remains the outstanding challenge of modern day materials science. This is exemplified by the transition metal oxides, prototypical Mott insulators, that remain insulating even in the absence of long range magnetic order. Capturing the non-magnetic insulating state of these materials presents a difficult challenge for any modern electronic structure theory. In this paper we demonstrate that reduced density matrix functional theory, in conjunction with the power functional, can successfully treat the non-magnetic insulating state of the transition metal oxides NiO and MnO. We show that the electronic spectrum retains a gap even in the absence of spin order. We further discuss the detailed way in which RDMFT performs for Mott insulators and band insulators, finding that for the latter occupation number minimization alone is required, but for the former full minimization over both occupation numbers and natural orbitals is essential.

The Born-Oppenheimer electronic wavefunction $\Phi_R^{BO}(r)$ picks up a topological phase factor $\pm 1$, a special case of Berry phase, when it is transported around a conical intersection of two adiabatic potential energy surfaces in $R$-space. We show that this topological quantity reverts to a geometric quantity $e^{i\gamma}$ if the geometric phase $\gamma = \oint \mathrm{Im} \langle \Phi_R |\nabla_{\mu} \Phi_R\rangle \cdot d\mathbf{R}_{\mu}$ is evaluated with the conditional electronic wavefunction $\Phi_R(r)$ from the exact electron-nuclear factorization $\Phi_R(r)\chi(R)$ instead of the adiabatic function $\Phi_R^{BO}(r)$. A model of a pseudorotating molecule, also applicable to dynamical Jahn-Teller ions in bulk crystals, provides the first examples of induced vector potentials and molecular geometric phase from the exact factorization. The induced vector potential gives a contribution to the circulating nuclear current which cannot be removed by a gauge transformation. The exact potential energy surface is calculated and found to contain a term depending on the Fubini-Study metric for the conditional electronic wavefunction.

We study the exact nuclear time-dependent potential energy surface (TDPES) for laser-induced electron localization with a view to eventually developing a mixed quantum-classical dynamics method for strong-field processes. The TDPES is defined within the framework of the exact factorization [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)] and contains the exact effect of the couplings to the electronic subsystem and to any external fields within a scalar potential. We compare its features with those of the quasistatic potential energy surfaces (QSPES) often used to analyse strong-field processes. We show that the gauge-independent component of the TDPES has a mean-field-like character very close to the density-weighted average of the QSPESs. Oscillations in this component are smoothened out by the gauge-dependent component, and both components are needed to yield the correct force on the nuclei. Once the localization begins to set in, the gradient of the exact TDPES tracks one QSPES and then switches to the other, similar to the description provided by surface-hopping between QSPESs. We show that evolving an ensemble of classical nuclear trajectories on the exact TDPES accurately reproduces the exact dynamics. This study suggests that the mixed quantum-classical dynamics scheme based on evolving multiple classical nuclear trajectories on the exact TDPES will be a novel and useful method to simulate strong field processes., Comment: 10 pages, 6 figures

Laser induced ultrafast demagnetization is the process whereby the magnetic moment of a ferromagnetic material is seen to drop significantly on a timescale of $10-100$s of femtoseconds due to the application of a strong laser pulse. If this phenomenon can be harnessed for future technology, it offers the possibility for devices operating at speeds several orders of magnitude faster than at present. A key component to successful transfer of such a process to technology is the controllability of the process, i.e. that it can be tuned in order to overcome the practical and physical limitations imposed on the system. In this paper, we demonstrate that the spin-orbit mediated form of ultrafast demagnetization recently investigated [arXiv:1406.6607] by ab-initio time-dependent density functional theory (TDDFT) can be controlled. To do so we use quantum optimal control theory (OCT) to couple our TDDDT simulations to the optimization machinery of OCT. We show that a laser pulse can be found which maximizes the loss of moment within a given time interval while subject to several practical and physical constraints. Furthermore we also include a constraint on the fluence of the laser pulses and find the optimal pulse that combines significant demagnetization with a desire for less powerful pulses. These calculations demonstrate optimal control is possible for spin-orbit mediated ultrafast demagnetization and lay the foundation for future optimizations/simulations which can incorporate even more constraints.

The nuclear velocity perturbation theory (NVPT) for vibrational circular dichroism (VCD) is derived from the exact factorization of the electron-nuclear wave function. This new formalism offers an exact starting point to include correction terms to the Born-Oppenheimer (BO) form of the molecular wave function, similarly to the complete-adiabatic approximation. The corrections depend on a small parameter that, in a classical treatment of the nuclei, is identified as the nuclear velocity. Apart from proposing a rigorous basis for the NVPT, we show that the rotational strengths, related to the intensity of the VCD signal, contain a new contribution beyond-BO that can be evaluated with the NVPT and that only arises when the exact factorization approach is employed. Numerical results are presented for chiral and non-chiral systems to test the validity of the approach., Comment: 13 pages, 5 figures, 4 tables

A novel strategy of stacking binary magnets to enhance the magneto crystalline anisotropy is explored. This strategy is used in the search for hard magnets by studying FePt/MnGa and FePt/MnAl stacks. The choice of these binaries is motivated by the fact that they already possess large magneto crystalline anisotropy. Several possible alternative structures for these materials are explored in order to reduce the amount of Pt owing to its high cost.

