Finite Electronic Temperature Research Articles

Semi-Empirical Shadow Molecular Dynamics: A PyTorch Implementation.

Extended Lagrangian Born-Oppenheimer molecular dynamics (XL-BOMD) in its most recent shadow potential energy version has been implemented in the semiempirical PyTorch-based software PySeQM. The implementation includes finite electronic temperatures, canonical density matrix perturbation theory, and an adaptive Krylov subspace approximation for the integration of the electronic equations of motion within the XL-BOMB approach (KSA-XL-BOMD). The PyTorch implementation leverages the use of GPU and machine learning hardware accelerators for the simulations. The new XL-BOMD formulation allows studying more challenging chemical systems with charge instabilities and low electronic energy gaps. The current public release of PySeQM continues our development of modular architecture for large-scale simulations employing semi-empirical quantum-mechanical treatment. Applied to molecular dynamics, simulation of 840 carbon atoms, one integration time step executes in 4 s on a single Nvidia RTX A6000 GPU.

Accelerating finite-temperature Kohn-Sham density functional theory with deep neural networks

We present a numerical modeling workflow based on machine learning (ML) which reproduces the the total energies produced by Kohn-Sham density functional theory (DFT) at finite electronic temperature to within chemical accuracy at negligible computational cost. Based on deep neural networks, our workflow yields the local density of states (LDOS) for a given atomic configuration. From the LDOS, spatially-resolved, energy-resolved, and integrated quantities can be calculated, including the DFT total free energy, which serves as the Born-Oppenheimer potential energy surface for the atoms. We demonstrate the efficacy of this approach for both solid and liquid metals and compare results between independent and unified machine-learning models for solid and liquid aluminum. Our machine-learning density functional theory framework opens up the path towards multiscale materials modeling for matter under ambient and extreme conditions at a computational scale and cost that is unattainable with current algorithms.

The ONETEP linear-scaling density functional theory program.

We present an overview of the onetep program for linear-scaling density functional theory (DFT) calculations with large basis set (plane-wave) accuracy on parallel computers. The DFT energy is computed from the density matrix, which is constructed from spatially localized orbitals we call Non-orthogonal Generalized Wannier Functions (NGWFs), expressed in terms of periodic sinc (psinc) functions. During the calculation, both the density matrix and the NGWFs are optimized with localization constraints. By taking advantage of localization, onetep is able to perform calculations including thousands of atoms with computational effort, which scales linearly with the number or atoms. The code has a large and diverse range of capabilities, explored in this paper, including different boundary conditions, various exchange-correlation functionals (with and without exact exchange), finite electronic temperature methods for metallic systems, methods for strongly correlated systems, molecular dynamics, vibrational calculations, time-dependent DFT, electronic transport, core loss spectroscopy, implicit solvation, quantum mechanical (QM)/molecular mechanical and QM-in-QM embedding, density of states calculations, distributed multipole analysis, and methods for partitioning charges and interactions between fragments. Calculations with onetep provide unique insights into large and complex systems that require an accurate atomic-level description, ranging from biomolecular to chemical, to materials, and to physical problems, as we show with a small selection of illustrative examples. onetep has always aimed to be at the cutting edge of method and software developments, and it serves as a platform for developing new methods of electronic structure simulation. We therefore conclude by describing some of the challenges and directions for its future developments and applications.

Charge density wave hampers exciton condensation in 1T−TiSe2

The Bose-Einstein condensation of excitons continues to garner immense attention as a prototypical example for observing emergent properties from many-body quantum effects. In particular, Titanium Diselenide (TiSe$_2$) is a promising candidate for realizing exciton condensation and was experimentally observed only very recently. Surprisingly, the condensate was experimentally characterized by a soft plasmon mode that only exists near the transition temperature, $T_c$, of the charge density wave (CDW). Here, we characterize and analyze the experimental spectra using linear-response time-dependent density functional theory and find that the soft mode can be attributed to interband electronic transitions. At the CDW state below $T_c$, the periodic lattice distortions hamper the spontaneous formation of the exciton by introducing a CDW gap. The band gap raises the soft mode and merges it into the regular plasmon. Our surprising results contradict previous simplistic analytical models commonly used in the scientific literature. In addition, we find that a finite electronic temperature, $T_e$, introduces a dissipation channel and prevents the condensation above $T_c$. The combined effect of the CDW and $T_e$ explains the fragile temperature-dependence of the exciton condensation. Taken together, our work provides the first \textit{ab initio} atomic-level framework for rationalizing recent experiments and further manipulating exciton condensates in TiSe$_2$.

