arXiv subjects

E. K. U. Gross

Publications and source records attributed to E. K. U. Gross.

At least 37 records · Page 2Linked to original sources

arXiv2020

Extending solid-state calculations to ultra long-range length scales

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 $γ$-Fe is correctly reproduced and the screening by the density of a saw-tooth potential over 20 unit cells of silicon is verified.

cond-mat.mtrl-sci↗

arXiv2020

Ab initio theory of plasmonic superconductivity within the Eliashberg and density-functional formalisms

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.

cond-mat.supr-con↗

arXiv2020

Many-body Green's function theory of electrons and nuclei beyond the Born-Oppenheimer approximation

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.

cond-mat.other↗

arXiv2019

Molecular dissociation in few-cycle laser pulses: From attosecond to femtosecond pulse duration

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 Schrödinger 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.

physics.atom-ph↗

arXiv2019

Exact factorization-based density functional theory of electron-phonon systems

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 $U=\{U_{\mathbf{q}λ}\}$, is coupled to the nuclear Schrödinger equation of the exact factorization method. The phonon modes are defined from the harmonic expansion of the nuclear Schrödinger 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 Fröhlich model.

cond-mat.mtrl-sci↗

arXiv2019

Model Hamiltonian for strongly-correlated systems: Systematic, self-consistent, and unique construction

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.

cond-mat.str-el↗

arXiv2019

A complete description of the magnetic ground state in spinel vanadates

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.

cond-mat.str-el↗

arXiv2018

Competing spin transfer and dissipation at Co/Cu(001) interfaces on femtosecond timescales

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.

cond-mat.mtrl-sci↗

arXiv2018

Coupled Kohn-Sham equations for electrons and phonons

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.

cond-mat.supr-con↗

arXiv2018

Approximate formula for the macroscopic polarization including quantum fluctuations

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.

cond-mat.str-el↗

arXiv2017

Spin-density fluctuations and the fluctuation-dissipation theorem in 3d ferromagnetic metals

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.

cond-mat.mtrl-sci↗

arXiv2017

Density functional theory of electron transfer beyond the Born-Oppenheimer approximation: Case study of LiF

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, $\nabla_R χ(R)$ 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 $y(n)$.

physics.chem-ph↗

arXiv2017

Asymptotic analysis of the Berry curvature in the $E\otimes e$ Jahn-Teller model

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.

physics.chem-ph↗

arXiv2017

How is the derivative discontinuity related to steps in the exact Kohn-Sham potential?

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.

physics.atom-ph↗

arXiv2017

Source-free exchange-correlation magnetic fields in density functional theory

Spin-dependent exchange-correlation energy functionals in use today depend on the charge density and the magnetization density: $E_{\rm xc}[ρ,{\bf m}]$. However, it is also correct to define the functional in terms of the curl of ${\bf m}$ for physical external fields: $E_{\rm xc}[ρ,\nabla\times{\bf m}]$. 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.

cond-mat.other↗

arXiv2017

Role of Spin Flips versus Spin Transport in Non Thermal Electrons Excited by Ultrashort Optical Pulses in Transition Metals

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.

cond-mat.mtrl-sci↗

arXiv2017

Ultrafast demagnetization in bulk vs thin films: an ab-initio study

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.

cond-mat.mtrl-sci↗

arXiv2017

Large magnetocrystalline anisotropy in tetragonally distorted Heuslers: a systematic study

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.

cond-mat.mtrl-sci↗