We present a novel quantum-classical approach to non-adiabatic dynamics, deduced from the coupled electronic and nuclear equations in the framework of the exact factorization of the electron-nuclear wave function. The method is based on the quasi-classical interpretation of the nuclear wave function, whose phase is related to the classical momentum and whose density is represented in terms of classical trajectories. In this approximation, electronic decoherence is naturally induced as effect of the coupling to the nuclei and correctly reproduces the expected quantum behaviour. Moreover, the splitting of the nuclear wave packet is captured as consequence of the correct approximation of the time-dependent potential of the theory. This new approach offers a clear improvement over Ehrenfest-like dynamics. The theoretical derivation presented in the Letter is supported by numerical results that are compared to quantum mechanical calculations.

We report on first principles calculations of superconductivity in a single layer of lead on a silicon substrate including a full treatment of phononic and RPA screened coulomb interactions within the parameter free framework of Density Functional Theory for superconductors. A thorough investigation shows that several approximations that are commonly valid in bulk systems fail in this constrained 2D geometry. The calculated critical temperature turns out to be much higher than the experimental value of 1.86K. We argue that the only plausible explanation for the experimental Tc suppression is the onset of fluctuations of the superconducting order parameter.

We present a first-principles approach to describe magnetic and superconducting systems and the phenomena of competition between these electronic effects. We develop a density functional theory: SpinSCDFT, by extending the Hohenberg-Kohn theorem and constructing the non-interacting Kohn- Sham system. An exchange-correlation functional for SpinSCDFT is derived from the Sham Schl\"uter connection between the SpinSCDFT Kohn-Sham and a self-energy in Eliashberg approximation. The reference Eliashberg equations for superconductors in the presence of magnetism are also derived and discussed.

We numerically investigate the Spin Density Functional theory for superconductors (SpinSCDFT) and the approximated exchange-correlation functional, derived and presented in the preceding paper I. As a test system we employ a free electron gas featuring an exchange-splitting, a phononic pairing field and a Coulomb repulsion. SpinSCDFT results are compared with Sarma, the Bardeen Cooper and Schrieffer theory and with an Eliashberg type of approach. We find that the spectrum of the superconducting Kohn-Sham SpinSCDFT system is not in agreement with the true quasi particle structure. Therefore, starting from the Dyson equation, we derive a scheme that allows to compute the many body excitations of the superconductor and represents the extension to superconductivity of the G0W0 method in band structure theory. This superconducting G0 W0 method vastly improves the predicted spectra.

In the context of the exact factorization of the electron-nuclear wave function, the coupling between electrons and nuclei beyond the adiabatic regime is encoded (i) in the time-dependent vector and scalar potentials and (ii) in the electron-nuclear coupling operator. The former appear in the Schroedinger-like equation that drives the evolution of the nuclear degrees of freedom, whereas the latter is responsible for inducing non-adiabatic effects in the electronic evolution equation. As we have devoted previous studies to the analysis of the vector and scalar potentials, in this paper we focus on the properties of the electron-nuclear coupling operator, with the aim of describing a numerical procedure to approximate it within a semiclassical treatment of the nuclear dynamics., Comment: 9 pages, 6 figures

Due to its low atomic mass hydrogen is the most promising element to search for high-temperature phononic superconductors. However, metallic phases of hydrogen are only expected at extreme pressures (400 GPa or higher). The measurement of a record superconducting critical temperature of 190 K in a hydrogen-sulfur compound at 200 GPa of pressure[1], shows that metallization of hydrogen can be reached at significantly lower pressure by inserting it in the matrix of other elements. In this work we re-investigate the phase diagram and the superconducting properties of the H-S system by means of minima hopping method for structure prediction and Density Functional theory for superconductors. We also show that Se-H has a similar phase diagram as its sulfur counterpart as well as high superconducting critical temperature. We predict SeH3 to exceed 120 K superconductivity at 100 GPa. We show that both SeH3 and SH3, due to the critical temperature and peculiar electronic structure, present rather unusual superconducting properties.

An efficient algorithm for time propagation of the time-dependent Kohn-Sham equations is presented. The algorithm is based on dividing the Hamiltonian into small time steps and assuming that it is constant over these steps. This allows for the time-propagating Kohn-Sham wave function to be expanded in the instantaneous eigenstates of the Hamiltonian. The stability and efficiency of the algorithm are tested not just for non-magnetic but also for fully non-collinear magnetic systems. We show that even for delicate properties, like magnetization density, large time-step sizes can be used indicating the stability and efficiency of the algorithm., Comment: 4 figs

We report the first-principles study of superconducting critical temperature and superconducting properties of Fe-based superconductors taking into account on the same footing phonon, charge and spin-fluctuation mediated Cooper pairing. We show that in FeSe this leads to a modulated s$\pm$ gap symmetry, and that the antiferromagnetic paramagnons are the leading mechanism for superconductivity in FeSe, overcoming the strong repulsive effect of both phonons and charge pairing.

We present the derivation of an ab-initio and parameter free effective electron-electron interaction that goes beyond the screened RPA and accounts for superconducting pairing driven by spin-fluctuations. The construction is based on many body perturbation theory and relies on the approximation of the exchange-correlation part of the electronic self-energy within time dependent density functional theory. This effective interaction is included in an exchange correlation kernel for superconducting density functional theory, in order to achieve a completely parameter free superconducting gap equation. First results from applying the new functional to a simplified two-band electron gas model are consistent with experiments., Comment: 13 pages, 3 figures