Three dimensional ion-acoustic rogons in quantized anisotropic magnetoplasmas with trapped/untrapped electrons.

Three-dimensional (3D) modulational instability (MI) and ion-acoustic (IA) envelopes are studied in a quantized degenerate magnetoplasma, whose constituents are the trapped/untrapped electrons and anisotropic positive ions. By using quantum hydrodynamic equations and the multiscale reductive perturbation technique, a 3D nonlinear Schrödinger equation is derived to account for electron quantization and ion pressure anisotrophy effects. The potential excitations are shown stable (unstable) against the perturbations for Kc<0(Kc>0), where Kc is a critical parameter that accounts for the longitudinal (transverse) dispersion(s) and nonlinearity effects. Numerically, the nonlinear evolution of IA wavepackets into a 3D MI may be revealed in the ranges of low and high frequencies 0<ω≤0.05 and 0.75≤ω≤1.1. The quantizing magnetic field reduces (enhances) the group speed (wave frequency) of IA excitations, concentrating the wave energy to favor the modulational instability. Finite electronic temperature (viz.,Te≤10keV) enhances the untrapped electrons and significantly widens the instability domain Kc>0. The ionic pressure anisotropy increases the wave frequency (ω), piles up the harmonics under Kc>0, and give rise to modulational instability. The quantized magnetic field and anisotropic pressure reduce the amplitude and spatial extension of the IA rogons. This study is important for understanding the 3D MI and unstable excitations in degenerate plasmas, relevant to white dwarfs, neutron stars, and high-energy density experiments, where strong magnetic field quantizes the dynamics of trapped/untrapped electrons.

Thermodynamic Limit of Crystal Defects with Finite Temperature Tight Binding

We consider a tight binding model for localised crystalline defects with electrons in the canonical ensemble (finite electronic temperature) and nuclei positions relaxed according to the Born--Oppenheimer approximation. We prove that the limit model as the computational domain size grows to infinity is formulated in the grand-canonical ensemble for the electrons. The Fermi-level for the limit model is fixed at a homogeneous crystal level, independent of the defect or electron number in the sequence of finite-domain approximations. We quantify the rates of convergence for the nuclei configuration and for the Fermi-level.

Electronic annealing Fermi operator expansion for DFT calculations on metallic systems.

Density Functional Theory (DFT) calculations with computational effort which increases linearly with the number of atoms (linear-scaling DFT) have been successfully developed for insulators, taking advantage of the exponential decay of the one-particle density matrix. For metallic systems, the density matrix is also expected to decay exponentially at finite electronic temperature and linear-scaling DFT methods should be possible by taking advantage of this decay. Here we present a method for DFT calculations at finite electronic temperature for metallic systems which is effectively linear-scaling (O(N)). Our method generates the elements of the one-particle density matrix and also finds the required chemical potential and electronic entropy using polynomial expansions. A fixed expansion length is always employed to generate the density matrix, without any loss in accuracy by the application of a high electronic temperature followed by successive steps of temperature reduction until the desired (low) temperature density matrix is obtained. We have implemented this method in the ONETEP linear-scaling (for insulators) DFT code which employs local orbitals that are optimised in situ. By making use of the sparse matrix machinery of ONETEP, our method exploits the sparsity of Hamiltonian and density matrices to perform calculations on metallic systems with computational cost that increases asymptotically linearly with the number of atoms. We demonstrate the linear-scaling computational cost of our method with calculation times on palladium nanoparticles with up to ∼13 000 atoms.

Linear scaling DFT calculations for large tungsten systems using an optimized local basis

Density functional theory (DFT) has become a standard tool for ab-initio simulations for a wide range of applications. While the intrinsic cubic scaling of DFT was for a long time limiting the accessible system size to some hundred atoms, the recent progress with respect to linear scaling DFT methods has allowed to tackle problems that are larger by many orders of magnitudes. However, as these linear scaling methods were developed for insulators, they cannot, in general, be straightforwardly applied to metals, as a finite (electronic) temperature is needed to ensure locality of the density matrix. In this paper we show that, once finite electronic temperature is employed, the linear scaling version of the BigDFT code is able to exploit this locality to provide a computational treatment that scales linearly with respect to the number of atoms of a metallic system. We provide prototype examples based on bulk Tungsten, which plays a key role in finding safe and long-lasting materials for Fusion Reactors; however we do not expect any major obstacles in extending this work to cover other metals. We believe that such an approach might help in opening the path towards novel approaches for investigating the electronic structure of such materials, in particular when large supercells are required.

Electron waiting times of a periodically driven single-electron turnstile

We investigate the distribution of waiting times between electrons emitted from a periodically driven single-electron turnstile. To this end, we develop a scheme for analytic calculations of the waiting time distributions for arbitrary periodic driving protocols. We illustrate the general framework by considering a driven tunnel junction before moving on to the more involved single-electron turnstile. The waiting time distributions are evaluated at low temperatures for square-wave and harmonic driving protocols. In the adiabatic regime, the dynamics of the turnstile is synchronized with the external drive. As the non-adiabatic regime is approached, the waiting time distribution becomes dominated by cycle-missing events in which the turnstile fails to emit within one or several periods. We also discuss the influence of finite electronic temperatures. The waiting time distributions provide a useful characterization of the driven single-electron turnstile with complementary information compared to what can be learned from conventional current measurements.

On‐demand entanglement generation using dynamic single‐electron sources

AbstractWe review our recent proposals for the on‐demand generation of entangled few‐electron states using dynamic single‐electron sources. The generation of entanglement can be traced back to the single‐electron entanglement produced by quantum point contacts (QPCs) acting as electronic beam splitters. The coherent partitioning of a single electron leads to entanglement between the two outgoing arms of the QPC. We describe our various approaches for generating and certifying entanglement in dynamic electronic conductors and we quantify the influence of detrimental effects such as finite electronic temperatures and other dephasing mechanisms. The prospects for future experiments are discussed and possible avenues for further developments are identified.(a) The coherent partitioning of a single electron on a QPC leads to entanglement between the outgoing arms. The entanglement can be detected using two copies of the state. (b) A time‐bin entangled state is generated by partitioning two electrons on a QPC followed by projection onto the subspace with one electron in each arm. The two‐electron entanglement is due to the entanglement of the individual single‐electron states. In both panels, circles represent single‐electron sources and squares represent detectors.

Dynamical generation and detection of entanglement in neutral leviton pairs

The entanglement of coherently split electron-hole pairs in an electronic conductor is typically not considered accessible due to particle number conservation and fermionic super-selection rules. We demonstrate here that current cross-correlation measurements at the outputs of an electronic Mach-Zehnder interferometer can nevertheless provide a robust witness of electron-hole entanglement. Specifically, we consider neutral excitations generated by modulating the transmission of an unbiased quantum point contact periodically in time. For an optimized modulation profile, an entangled state with one positively-charged leviton (a hole) and one negatively-charged leviton (an electron) gets delocalized over the two paths of the interferometer and is detected at the output arms. We evaluate the influence of finite electronic temperatures and dephasing corresponding to recent experiments.

Mach-Zehnder interferometry with periodic voltage pulses

We investigate a Mach-Zehnder interferometer driven by a time-dependent voltage. Motivated by recent experiments, we focus on a train of Lorentzian voltage pulses which we compare to a sinusoidal and a constant voltage. We discuss the visibilities of Aharonov-Bohm oscillations in the current and in the noise. For the current, we find a strikingly different behavior in the driven as compared to the static case for voltage pulses containing multiple charges. For pulses containing fractional charges, we find a universality at path-length differences equal to multiples of the spacing between the voltage pulses. These observations can be explained by the electronic energy distribution of the driven contact. In the noise oscillations, we find additional features which are characteristic to time-dependent transport. Finite electronic temperatures are found to have a qualitatively different influence on the current and the noise.

Distributions of electron waiting times in quantum-coherent conductors

The distribution of electron waiting times is useful to characterize quantum transport in mesoscopic structures. Here we consider a generic quantum-coherent conductor consisting of a mesoscopic scatterer in a two-terminal setup. We extend earlier results for single-channel conductors to setups with several (possibly spin-degenerate) conduction channels and we discuss the effect of a finite electronic temperature. We present detailed investigations of the electron waiting times in a quantum point contact as well as in two mesoscopic interferometers with energy-dependent transmissions: a Fabry-P\'erot interferometer and a Mach-Zehnder interferometer. We show that the waiting time distributions allow us to determine characteristic features of the scatterers, for instance the number of resonant levels in the Fabry-P\'erot interferometer that contribute to the electronic transport.

First-principles calculations of heat capacities of ultrafast laser-excited electrons in metals

Ultrafast laser excitation can induce fast increases of the electronic subsystem temperature. The subsequent electronic evolutions in terms of band structure and energy distribution can determine the change of several thermodynamic properties, including one essential for energy deposition; the electronic heat capacity. Using density functional calculations performed at finite electronic temperatures, the electronic heat capacities dependent on electronic temperatures are obtained for a series of metals, including free electron like, transition and noble metals. The effect of exchange and correlation functionals and the presence of semicore electrons on electronic heat capacities are first evaluated and found to be negligible in most cases. Then, we tested the validity of the free electron approaches, varying the number of free electrons per atom. This shows that only simple metals can be correctly fitted with these approaches. For transition metals, the presence of localized d electrons produces a strong deviation toward high energies of the electronic heat capacities, implying that more energy is needed to thermally excite them, compared to free sp electrons. This is attributed to collective excitation effects strengthened by a change of the electronic screening at high temperature.

Ab initio studies on phase transition, thermoelastic, superconducting and thermodynamic properties of the compressed cubic phase of AlH3

The phase transition, thermoelastic, lattice dynamic, and thermodynamic properties of the cubic metallic phase AlH3 were obtained within the density-function perturbation theory. The calculated elastic modulus and phonon dispersion curves under various pressures at 0 K indicate the cubic phase is both mechanically and dynamically stable above 73 GPa. The superconducting transition temperature Tc was calculated using the Allen-Dynes modification of the McMillan formula based on BCS theory. The calculations show that Tc for the cubic phase AlH3 is 8.5 K (μ*=0.1) at the onset of this phase (73 GPa), while decreases to 5.7 K at 80 GPa and almost disappears at 110 GPa, consisting with experimental phenomenon that there was no superconducting transition observed down to 4 K over a wide pressure range 110–164 GPa. It is found that the soft phonon mode for branch 1, namely, the lowest acoustic mode, plays a crucial role in elevating the total EPC parameter λ of cubic AlH3. And the evolution of Tc with pressure follows the corresponding change of this soft mode, i.e. this mode is responsible for the disappearance of Tc in experiments. Meanwhile, the softening of this lowest acoustic mode originates from the electronic momentum transfer from M to R point. This phenomenon provides an important insight into why drastic changes in the diffraction pattern were observed in the pressure range of 63–73 GPa in Goncharenko's experiments. Specifically, once finite electronic temperature effects are included, we find that dynamical instabilities can be removed in the phonon dispersion for P≥63 GPa, rendering the metastability of this phase in the range of 63–73 GPa, and Tc (15.4 K) becomes remarkably high under the lowest possible pressure (63 GPa) compared with that of under 73 GPa (8.5 K). Our calculations open the possibility that finite temperature may allow cubic AlH3 to be dynamically stabilized even for pressures below 73 GPa. It is reasonable to deduced that if special techniques, such as rapid decompression, quenching, and annealing, are implemented in experiments, higher Tc can be observed in hydrides or hydrogen-rich compounds under much lower pressure than ever before.

Smearing induced dynamical stability of NbN and MoN in rocksalt structure

The present paper reports a comprehensive first-principles calculation of electronic structure and lattice dynamical properties of niobium and molybdenum mononitrides in rocksalt phase at ground state as well as at finite electronic temperature applied using smearing parameter. The optimized structure with equilibrium parameters in rocksalt phase is dynamically unstable. An increase in smearing parameter or considering the finite temperature effects increases acoustic phonon frequencies at X point of the Brillouin zone and rocksalt structure dynamically stabilized for both compounds. This is because of the lowering of Fermi energy with increase of smearing parameter. Much better agreement between the calculated and experimental data is found as compared to previous calculations and a consistent description of the dynamical stability in the case of rocksalt phase of NbN and MoN is achieved. The thermodynamical functions are also calculated in the frame work of quasi harmonic approximation and discussed.

Extended Lagrangian free energy molecular dynamics

Extended free energy Lagrangians are proposed for first principles molecular dynamics simulations at finite electronic temperatures for plane-wave pseudopotential and local orbital density matrix-based calculations. Thanks to the extended Lagrangian description, the electronic degrees of freedom can be integrated by stable geometric schemes that conserve the free energy. For the local orbital representations both the nuclear and electronic forces have simple and numerically efficient expressions that are well suited for reduced complexity calculations. A rapidly converging recursive Fermi operator expansion method that does not require the calculation of eigenvalues and eigenfunctions for the construction of the fractionally occupied density matrix is discussed. An efficient expression for the Pulay force that is valid also for density matrices with fractional occupation occurring at finite electronic temperatures is also demonstrated.

Electronic temperature in divide‐and‐conquer electronic structure calculation revisited: Assessment and improvement of self‐consistent field convergence

AbstractWe investigated the electronic temperature dependence of divide‐and‐conquer (DC) self‐consistent field (SCF) method in calculations of uniform (U) and bond‐alternating polyene chains. It was found that part of total energy error of DC calculation is caused by a finite electronic temperature appeared in the DC formalism. As the electronic temperature decreases, the error by the finite temperature decreases to zero but the number of SCF iteration increases, especially in the U chain calculation. To improve the DC SCF convergence with a high energy accuracy, we introduced the temperature‐lowering technique into DC calculation. Numerical assessment reveals the good performance of the present method. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

A note on the Pulay force at finite electronic temperatures

Pulay's original expression for the basis-set dependent adjustment term to the Hellmann-Feynman force in electronic structure theory, which occurs for nonorthogonal local basis-set representations, is based on the idempotency condition of a pure ensemble. At finite electronic temperatures with a fractional occupation of the states, the conventional expression of the Pulay force is therefore no longer valid. Here we derive a simple and computationally efficient expression for a generalized Pulay force, which is suitable for large-scale ab initio simulations at finite electronic temperatures using local nonorthogonal basis-set representations. The generalized Pulay force expression is given in terms of the temperature-dependent density matrix. For the construction of the density matrix, we propose a recursive Fermi operator expansion algorithm that automatically converges to the correct chemical potential.

Dynamical stability of the cubic metallic phase ofAlH3at ambient pressure: Density functional calculations

We have characterized the high-pressure cubic phase of ${\text{AlH}}_{3}$ from ab initio using density functional theory to determine mechanical as well as electronic properties and lattice dynamics (phonon-dispersion relations) from the response function method. Our zero-temperature phonon calculations show the softening of a particular mode with decreasing pressure, indicating the onset of a dynamic instability that continues to persist at ambient conditions. This instability can, however, be removed when finite electronic temperature effects are considered in the calculations. We furthermore identify a particular momentum transfer in the phonon-dispersion relation, matching a corresponding momentum transfer in the electronic band structure.